Comsol Multiphysics - Science topic

You need velocity vectors to do this with Tecplot. You create these by selecting slicing planes through the flow or some spacing along the streamlines to arrive at locations for the vectors. You can use the same (constant) velocity for each vector. The components are obtained so that the vectors are tangent to the streamlines at the desired locations. Treat this process as a specific type of post-processing and make the code general so that you can use it over-and-over again. Or if you have the information inside the model, just write it out separately.

Hi,

Have you found a way to find these cross- and co-polarized components in Comsol?

Marcella Tulini An example of an Iron Sphere in a Magnetic Field (comsol.com) will help you

Alessio Pricci few days back i sent u a message thru RG. I just wanted to know if u have received that ?

In discussions regarding the appropriate Capillary Number (Ca) for ignoring capillary effects in microchannel studies, it's essential to consider the context of the interface interactions. Typically, for water flow inside silicone microchannels, many studies, including mine, use the water-air surface tension value of 0.0726 N/m. This is generally because the dominant interface under investigation is between the water and air, not between the water and the silicone walls, unless specific surface modifications of the silicone suggest otherwise.

Furthermore, concerning the critical value of Ca, while the standard threshold is often set at Ca = 1, I believe this may not be universally applicable. In my study, which investigates forced flow with Reynolds numbers between 125 and 1300, it appears that capillary effects could be non-negligible even above this threshold. This observation leads me to suggest that the traditional threshold of Ca = 1 might need adjustment based on specific experimental conditions and flow behaviors. Such an approach allows for a more nuanced understanding of when viscous forces indeed dominate over capillary forces in practical scenarios

Farshid Hesami

Simulating a chemical reaction in COMSOL Multiphysics involves using the Reaction Engineering interface. This interface allows you to set up and solve reaction systems involving multiple species and reactions. Here's a general guide on how to simulate a chemical reaction in COMSOL: The temperature influences the rate of a reaction. As the temperature increases, the rate of a reaction increases.

Aleksandr Markvart

No, I can't solve the problem.

yes

Start with these:

electron beam welding provision is there or not in comsol multiphysics

Enjoy it...

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Have you found the answer? I want to know the same, If you know could you please share with me. Thank you

I think it will be possible by CST. CST Software is easier comparing to LUMERICAL and COMSOL.

Bonjour,

Je veux savoir comment faire le réglage de Méthode Nelder-Mead sur C Multiphysics.

Merci d'avance

Ekaterina Zolotukhina, I checked my system. It was some error. Thanks for your input.

Quantifying the dielectrophoretic force in COMSOL involves setting up a simulation that includes the relevant physics and boundary conditions. Dielectrophoresis (DEP) is the phenomenon where a non-uniform electric field exerts a force on a dielectric particle. Here's a general guide on how to quantify the dielectrophoretic force using COMSOL:

By following these steps and utilizing COMSOL's capabilities for simulating dielectrophoresis, you can effectively quantify the dielectrophoretic force in your system.

If the material is not available in COMSOL's material library, you will have to define the material properties manually by introducing a blank material. First, assign the physics to the geometry, and then it will prompt you to input the necessary material properties in the material section.

Dear Sir

I've seen you message on ResearchGate, in fact, i have the same issue, i'm carring out a simulation of ferrofluids in a cylinder in the present of magnet , I'm using two models Laminar flow and Heat transfer in Fluids and i want to define the force volume on the heat transfer model in fuction of the magnetisation M and the magnetic field B.

The magnetization M is function of the temperature as this equation:

M(T)=3*〖10〗^5*exp⁡(〖-[((T-250))/40]〗^6

The volume force will be F= ∇(M.B)

The problem is when i set a variable in comsol of the magnetisation M this equation is not accepted and the temperature T is not recognized

Coud you please help me in my simulation

You can find attached the model and equation use

Thank you for your help

Hakeem Niyas the geometry has been created in comsol . I have solved the issue. Thank you for the link.

Now I can simulate a row of rotor and stator

My next problem is to run DSMC with Comsol software. Can I implement this method with this software?

Kırıcılık indisi ile frekans doğru orantılı.

Hello,

In my experience, COMSOL performed efficiently during each time step. However, attempting to accelerate the calculation time of your COMSOL model solely through Python scripting using the mph library may face constraints, particularly if the bottleneck stems from the model's complexity or the available computational resources. However, there are several strategies you can consider to optimize the performance:

1. Model Simplification: Simplify your COMSOL model by reducing the number of elements, adjusting mesh refinement settings, or simplifying physics assumptions while ensuring that the essential features of your fluid dynamics problem are retained.

2. Parallel Computing: Utilize parallel computing techniques to distribute the computational workload across multiple CPU cores or nodes. COMSOL Multiphysics supports parallel computing, and you can explore options for parallelizing your simulations within the COMSOL environment or using Python parallel processing libraries like multiprocessing.

3. Solver Settings Optimization: Fine-tune the solver settings within your COMSOL model to achieve better convergence and reduced solution time. Experiment with different solver types, preconditioners, and convergence criteria to find the optimal configuration for your specific problem.

4. Adaptive Mesh Refinement: Implement adaptive mesh refinement techniques to dynamically adjust the mesh density based on solution characteristics, focusing computational resources on regions of interest within the domain.

5. Parameter Optimization: If your simulations involve parameter sweeps or optimization studies, consider using optimization algorithms available within COMSOL or integrating external optimization libraries with Python to efficiently explore the parameter space and identify optimal solutions.

6. Model Order Reduction: Investigate techniques for model order reduction to reduce the computational complexity of your fluid dynamics model while preserving key system dynamics. Techniques such as proper orthogonal decomposition (POD) or reduced basis methods can be effective in achieving significant speedup while maintaining accuracy.

7. GPU Acceleration: Explore the possibility of leveraging GPU acceleration for certain computations within your COMSOL model, as GPUs can offer significant speedup for certain types of numerical calculations compared to traditional CPU-based computations.

8. Profiling and Benchmarking: Use profiling tools to identify computational bottlenecks and areas for optimization within your COMSOL model. Benchmark different configurations and optimization strategies to quantify the performance improvements achieved and guide further optimization efforts.

To implement this in a simulation (assuming you are using finite element analysis or another similar numerical method), you would generally need to :

-Define the interface between the solid and liquid

-Calculate the normal vector n at every point on the interface

-For each time step or iteration, calculate the electric field E at the interface

- Implement a conditional statement in your code that checks the sign of n.E at each point on the interface and applies the appropriate boundary condition for the flux. Danny Guana

There are many possibilities for the errors you have got. I am mentioning a few of them below. Hope it helps.

1) When there are not enough Governing equations to solve for the number of dependent variables you have set.

2) When there are not enough Boundary conditions for the given problem.

3) When some constraint / Physics is missing in the Problem.

4) You might have used an operator that directly implies '0' as the coefficient of dependent variables in one of the Governing equations, thus recheck all the operators and make sure all of them are used correctly.

There are always some things we unconsciously assume ourselves while solving problems and we might have missed giving that information to Simulation software / Comsol. Thus, you might have to look at it again in detail.

I imagine you do a time-integration then to find the power, although I am not too deep into transient analyses of your type.

If you have an electrical input, and the structure moves, then the coupling seems to be working. It could be that you are not plotting, what you think you are plotting. I imagine there is a stationary and perhaps a frequency study, so look into which you are actually plotting. I am not sure what you mean by Electromechanics coupling, but for electrostatics and structural mechanics to couple there is some manual setup to be done.

Numerical Investigations on Magnetohydrodynamic Pump Based Microchannel Cooling System for Heat Dissipating Element

1,*📷by📷Jae-Hyeong Seo1,†📷,📷Mahesh Suresh Patil1,†📷,📷Satyam Panchal2📷 and📷Moo-Yeon Lee

1

Department of Mechanical Engineering, Dong-A University, 37 Nakdong-Daero 550, Saha-gu, Busan 49315, Korea

2

Department of Mechanical and Mechatronics Engineering, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada

*

Author to whom correspondence should be addressed.

†

Equal contribution.

