Magnetic Field Influence on Thermophoretic Micropolar Fluid Flow over an Inclined Permeable Surface: A Numerical Study

Document Type : Research Paper


1 Department of Mathematics, Annamacharya Institute of Technology and sciences, Rajmpeta, Kadapa-516126, A.P., India

2 Department of Mathematics, Annamacharya Institute of Technology and sciences, C. K. Dinne, Kadapa-516003, A.P., India

3 Department of Engineering Mathematics, College of Engineering, Koneru Lakshmaiah Education Foundation, Vaddeswaram, Andhra Pradesh – 522302, India

4 Department of Mathematics, Narasaraopeta Engineering College, Narasaraopet, 522601, Andhra Pradesh, India

5 Department of Engineering and Architecture, University of Parma, Parco Area delle Scienze 181/A, Parma 43124, Italy


The researchers have reported numerous numerical and analytical efforts in recent years to understand technological and industrial processes. Microelectronics, heat exchangers, solar systems, energy generators are just a few numbers of recent applications of heat and mass transfer flow. Two dimensional steady incompressible MHD flow of micropolar fluid over an inclined permeable surface with natural convection is investigated in this research work, with the contribution of thermal radiation under thermophoretic effects as a heating source. As a result of this infestation, mathematical model of the problem equations based on energy, momentum, angular momentum, mass, and concentration are developed. To convert the current problem into dimensionless ordinary differential equations, non-dimensional variables have been assigned. The evolved mathematical model is numerically solved aside utilizing Shooting technique along with 4th order R-K method solver in MATHEMATICA. The outcomes are displayed and analyzed through figures and tables. Finally, skin friction, Nusselt and Sherwood numbers are tabulated for distinct parameter-factors. To validate the accuracy of numerical method used in this problem, we compare the numerical results with available findings, and it is evident that the outcomes of current work are in good agreement with those reported in the literature. Improving the values of thermophoresis, radiation factors, and Schmidt number, declines the velocity. Higher values of radiation parameter, thermophoresis parameter, the microrotation increase near plane-surface and gradually diminishes far away from plane-surface. Profiles of temperature enhances with increasing the viscous dissipation parameter. Profiles of the concentration decreases by increasing the thermophoresis parameter and Schmidt number. Profiles of Skin friction and mass transfer rate decreases for magnetic field, thermal radiation and Schmidt number values.


