Abstract
This paper analyzes the laminar, incompressible mixed convective transport inside vertical channel in an electrically conducting fluid saturated porous medium. In addition, this model incorporates the combined effects of Soret, Hall current and Joule heating. The nonlinear governing equations and their related boundary conditions are initially cast into a dimensionless form using suitable similarity transformations and hence solved using Adomian Decomposition Method (ADM). In order to explore the influence of various parameters on fluid flow properties, quantitative analysis is exhibited graphically and shown in tabular form.
References
[1] Ingham D.B., Pop I., Cheng P., Combined free and forced convection porous mediumbetween two vertical walls with viscous dissipation, Transp. Porous Media, 1990, 5, 381-398. 10.1007/BF01141992Search in Google Scholar
[2] Paul T., Jha B.K., Singh A.K., Free-convection between vertical walls partially filled with porous medium, Heat Mass Transfer, 1998, 33, 515-519. 10.1007/s002310050223Search in Google Scholar
[3] Umavathi J.C., Free convection of composite porous medium in a vertical channel, Heat Transfer Asian Res., 2011, 40(4), 308- 329. 10.1002/htj.20340Search in Google Scholar
[4] Biswas N., Mahapatra P.S., Manna N.K., Mixed convection heat transfer in a grooved channel with injection, Numerical Heat Transfer, Part A: Applications, 2015, 68(6), 663-685. 10.1080/10407782.2014.994411Search in Google Scholar
[5] Afify A.A., Similarity solution in MHD: Effects of thermal diffusion and diffusion thermo on free convective heat and mass transfer over a stretching surface considering suction or injection, Commun. Nonlinear Sci. Numer. Simul., 2009, 14, 2202- 2214. 10.1016/j.cnsns.2008.07.001Search in Google Scholar
[6] Srinivasacharya D., Kaladhar K., Soret and Dufour effects on free convection flow of a couple stress fluid in a vertical channel with chemical reaction, Chem. Ind. Chem. Eng. Q., 2013, 19(1), 45-55. 10.2298/CICEQ111231041SSearch in Google Scholar
[7] Srinivasacharya D., Pranitha J., Ramreddy Ch., Postelnicu A., Soret and Dufour effects on non-Darcy free convection in a power-law fluid in the presence of a magnetic field and strati- fication, Heat Transfer Asian Res., 2014, 43, 592-606. 10.1002/htj.21098Search in Google Scholar
[8] Tani I., Steady flow of conducting fluids in channels under transverse magnetic fields with consideration of Hall effects, J. Aerosp. Sci., 1962, 29, 297-305. 10.2514/8.9412Search in Google Scholar
[9] Srinivasacharya D., Mekonnen Shiferaw., Hall and Ion-slip effects on the flowof micropolar fluid between parallel plates, Int. J. App. Mech. and Engg., 2008, 13(1), 251-262. Search in Google Scholar
[10] Srinivasacharya D., Mekonnen Shiferaw.,MHDflowof a micropolar fluid in a circular pipe with Hall effects, ANZIAM Journal., 2009, 51, 277- 285. 10.1017/S1446181110000039Search in Google Scholar
[11] Manglesh A., Gorla M.G., MHD free convection flow through porous medium in the presence of Hall current, radiation and thermal difusion, Indian J. Pure Appl. Math., 2013, 44(6), 743- 756. 10.1007/s13226-013-0040-9Search in Google Scholar
[12] Garg B.P., Singh K.D., Bansal A.K., Hall current effect on viscoelastic (Walter’s liquid model-B) MHD oscillatory convective channel flow through a porous medium with heat radiation, Kragujevac Journal of Science, 2014, 36, 19- 32. 10.5937/KgJSci1436019BSearch in Google Scholar
[13] Rahman M., Saidur R., Rahim N., Conjugated effect of joule heating andmagneto-hydrodynamic on double-diffusive mixed convection in a horizontal channel with an open cavity, Int. J. Heat Mass Transfer, 2011, 54(15-16), 3201- 3213. 10.1016/j.ijheatmasstransfer.2011.04.010Search in Google Scholar