Symmetry 2020, 12(10), 1713; https://doi.org/10.3390/sym12101713

Submission received: 17 September 2020/ Revised: 7 October 2020/ Accepted: 12 October 2020/ Published: 16 October 2020

(This article belongs to the Special Issue Heat Transfer in Engineering)

Versions NotesDownload keyboard_arrow_downBrowse Figures

Abstract Numerical investigations are performed on the magnetohydrodynamic (MHD) pump-based microchannel cooling system for heat dissipating element. In the present study, the MHD pump performance is evaluated considering normal current density, magnetic flux density, volumetric Lorentz force, shear stress and pump flow velocity by varying applied voltage and Hartmann number. It is found that for a low Hartmann number, the Lorentz force increases with an increase in applied voltage and Hartmann number. The velocity distribution along dimensionless width, the shear stress distribution along dimensionless width, the magnetic flux density along the dimensionless width and radial magnetic field distribution showed symmetrical behavior. The MHD pump-based microchannel cooling system performance is evaluated by considering the maximum temperature of the heat dissipating element, heat removal rate, efficiency, thermal field, flow field and Nusselt number. In addition, the influence of various nanofluids including Cu-water, TiO2-water and Al2O3-water nanofluids on heat transfer performance of MHD pump-based microchannel is evaluated. As the applied voltage increased from 0.05 V to 0.35 V at Hartmann number 1.41, the heat removal rate increased by 39.5%. The results reveal that for low Hartmann number, average Nusselt number is increasing function of applied voltage and Hartmann number. At the Hartmann number value of 3.74 and applied voltage value of 0.35 V, average Nusselt numbers were 12.3% and 15.1% higher for Cu-water nanofluid compared to TiO2-water and Al2O3-water nanofluids, respectively. The proposed magnetohydrodynamic microcooling system is effective without any moving part.cooling; Lorentz force; magnetohydrodynamics; microchannel; MHD pumpKeywords:

1. Introduction Magnetohydrodynamic (MHD) pumps have been focus of research owing to various advantages over traditional pumps in many specific areas of application including biological fields, solar applications and heat transfer systems [1]. The major advantage of such pumps is that they are free of any moving parts. Additionally, the miniaturization of such pumps due to their simple structure, can be utilized in microfluidic systems, microcooling systems and microelectromechanical system (MEMS) applications [2,3]. In a few applications, where it is difficult to use conventional pumps such as molten metal pumping, these pumps are more useful and efficient. Moreover, the applications requiring no moving sections, for example, in spaceships and biological applications like blood pumping, these pumps can be used [4]. Out of various applications, one of the promising usages of MHD pumps is cooling of heat dissipating element. The coolant flow is generated by MHD pumps and can be made to flow in the microchannel where the dissipated heat from the heat dissipating element is taken away. Use of microchannels in a cooling system is one of the efficient ways of dissipating heat [5,6]. In such instances, heat transfer effectiveness and the thermal behavior of a cooling system with its influencing factors need to be investigated.Lemoff et al. [7] developed and presented one of the first MHD micropumps with AC current using Lorentz force to pump electrolytic solution in microchannel. The authors showed that the continuous flow without any pulse can be produced. Rivero and Cuevas [8] studied MHD micropumps in one and two-dimensional flow models for laminar flows in parallel plates and rectangular ducts by considering the influence of slip condition which can be used to design MHD micropumps and characterize the flow behavior in these microfluidic devices. The 2D model presented by the authors showed more accuracy with results of experimentation as compared to 1D model [8]. Zhao et al. [9] conducted an analytical study by using the separation of variables method for generalized Maxwell fluids in a MHD rectangular micropump operated under the AC electric field and found that for given oscillating Reynolds number, large Hartmann number leads to large amplitudes of velocity. Yousofvand et al. [10] investigated heat transfer and pumping performance of electromagnetic pump considering Cu-water nanofluid as working fluid and found that for low Hartmann numbers, body force increases whereas for Ha > 200, the opposite trend is observed. Moghaddam analytically investigated the MHD micropump performance considering circular channel. The author found that average dimensionless velocity initially increases with increase in Hartmann number and dimensionless radius. However, after attaining peak, the average dimensionless velocity decreases with increase in Hartmann number and dimensionless radius [11]. Miroshnichenko et al. [12] studied MHD natural convection in a partially open trapezoidal cavity under the influence of various magnetic field orientations and found that an increase in uniform magnetic field value decreases the rate of heat transfer. A comprehensive study of power-law fluids in MHD natural convection has been conducted by Kefayati [13,14]. Shirvan et al. [15] conducted numerical investigations on MHD flow in a square cavity with different inlet and outlet ports. The authors presented optimization of mean Nusselt number using orthogonal array optimization. Kiyasatfar et al. [16] investigated thermal behavior and fluid motion in direct current (DC) MHD pump by varying magnetic flux density, applied current and channel size. The authors found that the maximum velocity increases with increase in applied current and as Hartmann number increases the velocity profile becomes flatter. Larimi et al. [17] studied the effect of non-uniform transverse magnetic field arrangements with a different Reynolds number for magnetic nanofluids on heat transfer and found that applying external magnetic fluid is strongly effective in fluid cooling at low Reynolds number. Kolsi et al. [18] performed a numerical study for 3D MHD natural convection inside a cubical enclosure with an inclined plate and found an optimal inclination angle of 180° for the plate. Kefayati considered various flow types including non-Newtonian nanofluids [19], blood flow [20] and power-law fluids in an internal flow [21] with focus of investigation on the effects of the power-law index, Reynolds number on thermal behavior by varying magnetic field to find optimized conditions. Further research has been conducted to understand the flow behavior of MHD considering different cases [22,23].The MHD pump involves two types of heat transfer mechanism: forced convection and mixed convection. The micro-cooling of the heat dissipating element is a case of mixed convection owing to its microstructure and very low flow rate. Mixed convection heat transfer has attracted significant research attention of heat transfer engineers owing to various application fields including heat exchangers, electronic cooling [24], heat dissipating element cooling [25], micro-cooling, MEMS applications, solar energy applications and metal casting [26]. Micro-cooling application is one of the critical research areas which has gained importance due to recent trends of miniaturization of devices as well as high power applications, which results in large amount of heat generation in compact volume. The various cooling methods previously suggested, including direct fan cooling [27] and thermoelectric cooling, suffer from low efficiency and high-power consumption. In addition, the presence of moving components makes conventional cooling methods less desirable [28]. Therefore, in the present study, MHD pump-based microchannel cooling for a heat dissipating element is investigated. The MHD pump performance is evaluated by varying the applied voltage and Hartmann number, and its effect on various parameters including normal current density, magnetic flux density, volumetric Lorentz force, shear stress and pump flow velocity is reported. The heat transfer performance of the MHD pump-based microchannel cooling for a heat dissipating element is reported by considering the heat removal rate, efficiency, thermal field, flow field and Nusselt number. In addition, three different nanofluids, including Cu-water, TiO2-water and Al2O3-water, are considered, and their influence on heat transfer performance is compared. The comparative heat transfer performance and potentials of various nanofluids in MHD pump application for microchannel cooling have not been realized. This study provides a comprehensive understanding of MHD pump performance, heat transfer performance of MHD pump-based microchannel cooling systems, and the influence of various nanofluids on heat transfer performance.

