HPM Solution of Momentum Equation for Darcy-Brinkman Model in a Parallel Plates Channel Subjected to Lorentz Force

Authors: Asghar Shirazpour, Seyed Moein Rassoulinejad Mousavi, Hamid Reza Seyf

Abstract:

In this paper an analytical solution is presented for fully developed flow in a parallel plates channel under the action of Lorentz force, by use of Homotopy Perturbation Method (HPM). The analytical results are compared with exact solution and an excellent agreement has been observed between them for both Couette and Poiseuille flows. Moreover, the effects of key parameters have been studied on the dimensionless velocity profile.

Keywords: Lorentz Force, Porous Media, Homotopy Perturbation method

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1072856

References:

[1] Vafai, K., and Tien, C. L., 1980,"Boundary and Inertia Effects on Convection Mass Transfer In Porous Media," Int. J. Heat Mass Transfer, 25(8), pp. 1183-1190.
[2] Amiri, A. and Vafai, K., 1994, "Analysis of Dispersion Effects and Non-thermal Equilibrium, Non-Darcian, Variable Porosity Incompressible Flow Through Porous Media," int. J. Heat Mass Transfer, 37(6), pp. 939-954.
[3] Iyer, S. V. and Vafai, K., 1999, "Passive Heat Transfer Augmentation in a Cylindrical Annual Utilizing a Porous Perturbation," Numerical Heat Transfer, Part A, 36, pp.115-128.
[4] Alazmi, B. and Vafai, K., 1999, "Analysis of Variants within the Porous Media Transport Models," ASME J. Heat Transfer, 122, pp.303-326.
[5] Kuznestov, A. V. and Xiong, M., 2000, "Numerical Simulation of the Effect of Thermal Dispersion on Forced Convection in a Circular Duct Partly Filled With a Brinkman-Forchheimer Porous Medium," Int. J. Numerical Methods for Heat & Fluid Flow, 10(5), pp.488-501.
[6] Kuznetsov, A. V., Raleigh, 2000, "Investigation of the Effect of Transverse Thermal Dispersion on Forced Convection in Porous Media," Acta Mechanica, 145, pp. 35-43.
[7] Seyf, H.R., and Layeghi M., 2010, Numerical Analysis of Convective Heat Transfer From an Elliptic Pin Fin Heat Sink With and Without Metal Foam Insert,ASME Journal of Heat Transfer, 132(7), pp. 071401-071410.
[8] Chen, W., and Liu, W., 2004, Numerical analysis of heat transfer in a composite wall solar-collector system with a porous absorber, Applied Energy, 78(2), pp. 137-149.
[9] Kaviany, M., 1985, Laminar flow through a porous channel bounded by isothermal parallel plates,Int. J. Heat Mass Transfer ,28(4) , pp. 851-858.
[10] Vafai, K., Kim, S., 1989, Forced convection in a channel filled with porous medium: an exact solution, ASME J. Heat Transfer, 111 (4), pp. 1103-1106.
[11] Amiri, A., Vafai, K., 1994, Analysis of dispersion effects and nonthermal equilibrium, non-Darcian, variable porosity incompressible flow through porous media, Int. J. Heat Mass Transfer, 37 (6) , pp. 939-954.
[12] Hung, Y.M., and Tso, C.P., 2009, Effects of viscous dissipation on fully developed forced convection in porous media, International Communications in Heat and Mass Transfer, 36(6,), pp. 597-603.
[13] Nield, D. A., Junqueira, S. L. M, Lage, J. L., 1996, Forced convection in a fluid-saturated porous-medium channel with isothermal or isoflux boundaries, J. Fluid Mech, 322, pp.201-214.
[14] Haji-Sheikh, A., Vafai, K., 2004, Analysis of flow and heat transfer in porous media Imbedded inside various-shaped ducts,Int. J. Heat and Mass Transfer, 47, pp. 1889-1905.
[15] Gailitis,A., Lielausis,O. 1961 "On a possibility to reduce the hydrodynamic resistance of a plate in aelectro-lyte", Appl.Magnetohydrodyn, 12,143-146.
[16] Pantokratoras,A. 2007"Some new parallel flows in weakly conducting fluids with an exponentially decaying Lorentz,force", Math.Probl.Eng, Article ID87814.
[17] Pantokratoras A. and Fang T., 2010," Flow of a Weakly Conducting Fluid in a Channel Filled with a Porous Medium "83, pp.667-676.
[18] Magyari E, 2010, Comment on "Flow of a Weakly Conducting Fluid in a Channel Filled with a Porous Medium by A.Pantokratoras and T.Fang, Transport in Porous Media, 83, pp.677-680.
[19] He. J.H., 1999, Homotopy perturbation technique, Comput.Meth.Appl.Mech.Eng.178 (3-4) 257-262.
[20] He, J.H., 2003, Homotopy perturbation method: a new nonlinear analytical technique, Appl.Math.Comput, 135, pp.73-79.
[21] Dehghan M., and Shakeri F., 2008, Use of He's Homotopy Perturbation Method for Solving a Partial Differential Equation Arising in Modeling of Flow in Porous Media," Journal of Porous Media, 11, pp. 765-778.
[22] D.D.,Ganji and sadighi Application of homotopy perturbation and variational iteration Methods to nonlinear heattransfer and porous media equations,2008,j.computional and applied mathematics,vol 207,pp.24-34.
[23] Biazar J., Ayati Z., and Ebrahimi H., 2009, "Homotopy Perturbation Method for General Form of Porous Medium Equation," Journal of Porous Media, 12, pp. 1121-1127.
[24] Rafei M., Vaseghi J., and Ganji D., 2007, "Application of Homotopy-Perturbation Method for Systems of Nonlinear Momentum and Heat Transfer Equations," Heat Transfer Research, 38, pp. 361-379.
[25] Jafari H., Zabihi M., and Saidy M., 2008, "Application of Homotopy Perturbation Method for Solving Gas Dynamics Equation," Applied Mathematical Sciences, 2, pp.2393-2396.
[26] Ganj D., and Esmaeilpour M., 2008, "A Study on Generalized Couette Flow by He-s Methods and Comparison with the Numerical Solution," World Applied Sciences Journal, 4, pp.470-478.
[27] Siddiqui A.M., Mahmood R., Ghori Q.K., 2006, "Homotopy Perturbation Method for Thin Film Flow of Third Grade Fluid down an Inclined Plane," Chaos, Solitons and Fractals, 35, pp.140-147.