[14] Chen C.H., Combined effects of Joule heating and viscous dissipation on magnetohydrodynamic flow past a permeable, stretching surfacewith free convection and radiative heat transfer, J. Heat Transfer, 2010, 132, 064503-1-5. 10.1115/1.4000946Search in Google Scholar
[15] Hossain M.A., Gorla R.S.R., Joule heating effect on magnetohydrodynamic mixed convection boundary layer flowwith variable electrical conductivity, Int. J. Numer. Methods Heat Fluid Flow, 2013, 23(2), 275-288. 10.1108/09615531311293461Search in Google Scholar
[16] Nandkeolyar R., Motsa S.S., Sibanda P., Viscous and Joule heating in the stagnation point nanofluid flow through a stretching sheet with homogenous- heterogeneous reactions and nonlinear convection, Journal of Nanotechnology in Engineering and Medicine, 2013, 4, 0410011-1-9. 10.1115/1.4027435Search in Google Scholar
[17] Zhang J.K., Li B.W., Chen Y.Y., The Joule heating effects on natural convection of participating magnetohydrody- namics under different levels of thermal radiation in a cavity, J. Heat Transfer, 2015, 137, 052502-1-10. 10.1115/1.4029681Search in Google Scholar
[18] Srinivasacharya D., Mekonnen Shiferaw.,MHDflowof a micropolar fluid in a rectangular duct with Hall and Ion-slip effects, J. Braz. Soc. Mech. Sci. Eng., 2008b, 30(4), 313-318. 10.1590/S1678-58782008000400007Search in Google Scholar
[19] Eslami M., New Homotopy Perturbation Method for a Special Kind of Volterra Integral Equations in Two-Dimensional Space, Comput. Math. Model., 2014, 25(1), 135-148. 10.1007/s10598-013-9214-xSearch in Google Scholar
[20] Mallick A., Ghosal S., Sarkar P.K., Ranjan R., Homotopy Perturbation Method for Thermal Stresses in an Annular Fin with Variable Thermal Conductivity, J. Therm. Stresses., 2015, 38(1), 110- 132. 10.1080/01495739.2014.981120Search in Google Scholar
[21] Hetmaniok E., Nowak I., Slota D., Witula R., Convergence and error estimation of homotopy analysis method for some type of nonlinear and linear integral equations, Journal of Numerical Mathematics, 2015, 23(4), 331-344. 10.1515/jnma-2015-0022Search in Google Scholar
[22] Odibat Z., Sami Bataineh A., An adaptation of homotopy analysis method for reliable treatment of strongly nonlinear problems: construction of homotopy polynomials, Mathematical Methods in the Applied Sciences, 2015, 38(5), 991- 1000. 10.1002/mma.3136Search in Google Scholar
[23] Bellman R.E., Adomian G., Partial Differential Equations: New Methods for their Treatment and Solution, D. Reidel, Dordrech, 1985. 10.1007/978-94-009-5209-6Search in Google Scholar
[24] Adomian G., A review of the decomposition method in applied mathematics, Journal of Mathematical Analysis and Applications, 1988, 135(2), 501-544. 10.1016/0022-247X(88)90170-9Search in Google Scholar
[25] Wazwaz A.-M., Rach R., Duan J.-S., The modified Adomian decomposition method and the noise terms phenomenon for solving nonlinear weakly-singular Volterra and Fredholm integral equations, Open Engineering, 2013, 3(4), 669-678. 10.2478/s13531-013-0123-8Search in Google Scholar
[26] Chen F., Liu Q., Modified asymptotic Adomian decomposition method for solving Boussinesq equation of groundwater flow. Appl. Math. Mech., 2014, 35(4), 481-488. 10.1007/s10483-014-1806-7Search in Google Scholar
[27] Bougoffa L., Rach R., Wazwaz A.-M., Duan J.-S., On the Adomian decomposition method for solving the Stefan problem. Int. J. Numer. Methods Heat Fluid Flow., 2015, 25(4), 912-928. 10.1108/HFF-05-2014-0159Search in Google Scholar
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