2. Method 2.1. Numerical Modeling A schematic view of an MHD pump for cooling a heat dissipating element is presented in Figure 1. A heat dissipating element can be any microsystem including microfluidic devices, micro-batteries, electronic chips, light emitting diodes (LED), etc. The basic principle of operation of MHD pumps is based on the Lorentz force in which magnetic and electrical fields are kept perpendicular, which forces conducting fluids in a perpendicular direction to both electric currents and magnetic fields, creating an MHD pump effect. The magnetic field strength and applied current both affect the flow velocity. The magnetic field is created by keeping two small permanent magnets. The origin of the coordinate system lies between two magnets and it is equidistance from the magnets. The origin of the coordinate system lies exactly at the center of the MHD pump without considering the microchannel dimensions (Figure 1). The origin of the coordinate system has been chosen specifically at the center of the MHD pump (without considering microchannel dimensions) for simplicity in the calculations. The width of the MHD pump is chosen as a characteristic length of the system considering width as an important dimension of the MHD pump system along which various parameters are evaluated. Due to the Lorentz force, the coolant flows in the positive X-axis direction (i.e., from the MHD pump and towards the microchannel) as shown in Figure 1. The microchannel consists of four slots. Details of the MHD pump dimensions are provided in Table 1.📷Figure 1.Schematic view of the magnetohydrodynamic (MHD) pump microchannel cooling system for a heat dissipating element.Table 1.MHD pump and microchannel dimensions.📷 2.2. Governing Equations and Boundary Conditions The modeling of the MHD phenomena involves a multiphysics problem with coupled equations between fluid flow, heat transfer, current flow, and magnetic fields, which are solved numerically. The different fields of physics involved are expressed by partial differential equations, which can be solved via the finite element method. In the present study, the numerical modeling of the MHD phenomena is conducted using COMSOL. The partial differential equations involving multiphysics behavior with coupling between fluid flow, heat transfer, electric current and magnetics are solved using the finite element method. The fluid flow and heat transfer are governed by the Navier–Stokes equation as shown below [29]. Equations (1)–(3) show continuity, momentum and energy conservation, respectively [30], where 𝑉→

is velocity, 𝜌 is density, 𝑝 is pressure and 𝛼 is thermal diffusivity.

∇·𝑉→=0

(1)

(𝑉→·∇)𝑉→=1𝜌∇𝑃+∇2𝑉→+1𝜌𝐹→

(2)

(𝑉→·∇)𝑇=𝛼∇2𝑇

(3)

𝐹→=𝐽→×𝐵→

(4)

𝐽→=𝜎(𝐸→+𝑉→×𝐵→)

(5)

𝐹→

is the body force due to Lorentz forces which causes fluid motion as shown in Equation (4) [9]. The electric current density which is defined by Ohm’s law is shown in Equation (5) [31], where 𝐽→ is the electric current in y-direction and 𝐵→

is the magnetic field in the z-direction. The electric current and magnetic field are perpendicular which creates a Lorentz force in the x-direction.The working fluid is Newtonian fluid with flow considered as steady and laminar based on the low Reynolds number. The thermo-physical properties of working fluid, nanoparticle and boundary conditions are presented in Table 2. The heat dissipating element that is acting on the pump’s wall is assumed to be a constant volumetric heat generation source. The applied electric voltage is varied from 0.05 V to 0.35 V with an interval of 0.05 V. The Hartmann number is varied from 1.41 to 3.74. The cylindrical type permanent magnets are used for providing the magnetic field intensity. Three different types of nanofluids are considered including Cu-water, TiO2-water, and Al2O3-water nanofluids. The base fluid for all the nanofluids is water. The boundary condition of opening at atmospheric pressure is applied at the coolant inlet and coolant outlet. The density of water is considered as 997.0 kg/m3 at 25 °C and assumed as an incompressible fluid. The thermal conductivity of water is considered as 0.6069 W/m-K at 25 °C. The specific heat of water is considered as 4181.7 J/kg-K. The details about the boundary conditions and thermophysical properties of water and nanoparticles are presented in Table 2.Table 2.Boundary conditions and thermophysical properties.📷

2.3. Nanofluid Relations The density of nanofluid with various nanoparticle volume fraction is predicted by the Pak et al. [34] as shown in Equation (6). Zhong et al. [35] experimentally measured the density of TiO2-water nanofluid and compared the predictions using the Equation (6) within 0.54%. Therefore, in the current study, the density of various nanofluids with different volume fraction is calculated using Equation (6), where 𝜌

denotes density and 𝜙 denotes volume fraction.

𝜌𝑛𝑓=𝜙𝜌𝑛+(1−𝜙)𝜌𝑓

(6)

The viscosity of the nanofluid (𝜇𝑛𝑓

) with various nanoparticle volume fraction (𝜙) using viscosity of fluid (𝜇𝑓) is predicted by various researchers including Batchelor [36], Vand [37], Wang et al. [38], Duangthongsuk et al. [39] and Bobbo et al. [40], as shown in Equations (7)–(11), respectivelyBased on the model prediction accuracy with experimental data [35], in the present study, the model proposed by Want et al. [38] is used for calculating the viscosity of nanofluid.

𝜇𝑛𝑓=𝜇𝑓(1+2.5𝜙+6.5𝜙2)

(7)

𝜇𝑛𝑓=𝜇𝑓(1+2.5𝜙+7.349𝜙2)

(8)

𝜇𝑛𝑓=𝜇𝑓(1+7.3𝜙+123𝜙2)

(9)

𝜇𝑛𝑓=𝜇𝑓(1.013+0.092𝜙−0.015𝜙2)

(10)

𝜇𝑛𝑓=𝜇𝑓(1+0.36838𝜙+0.25271𝜙2)

(11)

The thermal conductivity and specific heat of nanofluid for various volume fractions are calculated using Equation (12) [41] and Equation (13) [42], respectively. The effect of the nanoparticle volume fraction on the mixture properties is presented in Figure 2.

𝑘𝑛𝑓=𝑘𝑓𝑘𝑝+2𝑘𝑓+2𝜙(𝑘𝑝−𝑘𝑓)𝑘𝑝+2𝑘𝑓−2𝜙(𝑘𝑝−𝑘𝑓)

(12)

(𝜌𝐶𝑝)𝑛𝑓=(1−𝜙)(𝜌𝐶𝑝)𝑓+𝜙(𝜌𝐶𝑝)𝑛

(13)📷Figure 2.Effect of nanoparticle volume fraction on the mixture properties.

2.4. Mesh Independency Figure 3 shows the details of the mesh independency test. The Lorentz force and average velocity are considered as parameters to evaluate the mesh independency. In the present study, the mesh type is defined as the number of elements in the generated mesh. Mesh type 1 contains 5.43 × 104 elements, which is a coarse mesh, whereas mesh type 5 contains 1.45 × 106 elements, which is a finer mesh. As the mesh elements increased from 9.65 × 105 to 1.45 × 106, the Lorentz force and average velocity varied only 0.008% and 0.166%, respectively. Considering the computational cost and accuracy of the numerical simulations, mesh type 4 with 9.65 × 105 elements, is selected for carrying out numerical simulations as shown in Table 3.📷Figure 3.Mesh details (a) Mesh independency test (b) Meshing of magnetohydrodynamic (MHD) pump microchannel cooling system for heat dissipating element.Table 3.Mesh details.📷

2.5. Data Reduction The MHD pump flow is generated by the application of electric and magnetic field, which interacts with the conducting fluid. The developed flow is described as Hartmann flow and the non-dimensional number, known as the Hartmann number (Ha), is defined as shown in Equation (14), where B is magnetic flux intensity, L is characteristics length, σ is electrical conductivity and μ is dynamic viscosity [21]. The Hartmann number gives an estimation of the magnetic forces compared to viscous force [9].𝐻𝑎=𝐵𝐿(𝜎/𝜇)0.5

(14)

The convective heat transfer rate is used to obtain heat transfer coefficient and calculate average Nusselt number (Nuavg). The heat transfer rate is evaluated as shown in Equation (15) [43].

𝑄𝑐𝑜𝑛𝑣=𝑚𝑖𝑛𝐶𝑝(𝑇𝑏𝑢𝑙𝑘,𝑜𝑢𝑡−𝑇𝑏𝑢𝑙𝑘,𝑖𝑛)

(15)

The average heat transfer coefficient is evaluated from Equation (16). The numerator is convective heat transfer from wall to fluid and the denominator is a combined term consisting of the wall convective surface area and logarithmic mean temperature difference of the wall-and-bulk fluid [25].