Main Subjects

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[1] Eringen, A.C., Theory of micropolar fluids, Journal of Mathematics and Mechanics, 16(1), 1966, 1–18.
[2] Eringen, A.C., Theory of Thermomicrofluids, Journal of Mathematical Analysis and Applications, 38, 1972, 480-496.
[3] Kumar, K.A., Sugunamma, V., Sandeep, N., Mustafa, M., Simultaneous solutions for first order and second order slips on micropolar fluid flow across a convective surface in the presence of Lorentz force and variable heat source/sink, Scientific Reports, 9(1), 2019, 14706.
[4] Anantha Kumar, K., Sugunamma, V., Sandeep, N., Influence of viscous dissipation on MHD flow of micropolar fluid over a slendering stretching surface with modified heat flux model, Journal of Thermal Analysis and Calorimetry, 139, 2020, 3661-3674.
[5] Chiu, C.P., Chou, H.M., Free convection in the boundary layer flow of a micropolar fluid along a vertical wavy surface, Acta Mechanica, 101, 1993, 161–174.
[6] Hassanien, I.A., Gorla, R.S.R., Heat transfer to a micropolar fluid from a non-isothermal strething sheet with suction and blowing, Acta Mechanica, 84, 1990, 191–199.
[7] Gorla, R.S.R., Mixed convection boundary layer flow of a micropolar fluid on a horizontal plate, Acta Mechanica, 108, 1995, 101–109.
[8] Sharma, R.P., Shaw, S., MHD non-Newtonian fluid flow past a stretching sheet under the influence of non-linear radiation and viscous dissipation, Journal of Applied and Computational Mechanics, 8(3), 2022, 949-961.
[9] Dash, A.K., Mishra, S.R., Free convection of micropolar fluid over an infinite inclined ‎moving porous plate, Journal of Applied and Computational Mechanics, 8(4), 2022, 1154-1162.
[10] Ibrahim, S.M., Reddy, T.S., Reddy, N.B., Radiation and mass transfer effects on MHD free convective stream of micropolar fluid past a stretching surface embedded in a non-Darcian porous medium with heat generation, International Scholarly Research Notices, 2013, 2013, 1534750.
[11] Roja, P., Reddy, T., Ibrahim, S.M., Lorenzini, G., Che Sidik, N.A., The Effect of thermophoresis on MHD stream of a micropolar liquid through a porous medium with variable heat and mass flux and thermal radiation, CFD Letters, 14(5), 2022, 106-124.
[12] Harish, M., Ibrahim, S.M., Kumar, P.V., Lorenzini, G., A Study on Effects of Thermal Radiative Dissipative MHD Non-Newtonian Nanofluid above an Elongating Sheet in Porous Medium, Journal of Applied and Computational Mechanics, 9(4), 2023, 945-954.
[13] Krishna, M.V., Anand, P.V.S., Chamkha, A.J., Heat and mass transfer on free convective flow of amicropolar fluid through a porous surface with inclined magnetic field and hall effects, Special Topics & Reviews in Porous Media: An International Journal, 10(3), 2019, 1-10.
[14] Abbas, N., Nadeem, S., Khan, M.N., Numerical analysis of unsteady magnetized micropolar fluid flow over a curved surface, Journal of Thermal Analysis and Calorimetry, 147(11), 2022, 6449-6459.
[15] El-Arabawy, H.A., Effect of suction/injection on the flow of a micropolar fluid past a continuously moving plate in the presence of radiation, International Journal of Heat and Mass Transfer, 46(8), 2003, 1471-1477.
[16] Hossain, M.A., Alim, M.A., Natural convection-radiation interaction on boundary layer flow along a thin vertical cylinder, Journal of Heat and Mass Transfer, 32, 1997, 515-520.
[17] Hossain, M.A., Takhar, H.S., Thermal radiation effects on natural convection flow over an isothermal horizontal plate, Heat and Mass Transfer, 35, 1999, 321-326.
[18] Abd El-Naby, M.A., Elsayed, M.E.E., Nader, Y.A., Finite difference solution of radiation effects on MHD unsteady free convection flow over vertical plate with variable surface temperature, Journal of Applied Mathematics, 21(1), 2003, 65-86.
[19] Hossain, M.A., Viscous and Joule heating effects on MHD free convection flow with variable surface temperature, International Journal of Heat and Mass Transfer, 1992, 35, 3485-3487.
[20] Mamun, A.A., Chowdhury, Z.R., Azim, M.A., Molla, M.M., MHD-conjugate heat transfer analysis for a vertical flat plate in presence of viscous dissipation and heat generation, International Journal Communications in Heat and Mass Transfer, 35, 2008, 1275-1280.
[21] Palani, G., Kwang, Y.K., Joule heating and viscous dissipation effects on MHD flow past a semi-infinite inclined plate with variable surface temperature, Journal of Engineering Thermophysics, 20, 2011, 501-517.
[22] Rashad, A.M., Abbasbandy, S., Chamkha, A.J., Mixed convection flow of a micropolar fluid over a continuously moving vertical surface immersed in a thermally and solutally stratified medium with chemical reaction, Journal of the Taiwan Institute of Chemical Engineers, 45(5), 2014, 2163-2169.
[23] Eid, M.R., Jamshed, W., Goud, B.S., Ibrahim, R.W., El Din, S.M., Abd-Elmonem, A., Abdalla, N.S.E., Mathematical analysis for energy transfer of micropolar magnetic viscous nanofluid flow on permeable inclined surface and Dufour impact, Case Studies in Thermal Engineering, 49, 2023, 103296.
[24] Rafique, K., Alotaibi, H., Nofal, T.A., Anwar, M.I., Misiran, M., Khan, I., Numerical solutions of micropolar nanofluid over an inclined surface using Keller box analysis, Journal of Mathematics, 2020, 2020, 1-13.