ℎ𝑎𝑣𝑔=𝑄𝑐𝑜𝑛𝑣𝐴𝑤𝑎𝑙𝑙(𝑇𝑤𝑎𝑙𝑙−𝑇𝑏𝑢𝑙𝑘)𝐿𝑀𝑇𝐷

(16)

(𝑇𝑤𝑎𝑙𝑙−𝑇𝑏𝑢𝑙𝑘)𝐿𝑀𝑇𝐷=Δ𝑇𝑤𝑎𝑙𝑙−𝑏𝑢𝑘,𝑖𝑛−Δ𝑇𝑤𝑎𝑙𝑙−𝑏𝑢𝑘,𝑜𝑢𝑡𝑙𝑜𝑔(Δ𝑇𝑤𝑎𝑙𝑙−𝑏𝑢𝑘,𝑖𝑛/Δ𝑇𝑤𝑎𝑙𝑙−𝑏𝑢𝑘,𝑜𝑢𝑡)

(17)

where Δ𝑇𝑤𝑎𝑙𝑙−𝑏𝑢𝑘,𝑖𝑛 and Δ𝑇𝑤𝑎𝑙𝑙−𝑏𝑢𝑘,𝑜𝑢𝑡 indicate the differences between the wall temperature and bulk fluid temperature at the inlet and outlet of the channel, respectively (Equation (17)). The average Nusselt number is calculated as shown in Equation (10) where Dh represents the hydraulic diameter and kf represents the thermal conductivity of the fluid.

𝑁𝑢𝑎𝑣𝑔=ℎ𝑎𝑣𝑔×𝐷ℎ𝑘𝑓

(18)

3. Results and Discussion The results of the numerical study on the MHD pump subjected to the mentioned boundary conditions are presented in terms of normal current density, magnetic flux density, volumetric Lorentz force, shear stress and pump flow velocity by varying applied voltage and Hartmann number. For evaluating the MHD pump performance, Cu-water nanofluid with 0.1% volume fraction was considered. In the subsequent sub-sections, the performance of the MHD pump-based microchannel cooling system is presented considering various parameters, including the maximum temperature of a heat dissipating element, heat removal rate, efficiency, thermal field, flow field and Nusselt number. In addition, the heat transfer performance of Cu-water nanofluid is compared with TiO2-water nanofluid and Al2O3-water nanofluid. The study provided an in-depth understanding of the MHD pump functioning and its application in micro-cooling systems. 3.1. Validation The numerical study is validated with the previously published literature. The server workstation with an Intel (R) Xenon(R) CPU E5-2620 v3 @2.40 GHz including 24 cores and 64 GB computation memory is used to run the simulations. To ensure the accuracy of the numerical study method, numerically predicted velocity is compared with previously published experimental data [7] and numerical data [10] as shown in Figure 4. It is demonstrated that the predicted velocity closely matches with the linear fit to the experimental data and numerical data. Thus, the validation of the numerical model is confirmed.📷Figure 4.Velocity comparison between present study and the Lemoff et al. [7] experimental study and Yousofvand et al. [10] numerical study. 3.2. Magnetohydrodynamic Pump (MHD) Performance Figure 5a shows the variation of normal current density with the applied voltage and Hartmann number. The normal current density increased with the increase in applied voltage. For example, as the applied voltage increased from 0.05 V to 0.35 V, at a Hartmann number value of 2.0, the normal current density increased 600%, or 6 times. For the same applied voltage, a higher normal current density is observed for the higher Hartmann number. As the Hartmann number increased from 1.41 to 3.76 at a constant applied voltage of 0.35 V, the normal current density increased 600%, or 6 times. The combined influence of a higher applied voltage and higher Hartmann number are visible with a significant increase in the normal current density.📷📷Figure 5.Current density and velocity (a) Normal current density variation for different applied voltage and different Hartmann number (b) Induced current density distribution (c) Variation of average velocity with current density.Figure 5b shows the spatial variation of induced current and it can be seen that the induced current density is higher near electrode area. Figure 5c shows the variation of the average velocity with respect to current density. The average velocity increased linearly with the increase in current density. The flow rate can be increased either by increasing applied current, keeping magnetic flux constant or by increasing magnetic flux while keeping the applied current constant to enhance the pump performance. Similar trends have been observed by previously conducted studies [16]. For low Hartmann numbers, the velocity increased with an increase in the Hartmann number. However, the high Hartmann number can have a negative effect on the velocity as well as volumetric flow rate [11]. For a low Hartmann number, forced convection dominates with higher velocities which is useful for enhancing the pump performance.Figure 6a shows the variation of magnetic flux along the dimensionless width in the Y-axis at the center of the magnetohydrodynamic pump. The maximum value of the magnetic flux attained is about 0.25 T at the center of the MHD pump channel. However, the value of the magnetic flux density near the conducting electrode is found to be in the order of 0.11 T. Similar results have been obtained by Aoki et al. [44]. The magnetic flux showed axisymmetric behavior for the axis passing through the center of the dimensionless width. Figure 6b shows the magnetic field distribution for the MHD pump on the XY-plane. As in the present study, the cylindrical permanent magnet is considered for the MHD pump application and the circular magnetic field pattern is observed. The maximum magnetic field value of the order of 100 kA/m is observed. The magnetic field showed radial symmetric behavior for the axis passing through the center of the magnet.📷Figure 6.Magnetic flux density and magnetic field (a) Magnetic flux density variation with dimensionless width for different applied voltages and different Hartmann number (b) Magnetic field distribution at the center of the MHD pump in the XY-plane.Figure 7 shows the volumetric Lorentz force variation for applied voltage and Hartmann number. The volumetric Lorentz force increased with increase in applied voltage. For example, as the applied voltage increased from 0.05 V to 0.35 V at a Hartmann number value of 2.0, the volumetric Lorentz force increased 600%, or 6 times. For the same applied voltage, a higher volumetric Lorentz force is observed for a higher Hartmann number. As the Hartmann number increased from 1.41 to 3.76, at a constant applied voltage of 0.35 V, the volumetric Lorentz force increased 600%, or 6 times. In the study conducted by Moghaddam on MHD micropumps, the volumetric flow rate increased owing to an increase in the Hartmann number to a value of 40, then volumetric flow rate started to decrease [11]. Similarly, the volumetric flow rate increased until a Hartmann number of 200, and then decreased in the study conducted on the MHD pump by Yousofvand et al. [10]. The present study is focused on low Hartmann numbers (Ha < 4) where the volumetric flow rate and Lorentz force increases with the increase in Hartmann number, as the defined Hartman number compares the magnetic force with the viscous force. At low Hartmann numbers, the viscous forces dominate giving a higher volumetric flow rate. As a result, the lower Hartmann number is favorable for the enhancement of heat transfer. However, a higher Hartmann number can have an adverse effect on heat transfer [10].📷Figure 7.Volumetric Lorentz force variation for different applied voltages and different Hartmann number.Figure 8a shows the shear stress variation along the non-dimensional width at the center of the magnetohydrodynamic pump. The shear stress values for all the Hartmann numbers are compared in the middle section of the channel. Regions of higher shear stress are observed near the wall for all the Hartmann numbers. The values of shear stress in the region near the walls of the channel increased as the Hartmann number increased. Shear stress is directly proportional to the rate of change of velocity. The increase in shear stress at the walls for a higher Hartmann number is observed due to the typical velocity profile of the MHD pump flow inside the channel, where the velocity profile becomes flatter at the center, and a large velocity change is seen near the walls. As the Hartmann number increased from 1.41 to 3.74, the shear stress value near the channel walls increased around 7 times, or 714%. The shear stress variation showed axisymmetric behavior for the axis passing through the center of the dimensionless width. Figure 8b shows the pressure contours for the flow cross-sectional area at the center of the pump in the YZ-plane, and it could be seen that higher pressure regions are observed near the wall owing to the Hartmann effect.📷Figure 8.Shear stress and Pressure (a) Shear stress variation with dimensionless width for different applied voltages and different Hartmann numbers (b) Pressure contours for the flow cross-sectional area at the center of the pump in the YZ-planeFigure 9 shows the variation of the velocity profile along the dimensionless width in the Y-axis imposed by the Lorentz force at the center of the magnetohydrodynamic pump. The velocity profiles show maximum values near the walls and lower values in the center of the channel owing to the Lorentz force distribution [44]. The velocity variation showed axisymmetric behavior for the axis passing through the center of a dimensionless width. The M-shape velocity profiles as observed in Figure 9 are present in many MHD pumps. This can be attributed to the position of conducting electrodes on the two opposite walls to provide the DC power supply. Moreover, the different fluids have responded with a similar velocity profile indicating that it is a geometrically affected phenomenon with the position of the electrode [45]. It could be seen from Figure 9 that as the Hartmann number increased, the velocity increased. Moreover, as the value of the Hartmann number increased, the velocity profile became flatter. The plug-like shape remained constant for a large portion of the channel width [46,47]. The current flowing in the closed loop generated a non-uniform negative small electromagnetic Lorentz force which counteracted the conducting fluid flow in the magnetic field creating a flat velocity boundary layer [45]. This phenomenon is called the Hartmann effect. For example, as the value of the Hartmann number increased from 1.41 to 3.74, the maximum velocity increased by 280% at the center of the magnetohydrodynamic pump. Moreover, as the value of the Hartmann number increased, its effect on velocity change was slightly reduced. This is evident from Figure 9, as the change in maximum velocity for the Hartmann number variation from 3.46 to 3.74 is less as compared to the variation from 1.41 to 2.00.📷Figure 9.Velocity variation with dimensionless width.Figure 10 shows the velocity field variation in the X-axis along the width at the center of the magnetohydrodynamic pump. The velocity at the center of the channel is higher compared to the channel wall, owing to the high shear stress observed along the channel wall. The average velocity of 0.0034, 0.0061, 0.0085, 0.0106, 0.0126, 0.0145 and 0.0164 m/s are developed for the applied voltage of 0.05, 0.10, 0.15, 0.25, 0.30 and 0.35 V at Hartmann number value of 2.0, respectively.📷Figure 10.Velocity variation with dimensionless width.The increase in average velocity with increase in the applied voltage is attributed to development of higher Lorentz force. It is obvious from Equation (4) that the Lorenz force will increase if the cross product of current density and magnetic field increases. 3.3. MHD-Based Microchannel Cooling System The magnetohydrodynamic pump has various advantages over traditional pumps including low cost, low electric field and no moving parts. The Lorentz force developed by the interaction between the electric current and magnetic field can be used to propel, stir or manipulate the flow behavior in the channel. This section provided the details of the MHD micropump performance considering the applied voltage and Hartmann number.Figure 11 shows the variation of the maximum temperature of the heat dissipating element for the varied applied voltage and Hartmann number with Cu-water with volume fraction of 0.1% as coolant. As the applied voltage is increased, the maximum temperature of the heat dissipating element decreased. For example, as the applied voltage increased from 0.05 V to 0.35 V at a Hartmann number value of 2.0, the maximum temperature of the heat dissipating element decreased by 7.7%. For the same applied voltage, lower maximum temperatures of the heat dissipating element are observed for a higher Hartmann number. As the Hartmann number increased from 1.41 to 3.76 at a constant applied voltage of 0.05 V, the maximum temperature of the heat dissipating element decreased by 11.0%. The combined influence of higher applied voltage and higher Hartmann number are visible with significant decrease in the maximum temperature of the heat dissipating element. These findings show that the applied voltage and Hartmann number have a significant effect on maintaining and controlling the maximum temperature of the heat dissipating element.📷Figure 11.Maximum temperature.Figure 12 shows variation of the heat removal rate for the varied applied voltage and Hartmann number with Cu-water with the volume fraction of 0.1% as coolant. As the applied voltage is increased, the heat removal rate increased. For example, as the applied voltage increased from 0.05 V to 0.35 V at a Hartmann number value of 2.0, the heat removal rate increased by 34.5%. For the same applied voltage, higher heat removal rates are observed for a higher Hartmann number. As the Hartmann number increased from 1.41 to 3.76 at a constant applied voltage of 0.05 V, the heat removal rate increased by 39.5%. The combined influence of a higher applied voltage and higher Hartmann number are visible with significant increase in heat removal rate. The increase in heat removal rate with a higher applied voltage is attributed to an increase in the volumetric Lorentz force as shown in Figure 7, which subsequently results in the higher volumetric flow rate. It can be seen that for a lower Hartmann number, the rate of change heat removal rate is large, whereas for a higher Hartmann number, the rate of change of heat removal rate is small. This is because the dominance of the magnetic force increased as the Hartmann number increased [10].📷Figure 12.Heat removal rate variation.Figure 13 shows the variation of efficiency for the varied applied voltage and Hartmann number with Cu-water with volume fraction of 0.1% as coolant. The efficiency is defined as shown in Equation (19).𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦=𝐻𝑒𝑎𝑡 𝑟𝑒𝑚𝑜𝑣𝑎𝑙 𝑟𝑎𝑡𝑒𝐼𝑛𝑝𝑢𝑡 𝑝𝑜𝑤𝑒𝑟

(19)📷Figure 13.Variation of efficiency with applied voltage.As shown, the efficiency decreased continuously with increase in applied voltage. This shows that, even though for higher applied voltage the heat removal rate is higher, and the temperature of the heat dissipating element is minimum, the heat removal process is less efficient. Therefore, an optimum operating range considering the heat removal rate, temperature of heat dissipating element and efficiency could be considered. As the applied voltage increased from 0.05 to 0.35 V at a Hartmann number value of 3.46, the efficiency decreased from 204.4 to 4.9. For the same applied voltage, a lower efficiency is observed for a higher Hartmann number. As the Hartmann number increased from 1.41 to 3.76 at a constant applied voltage of 0.35 V, the efficiency decreased from 29.1 to 4.9. The combined influence of the higher applied voltage and higher Hartmann number are visible with a significant decrease in efficiency. These findings show that the applied voltage and Hartmann number have a significant effect on efficiency.Figure 14 shows the velocity and temperature distribution in the MHD pump microchannel cooling system with Cu-water with volume fraction of 0.1% as coolant. As shown in Figure 14a, the velocity is uniformly distributed in the microchannel throughout, which makes it an attractive method for the cooling heat dissipating element, especially where space and noise are constraints such as electronic devices. The rate of increase of the developed flow velocity in the magnetohydrodynamic pump cooling system is an indication of cooling performance as a higher velocity development leads to higher cooling performance. However, the increase in flow velocity has limitations owing to applied voltage and applied magnetic field. As expected, the flow velocity in the thin microchannel increased as it passed through the narrow duct of microchannel cooling system [6]. This is desirable as the heat dissipating element is placed exactly at the center of the microchannel. As shown in Figure 14b, the temperature of the coolant increased as it passed through microchannel. In the present study, the square microchannel design is investigated considering the manufacturing simplicity of the square duct. The future scope of the study involves the use of different shapes of microchannel including circular and trapezoidal. The temperature field distribution for the MHD pump microchannel at the center plane showed that heat transfer occurred along the edges of the microchannel and heat is taken away as the flow proceeded [48]. The geometry based microchannel optimization for effective thermal performance could be carried out considering the requirement of cooling performance and these findings can be used to design an effective cooling by optimizing influencing parameters.📷Figure 14.Velocity and temperature distribution in MHD pump microchannel cooling system.Figure 15 shows the variation of the average Nusselt number for the applied voltage and Hartmann number with Cu-water with a volume fraction of 0.1% as the coolant. The Nusselt number is an indication of enhanced heat transfer due to convection as compared to conduction [49]. The higher Nusselt number indicates the effectiveness of magnetohydrodynamic cooling systems for the heat dissipating element. The average Nusselt number increased with the applied voltage. For example, as the applied voltage increased from 0.05 V to 0.35 V at a Hartmann number value of 2.0, the average Nusselt number increased by 112.6%. For the same applied voltage, a higher average Nusselt number is observed for higher Hartmann numbers. As the Hartmann number increased from 1.41 to 3.76 at a constant applied voltage of 0.25 V, the heat removal rate increased by 100.0%. The combined influence of a higher applied voltage and higher Hartmann number are visible with a significant increase in the average Nusselt number. However, the rate of increase of the average Nusselt number decreased as the applied voltage and Hartmann number increased. The heat transfer performance slightly deteriorated as the value of the Hartmann number increased due to suppression of convection due to the magnetic field [10,50]. These findings show that the applied voltage and Hartmann number have a significant effect on the heat transfer performance of MHD micropumps.📷Figure 15.Variation of average Nusselt number with applied voltage. 3.4. Influence of Various Nanofluids The thermal performance of the MHD pump is compared using various nanofluids. Three types of nanofluids including Cu-water, TiO2-water and Al2O3-water are considered with a volume fraction of 0.1%. For performance comparison, the volume fraction of nanoparticles in nanofluids is kept constant. To evaluate the thermal performance of MHD pumps with various nanofluids, the heat transfer rate, efficiency and Nusselt number variation are considered.Figure 16 shows variation of the heat removal rate for the varied Hartmann number. As the Hartmann number is increased, the heat removal rate increased. For example, as the Hartmann number increased from 1.41 to 3.74 at an applied voltage value of 0.35 V, the heat removal rate increased by 18.0% for Cu-water nanofluids. For the same applied voltage, higher heat removal rates are observed for Cu-water nanofluid as compared to TiO2-water and Al2O3-water nanofluids. As previously noted, for a lower Hartmann number, the rate of change heat removal rate is large, whereas for higher Hartmann number, the rate of change of heat removal rate is small. The Cu-based nanofluid showed a better heat transfer rate owing to the high thermal conductivity of copper nanoparticles.📷Figure 16.Variation of heat removal rate with various nanofluids at different Hartmann numbers.Figure 17 shows variation of the efficiency for the varied Hartmann number. As the Hartmann number is increased, the efficiency decreased. For example, as the Hartmann number increased from 1.41 to 3.74 at applied voltage value of 0.35 V, efficiency decreased from 29.16% to 4.92% for Cu-water nanofluid. For the same applied voltage, higher efficiencies are observed for Cu-water nanofluid as compared to TiO2-water and Al2O3-water nanofluids. For lower Hartmann number, the rate of change efficiency is large, whereas for higher Hartmann number, the rate of change of efficiency is small. This is because the dominance of magnetic force increased as the Hartmann number increased. The Cu-based nanofluid shows better efficiency owing to high thermal conductivity of copper nanoparticles.📷Figure 17.Variation of efficiency with various nanofluids at different Hartmann numbers.Figure 18 shows variation of the average Nusselt number for the varied Hartmann number. As the Hartmann number is increased, the average Nusselt number increased. For example, as the Hartmann number increased from 1.41 to 3.74 at an applied voltage value of 0.35 V, the average Nusselt number increased by 96.5% for Cu-water nanofluid. For the same applied voltage, higher average Nusselt numbers are observed for Cu-water nanofluid as compared to TiO2-water and Al2O3-water nanofluids. Interestingly, the Nusselt number for the TiO2 based nanofluid and Al2O3 based nanofluid are found to be close. The Cu-based nanofluid showed a better average Nusselt number owing to the high thermal conductivity of copper nanoparticles.📷Figure 18.Variation of average Nusselt number with various nanofluids at different Hartmann numbers.