[25] Goren, S.L., Thermophoresis of aerosol particles in laminar boundary layer on flat plate, Journal of Colloid and Interface Science, 61(1), 1977, 77–85.
[26] Goldsmith, P., May, F.G., Diffusiophoresis and Thermophoresis in Water Vapour Systems: Aerosol Science, Academic Press, London, UK, 1966.
[27] Abbas, A., Ashraf, M., Chamkha, A.J., Combined effects of thermal radiation and thermophoretic motion on mixed convection boundary layer flow, Alexandria Engineering Journal, 60(3), 2021, 3243-3252.
[28] Das, K., Jana, S., Kundu, P.K., Thermophoretic MHD slip flow over a permeable surface with variable fluid properties, Alexandria Engineering Journal, 54(1), 2015, 35-44.
[29] Swain, K., Mahanthesh, B., Mebarek‐Oudina, F., Heat transport and stagnation‐point flow of magnetized nanoliquid with variable thermal conductivity, Brownian moment, and thermophoresis aspects, Heat Transfer, 50(1), 2021, 754-767.
[30] Hazarika, S., Ahmed, S., Impact of thermal conductivity on a horizontal absorbent isothermal wall in a porous medium with heat source and thermophoretic forces: Application of suction/blowing, Heat Transfer, 51(8), 2022, 7972-7989.
[31] Nabwey, H.A., Rashad, A.M., Mahdy, A.E.N., Shaaban, S.M., Thermal conductivity and thermophoretic impacts of micropolar fluid flow by a horizontal absorbent isothermal porous wall with heat source/sink, Mathematics, 10(9), 2022, 1514.
[32] Irfan, M., Farooq, M.A., Thermophoretic MHD free stream flow with variable internal heat generation/absorption and variable liquid characteristics in a permeable medium over a radiative exponentially stretching sheet, Journal of Materials Research and Technology, 9(3), 2020, 4855-4866.
[33] Yu, Y., Madhukesh, J.K., Khan, U., Zaib, A., Abdel-Aty, A.H., Yahia, I.S., Alqahtani, M.S., Wang, F., Galal, A.M., Nanoparticle aggregation and thermophoretic particle deposition process in the flow of micropolar nanofluid over a stretching sheet, Nanomaterials, 12(6), 2022, 977.
[34] Pakravan, H.A., Yaghoubi, M., Combined thermophoresis, Brownian motion and Dufour effects on natural convection of nanofluids, International Journal of Thermal Sciences, 50(3), 2011, 394-402.
[35] Bahiraei, M., Hosseinalipour, S.M., Particle migration in nanofluids considering thermophoresis and its effect on convective heat transfer, Thermochimica Acta, 574, 2013, 47-54.
[36] Anbuchezhian, N., Srinivasan, K., Chandrasekaran, K., Kandasamy, R., Thermophoresis and Brownian motion effects on boundary layer flow of nanofluid in presence of thermal stratification due to solar energy, Applied Mathematics and Mechanics, 33, 2012, 765-780.
[37] Batchelor, G.K., Shen, C., Thermophoretic deposition of particles in gas flowing over cold surfaces, Journal of Colloid and Interface Science, 107(1), 1985, 21-37.
[38] Talbot, L., Cheng, R.K., Schefer, A.W., Wills, D.R., Thermophoresis of particles in a heated boundary layer, Journal of Fluid Mechanics, 101, 1980, 737-758.
[39] Mills, A.F., Hang, X., Ayazi, F., The effect of wall suction and thermophoresis on aerosol-particle deposition from a laminar boundary layer on a flat plate, International Journal of Heat and Mass Transfer, 27, 1984, 1110–1114.
[40] Jalili, B., Ganji, A.M., Shateri, A., Jalili, P., Ganji, D.D., Thermal analysis of Non-Newtonian visco-inelastic fluid MHD flow between rotating disks, Case Studies in Thermal Engineering, 49, 2023, 1-17.
[41] Jalili, P., Azar, A.A., Jalili, B., Ganji, D.D., The HAN method for a thermal analysis of forced non-Newtonian MHD Reiner-Rivlin viscoelastic fluid motion between two disks, Heliyon, 9(6), 2023, 1-18.
[42] Jalili, P., Azar, A.A., Jalili, B., Ganji, D.D., Study of nonlinear radiative heat transfer with magnetic field for non-Newtonian Casson fluid flow in a porous medium, Results in Physics, 48, 2023, 1-27.
[43] Dogonchi, A.S., Bondareva, N.S., Sheremet, M.A., El-Sapa, S., Chamkha, A.J., Shah, N.A., Entropy generation and heat transfer performance analysis of a non-Newtonian NEPCM in an inclined chamber with complicated heater inside, Journal of Energy Storage, 72, 2023, 108745.
[44] Dogonchi, A.S., Karimi, N., Hu, G.J., Chamkha, A.J., Elmasry, Y., Thermo-economic and entropy generation analyses of magnetic natural convective flow in a nanofluid-filled annular enclosure fitted with fins, Sustainable Energy Technologies and Assessments, 46, 2021, 101274.
[45] Dogonchi, A.S., Waqas, M., Afshar, S.R., Seyyedi, S.M., Hashemi-Tilehnoee, M., Chamkha, A.J., Ganji, D.D., Investigation of magneto-hydrodynamic fluid squeezed between two parallel disks by considering Joule heating, thermal radiation, and adding different nanoparticles, International Journal of Numerical Methods for Heat & Fluid Flow, 30(2), 2020, 659-680. 
[46] Mondal, H., Unsteady MHD micropolar fluid in a stretching sheet over an inclined plate with the effect of non-linear thermal radiation and Soret-Dufour, Journal of Thermal Engineering, 5(6), 2019, 205-213.
[47] Brewster, M.Q., Thermal radiative Transfer and properties, John Wiley and Sons, New York, 1992.