4. Conclusions Magnetohydrodynamic pump-based microchannel cooling is proposed for cooling heat dissipating elements. The proposed magnetohydrodynamic pump has many advantages including vibration-free and noise-free applications. In the present study, the applied voltage and Hartmann number are varied to evaluate the effect on the MHD pump performance considering normal current density, magnetic flux density, volumetric Lorentz force, shear stress and pump flow velocity as evaluating parameters. The MHD pump-based microchannel cooling system performance with Cu-water nanofluid is evaluated considering the maximum temperature of the heat dissipating element, heat removal rate, efficiency, thermal field, flow field and Nusselt number for various applied voltages and Hartmann numbers. It is found that for a low Hartmann number, the Lorentz force increased with an increase in the applied voltage and Hartmann number. As the applied voltage increased from 0.05 V to 0.35 V at a Hartmann number of 1.41, the heat removal rate increased by 39.5%. The results revealed that for a low Hartmann number, the average Nusselt number increased with increase in the applied voltage and Hartmann number. As the applied voltage increased from 0.05 V to 0.35 V at a Hartmann number of 1.41, the average Nusselt number increased by 112.6%. In addition, the influence of various nanofluids including Cu-water, TiO2-water and Al2O3-water nanofluids on heat transfer performance of MHD pump-based microchannels is evaluated. At the Hartmann number value of 3.74 and applied voltage value of 0.35 V, average Nusselt numbers are 12.3% and 15.1% higher for Cu-water nanofluid compared to TiO2-water and Al2O3-water nanofluids, respectively. The MHD pump is more useful in cases where space and noise constraint are of particular interest. Especially in the microelectronics device cooling, the removal of heat is important and due to miniaturization, the MHD pump for cooling provides a promising option. The investigations provide an opportunity to further explore the application of MHD pumps in electronics cooling.

Author Contributions Conceptualization, J.-H.S.; M.S.P. and M.-Y.L.; methodology, J.-H.S.; software, M.S.P.; validation, J.-H.S. and M.S.P.; Numerical investigation, J.-H.S. and M.S.P.; resources, M.-Y.L. and S.P.; data reduction, M.S.P. and S.P.; writing—original draft preparation, J.-H.S. and M.S.P.; writing—review and editing, M.-Y.L., and S.P.; visualization, M.S.P.; supervision, M.-Y.L.; project administration, M.-Y.L.; funding acquisition, M.-Y.L. All authors have read and agreed to the published version of the manuscript.

Funding This research received no external funding.

Acknowledgments This work was supported by the Dong-A University research fund.

Conflicts of Interest The authors declare no conflict of interest.

Across-sectional area (m2)𝐵→Nomenclature

magnetic field vector (T)Bmagnitude of the magnetic field (T)Cpspecific heat at constant pressure (J/kg-K)Dhhydraulic diameter (m)𝐸→electric field vector (V/m)𝐹→electromagnetic force (N)havgaverage heat transfer coefficient (W/m2-K)HaHartmann number𝐽→current density (A/m2)Lcharacteristic length (mm)MHDmagnetohydrodynamic𝑁𝑢𝑎𝑣𝑔average Nusselt numberPpressure (Pa)Qheat transfer rate (W)Ttemperature (°C/K)ttime (s)𝑉→velocity (m/s)Greek symbols∇gradient operatorαthermal diffusivity (m2/s)σelectrical conductivity (S/m)ρdensity (kg/m3)νkinematic fluid viscosity (m2/s)μdynamic viscosity (Pa-s)kthermal conductivity (W/m-K)𝜙

volume fraction (%)Subscriptsavgaveragebulkbulk propertyconvconvective heat transferffluidininletLMTDlogarithmic mean temperature differencennanoparticlenfnanofluidoutoutletwallwall

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Seo, J.-H.; Patil, M.S.; Panchal, S.; Lee, M.-Y. Numerical Investigations on Magnetohydrodynamic Pump Based Microchannel Cooling System for Heat Dissipating Element. Symmetry 2020, 12, 1713. https://doi.org/10.3390/sym12101713

Seo J-H, Patil MS, Panchal S, Lee M-Y. Numerical Investigations on Magnetohydrodynamic Pump Based Microchannel Cooling System for Heat Dissipating Element. Symmetry. 2020; 12(10):1713. https://doi.org/10.3390/sym12101713

Seo, Jae-Hyeong, Mahesh Suresh Patil, Satyam Panchal, and Moo-Yeon Lee. 2020. "Numerical Investigations on Magnetohydrodynamic Pump Based Microchannel Cooling System for Heat Dissipating Element" Symmetry 12, no. 10: 1713. https://doi.org/10.3390/sym12101713

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Victor F Petrenko, probably you should use setting "B-H curve in Magnetization model of Constructive Relation B-H in Ampère`s Law 1 and 2"

Hi Zhuoyuan Leng , could you provide more details of the boundary conditions you are using ?

The explosion usually occurs mainly due to hydrogen build-up if the excess heat is not removed via the cooling water. You need to model the process of dissociation of H20 into H2+02 and then estimate the pressure developed inside the dome of the plant. Suppose this pressure exceeds the yield limit of the material. You may assume it has failed. i.e. (exploded, cracked). This is a fundamental approach that you can build on by adding complexities at later stages.

how

I prefer Lumerical and Comsol for designing and investigating solar cells.

Analyzing capillary action in CFD necessitates the integration of multiphase flow models to accurately depict the interactions between distinct phases, such as a liquid and a gas, which are essential for capturing the dynamics of capillarity. Crucial to this simulation is the modeling of surface tension, a key force driving the fluid within narrow spaces, requiring CFD software to precisely account for surface tension forces at the interface of different fluids or between a fluid and a solid. Equally important is the implementation of the contact angle, the angle at which a liquid/vapor interface meets a solid surface, which plays a pivotal role in determining the hydrophilic or hydrophobic nature of the material and thus impacts the capillary action.

Hope this helps

hi Anvi Gaonkar ,

go through this one. Maybe it will help.

https://www.comsol.com/video/modeling-magnetohydrodynamic-flow-with-comsol-multiphysics#:~:text=In%20this%20archived%20webinar%2C%20we,the%20use%20of%20multiphysics%20software.

Regards

Gautam

Space between "range" and "(", perhaps?

I haven't completed my 3D modelling yet, but I will send you the file, and you can get an idea of how to feed AM1.5 G into a solar cell.

and then you can help me complete my 3D model by sharing your 3D model file.

I will also send you the AM1.5 G data file.

Are you okay with that?

Go one level up to Bio Concentrations and tick Show legend.

Many hyporheic zone related studies have modelled this. The river-groundwater interface is treated as a pressure boundary.

Suliman S Alfarawi

Abdulmaged Omer Algareu

If you want a quick answer and result to your problem better to use Flow 3D but if you want to know the physics underlying the problem being solved and build your own model then COMSOL is the best option.

If you mean the built in functions and operators then check the COMSOL Documentation.

hi ziang gao

thank for your guidance about my question

accordingly, i asked from many researchers and they said that it's very complicated, also if you look at many publications they didnt simulated with comsol.

best wishes

Some suggestions for you:

Particle Definitions- Verify accurate definitions for all particles in terms of sizes, charges, masses, and other properties.

Physics Settings- Confirm inclusion of relevant physics interfaces (Fluid Flow, Electric Fields, Particle Tracing) with proper configuration for particle sizes.

Force Calculation- Check expressions for drag force, electric force, etc., ensuring correct definitions of variables and parameters.

Solver Settings- Adjust solver settings, focusing on the time-stepping method, time step size, and tolerance values. Smaller time steps may enhance accuracy.

Initial Conditions- Provide precise initial conditions for particles, including positions and velocities.

Meshing- Ensure a well-defined mesh with appropriate settings and resolution to capture particle behavior.

Check for Errors- Review solver logs and error messages for insights into convergence issues.

Documentation and Tutorials- Refer to COMSOL documentation and tutorials, specifically for Particle Tracing in Fluid Flow.

Contact COMSOL Support- If issues persist, reach out to COMSOL support for personalized assistance.

If you encounter the mentioned error in COMSOL Multiphysics with a RANS turbulence model, ensure proper initialization of the Reciprocal Wall Distance variable in study steps. Confirm correct settings for turbulence model and wall treatment, validate boundary conditions, and check solver settings. Consult COMSOL documentation for model-specific guidance. If issues persist, contact COMSOL support for assistance. Review and ensure proper definition and initialization of all required variables in accordance with RANS turbulence model requirements.

Hi, I hope you're very well. It will help if you use the piezoelectric devices branch of the AC/DC COMSOL module. Also, you may visit COMSOL's applications library to familiarize yourself with piezoelectric devices.

using the piezoelectric device module is possible to define completely the reverse and direct piezoelectric effects as in SAW devices.

Dear Suresh Ahuja,

Thank you very much for providing me with these documents. However, the difficulty I am facing is that I am not proficient in operating COMSOL, and I do not know how to introduce LGD approach in COMSOL. I would be extremely grateful if you have any relevant materials that could be provided to me for learning.

Best rewards,

Dear Cheng Xiong, I am facing the same issue. I am writing to you to know if you have resolved the issue and if you know how to solve such a case. Do you have anything to help me with for out-of-plane mode calculations?

Thank you, and I look forward to hearing from you.

Again here is Jürgen Weippert with his dum chatboat. A lot of words, no help.

@Hiwa aryan

Sir I'm in a trouble of calculating osi using comsol.

Will you please explain detail how to write the expression?

Actually I can't calculate the average wss.

Jafar Behtarinik Thank you so much for your kind suggestion.

-Akshay

Hey there Mostafa Shabani! Look, when it comes to the `atlocal` command in COMSOL, you've stumbled upon a bit of a tricky one. Now, I'm not claiming to be the absolute guru of COMSOL, but let me throw in my two cents.

The `atlocal` command in COMSOL is used to evaluate variables at a specific geometric location. It sounds like you're trying to use coordinates but aren't getting the expected results. First things first, are you Mostafa Shabani sure your coordinates are set up correctly? Double-check those values, and don't forget about the unit consistency—COMSOL can be a stickler for that.

If you're still hitting a wall, consider the surrounding context of your simulation. Sometimes, issues with `atlocal` can stem from the mesh or the way your model is defined. Ensure your geometry and mesh are accurate.

And hey, reaching out to the COMSOL community or forums might be a good move. There's a wealth of knowledge out there, and sometimes a fresh set of eyes can spot what you might be missing. Good luck, and let me know if you need more wisdom!

Simulate Three-Phase Flow with a New Phase Field Interface

📷

by Ed Fontes

December 16, 2015

In COMSOL Multiphysics version 5.2, the CFD and Microfluidics modules include a new fluid flow interface for modeling separated three-phase flow. The model behind this fluid flow interface accounts for surface tension between each pair of fluids, contact angles with the walls, as well as the density and viscosity of each of the fluids. The phase field method computes the shape of the interfaces between the three phases and also accounts for interactions with walls.

Modeling Separated Multiphase Flow

COMSOL Multiphysics has offered modeling and simulation capabilities for multiphase flow for many years. However, the equation-based formulation of three-phase flow problems has been used successfully by only a few experts in our user community, as seen in the figure below. In the last two or three years, we have received numerous requests for a more user-friendly, ready-made three-phase flow interface. In COMSOL Multiphysics version 5.2, we have satisfied these requests.

📷 Simulation results of a rotating drum with three-phase flow, performed by a COMSOL Multiphysics user with equation-based modeling.

The description used in this new flow interface, the Three-Phase Flow, Phase Field interface, is a separated multiphase flow model. This interface is similar to the level set and phase field models for the two-phase flow interfaces included in earlier versions of the software. This means that the interface between the three immiscible phases (air, oil, and water, for example) is resolved in detail, including the effects of surface tension and contact angles.

Separated multiphase flow models are used for studying microfluidic systems and for fundamental studies of bubble coalescence and droplet breakup mechanisms. These are processes and phenomena where surface tension, contact angles, and buoyancy effects play a significant role on the shape of the phase boundaries between the different fluids and on the velocity field. Microfluidic devices and processes are typically found in analytical chemistry, biotechnology, medical technology, and nanotechnology. They include inkjets, sensors, separation devices, lab-on-a-chip devices, and microreactors.

High-fidelity separated multiphase flow models are usually too computationally expensive for direct use in macroscopic descriptions, since that may require resolving the surface of thousands or millions of droplets and bubbles. However, the results of detailed fundamental studies on a few bubbles and droplets can be used to develop simplified, less computationally expensive models. These simplified descriptions can usually be included in macroscopic dispersed multiphase flow models, which can describe systems with millions of bubbles and droplets. Macroscopic dispersed multiphase flow models are interesting in the study and design of devices and processes in the pharmaceutical, food, chemical, and household product industries.

The tutorial included in the Application Library, shown in the image below, deals with a droplet of air that rises through a layer of water at the bottom of a container and then into a layer of oil, lighter than water, resting on the water’s surface. As the air bubble moves through the water-oil interface, it carries some water in its wake and into the layer of oil. The water entrained in the bubble’s wake forms a “water tail” behind the bubble in the oil layer. This example is a benchmark from scientific literature, which we used to verify the equations in this fluid flow interface.

📷 An air bubble penetrates the phase boundary between water and oil and entrains a small amount of water in its wake. The entrained water droplet forms a tail behind the rising bubble.

This problem is interesting in a microfluidic system, since this mechanism can be used to transport small droplets of water into a layer of oil. The water droplets can, for example, be used to extract water soluble species from the oil into the water droplets, while keeping the hydrophobic species in the oil, to perform separation in a very controlled way. If the size of the water droplets is small enough, coalescence of the droplets in the oil phase may be avoided, thus creating droplets with a specific content and weight.

The same model can also be used to calculate the size distribution and coalescence kinetics, which can in turn be used in a dispersed multiphase flow model of an air-water-oil mixture. Emulsions can be used to create powders and structured mixtures.

The Physics and Model Behind the Three-Phase Flow, Phase Field Interface

The schematic below shows the three immiscible phases. The model is based on a free energy formulation of the system using three different phase field variables, with one for each phase (A, B, and C). The phase boundary is determined by the isosurface of a phase field variable for the value of 0.5, which corresponds to the pink and gray isosurfaces in the image above. The sum of all phase field variables in each point in space has to be equal to 1. The phase field variables are thus measures of the content of each phase in every point in space.

📷 A schematic drawing of the three-phase system, visualized in a projection plane perpendicular to the container walls.

The free energy equation is a function of the phase field variables and the surface tension for each pair of possible boundary interfaces, i.e., AB, AC, and BC. Each of the phase field functions is then used in the conservation equations for each field, which include the minimization of the free energy of the system. The formulated equations are the so-called Cahn-Hilliard equations.

Note also that this formulation accurately treats the triple point between the three phases, which is the point between the blue, pink, and white colored regions for phases A, B, and C shown above. This allows for the simulation of partial and absolute wetting between the three phases.

The interaction with the walls is determined by the contact angles in figure 2, θi, which are set to fixed values. The contact angles are used to express the boundary conditions for each of the phase field variables at the walls. Each angle is computed as the angle between an isosurface of the phase field variable at the value of 0.5, using the projection on a plane perpendicular to the walls, as shown above.

The surface tension forces in the system are also introduced in the equations for the conservation of momentum (Navier-Stokes equations) as sources of momentum. The density and viscosity, at each point in space in the equations for conservation of momentum and mass, are computed from the phase field variables, switching from the values of one fluid to another. Each phase gets the density and viscosity of the pure phase, which smoothly but rapidly changes across the phase boundary at the phase field value of 0.5.

The formulation described above is the one used in the phase field method, which is considered one of the most accurate ways of describing multiphase flow in continuum models.

An Intuitive User Interface

The user interface in the Three-Phase Flow, Phase Field interface in the CFD and Microfluidics modules is a so-called multiphysics interface. This means that, as a user, you have control of both the Cahn-Hilliard equations for the phase fields and the fluid flow equations. Although the settings are available in predefined formulations, an experienced user may also easily extend the equations to include other phenomena; for example, electric fields for studying electrocoalescence.

The image below shows the physics interfaces to the left, in the model tree, which are defined by the Three-Phase Flow, Phase Field interface. The included physics interfaces are the Laminar Flow and Ternary Phase Field interfaces. In addition, the Multiphysics node couples these two physics interfaces in its child node, the Three Phase Flow, Phase Field coupling node.

In the Ternary Phase Field interface, the Mixture node settings contain the input fields for surface tension, as shown below. In addition, the convection term is displayed, showing that the velocity field is obtained from the coupling formulated in the Three Phase Flow, Phase Field coupling node.

📷 The Mixture node contains the settings for the Cahn-Hilliard equations, which are the surface tension for the mixture and the coupling velocity field. The Equation section shows the domain equations.

The interaction with the container wall is defined by the settings for the Wetted Wall node, shown in the image below. Here, we find the input fields for the contact angles and a description of the notations used for these angles.

📷 Settings for the Wetted Wall boundary condition, which sets the contact angles for the different phase boundaries with the walls of the container.

The settings for the Three Phase Flow, Phase Field coupling node are shown below. Here, we can see that the coupled physics interfaces are the Laminar Flow and Ternary Phase Field interfaces. For an advanced user, the coupling node gives the possibility to couple the Ternary Phase Field interface to different fluid flow interfaces, which may be defined in different ways or in different domains.

📷 The settings for the Three Phase Flow, Phase Field coupling node.

Possible Future Extensions to the Functionality

The first version of the Three-Phase Flow, Phase Field interface is formulated for laminar flow problems. A natural extension is to also formulate this model for turbulent flow. We are planning to offer this capability in a future release of COMSOL Multiphysics. Another natural addition is to include solid particles in the flow. This can, in fact, already be done using the Particle Tracing for Fluid Flow interface. We also plan to provide related Application Library examples in future software versions.

Further Reading

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8 Uses of COMSOL Multiphysics® in the Biomedical Industry

Analyisis means that I should enter the equations?

Kaushik Shandilya When you use ChatGPT for creating an answer, can you please at least check its answer for plausibility? "Your" first four suggestions are all experimental and not helpful at all for the question asked which is purely theoretical. The last four ones are ultrageneric. That leaves the middle block in which the first thing, calculating the DOS is the only thing that needs to be done because the electronic band gap is the gap between occupied and unoccupied states. The optical band gap can be derived from the band structure, but unless someone is actually asking for that, it's pointless to calculate the absorption spectrum.

Actually helpful links are found here: https://www.researchgate.net/post/How-to-Calculate-band-structrueBand-gap-with-Comsol

Yes! Thanks!

Below is not clear to me:

what kind of a resistance you are looking for.

Crystal fiber photon!

Bonjour Nicolas, avez- vous réussi depuis à résoudre ce problème? Je vous remercie d'avance. Cordialement.

Dear Yavuz,

Thanks for the reply. Yes, I know that but I want to add grounding resistance. The ground surface under the magnetic insulation node only adds ground with V=0V to the surface.

The grounding resistance in the form to model a line to ground fault where the line touches the ground and the fault current experiences a grounding resistance Rg.

Hi. The calculations are probably correct as it is a simple case/ geometry. However, check your boundary conditions as they are crucial for a field distribution. You could try https://www.comsol.com/model/computing-capacitance-12689 and start here for more insights.

Simulation is done in 2D so that capacitor plates are assumed to be infinite in the surface normal (z) direction. Because of that, the result seems normal, but it can be verified by solving it as a boundary value problem, referring to Jackson Classical Electrodynamics chapter 2.

Hi Joseph!

No, not actually. i want to simulate a channel with 3 inlet (They are all liquid). i triied to use Two phase levelset ... but i could not. as in the level set it asks me like ꬾ = 1 or 0 for Fluid 1 and Fluid 2. But there is not any for fluid 3. I dont know how to introduce fluid 3. Can you help me with this please, its many days that i could not solve it .. :( Joseph Ackermann

It seems like you are encountering a specific problem with a COMSOL Multiphysics simulation related to a feature called "Stationary Solv." To help you troubleshoot and solve this issue, you can follow these general steps:

ü Ensure that your model geometry is correctly defined, and all boundaries and domains are properly assigned.

ü Double-check the material properties you have assigned to your domains and boundaries to make sure they are accurate.

ü Verify that the boundary conditions are correctly specified. Ensure that you have set up the appropriate physics boundary conditions for your simulation.

ü Pay attention to the mesh quality. Make sure the mesh is fine enough in areas where you expect significant variations in the solution.

ü Review your study settings, making sure that the "Stationary" solver is the correct choice for your simulation.

ü Check the solver settings, such as the solver type, tolerances, and convergence criteria. Adjust these settings as needed.

ü Ensure that you have provided reasonable initial values for your variables if required.

ü Make sure that you have imported or defined accurate material data for the components involved.

ü Examine any source terms or boundary conditions you have specified. They should reflect the physical behavior of your problem accurately.

ü Ensure that you have set the correct units and scaling for your simulation. Inconsistent units can lead to convergence issues.

ü Check the logs and error messages provided by COMSOL. They can often point you towards the source of the problem.

ü If the problem is particularly complex, consider simplifying your model to isolate the issue. Remove or disable parts of the model to see if that helps identify the problem.

ü COMSOL has an extensive knowledge base and user forums where you can search for solutions to common issues and ask for help from the community.

If you can't resolve the issue on your own, consider reaching out to COMSOL support for assistance. They can provide guidance on troubleshooting and resolving specific simulation problems.

Thank you Mehmet.

I don't know what DLD is, I haven't modeled microfluidics, I just have to study the process and see how to find the appropriate expressions that simulate it.

No