Chutia, M. (2018). Effect of Variable Thermal Conductivity and the Inclined Magnetic Field on MHD Plane Poiseuille Flow in a Porous Channel with Non-Uniform Plate Temperature. Journal of Computational & Applied Research in Mechanical Engineering (JCARME), 8(1), 75-84. doi: 10.22061/jcarme.2017.1620.1137

Muhim Chutia. "Effect of Variable Thermal Conductivity and the Inclined Magnetic Field on MHD Plane Poiseuille Flow in a Porous Channel with Non-Uniform Plate Temperature". Journal of Computational & Applied Research in Mechanical Engineering (JCARME), 8, 1, 2018, 75-84. doi: 10.22061/jcarme.2017.1620.1137

Chutia, M. (2018). 'Effect of Variable Thermal Conductivity and the Inclined Magnetic Field on MHD Plane Poiseuille Flow in a Porous Channel with Non-Uniform Plate Temperature', Journal of Computational & Applied Research in Mechanical Engineering (JCARME), 8(1), pp. 75-84. doi: 10.22061/jcarme.2017.1620.1137

Chutia, M. Effect of Variable Thermal Conductivity and the Inclined Magnetic Field on MHD Plane Poiseuille Flow in a Porous Channel with Non-Uniform Plate Temperature. Journal of Computational & Applied Research in Mechanical Engineering (JCARME), 2018; 8(1): 75-84. doi: 10.22061/jcarme.2017.1620.1137

Effect of Variable Thermal Conductivity and the Inclined Magnetic Field on MHD Plane Poiseuille Flow in a Porous Channel with Non-Uniform Plate Temperature

The aim of this paper is to investigate the effect of the variable thermal conductivity and the inclined uniform magnetic field on the plane Poiseuille flow of viscous incompressible electrically conducting fluid between two porous plates Joule heating in the presence of a constant pressure gradient through non-uniform plate temperature. It is assumed that the fluid injection occurs at lower plate and fluid suction occurs at upper plate. The governing equations of momentum and energy are transformed into coupled and nonlinear ordinary differential equations using similarity transformation and then solved numerically using finite difference technique. Numerical values for the velocity and temperature have been iterated by Gauss Seidal iteration method in Matlab programming to a suitable number so that the convergent solutions of velocity and temperature are considered to be achieved. Numerical results for the dimensionless velocity and the temperature profiles for different governing parameters such as the Hartmann Number (M) angle of inclination of magnetic field (α), suction Reynolds number (Re) Prandtl Number (Pr), Eckert number (Ec) and variable thermal conductivity (ԑ) have been discussed in detail and presented through graphs.

[1] E. Palm, J. E. Weber and O. Kvernold, “On steady Convection in a Porous Medium”, Journal of Fluid Mechanics, Vol. 54, No. 1, pp. 153-161, (1972).

[2] J. L. Bansal and N. C. Jain, “Variable viscosity plane Poiseuille flow with unequal wall temperatures”. Indian Journal of Pure Applied Mathematics, Vol. 6, No. 7, pp. 800-808, (1975).

[3] Ali J. Chamkha, “Steady and transient magnetohydrodynamic flow and heat transfer in a porous medium channel”,. Fluid/Particle Separation Journal, Vol. 9, No. 2, pp. 129-135, (1996).

[4] M. Arunachalam and N. R. Rajappa, “Forced Convection in liquid metals with variable thermal conductivity and capacity”, Acta Mechanica, Vol. 31, No. 1-2, pp. 25-31, (1978).

[5] T. C. Chaim, “Heat transfer in a fluid with variable thermal conductivity over stretching sheet”, Acta Mechanica, Vol. 129, No. 1, pp. 63-72, (1998).

[6] R. Nasrin and M. A. Alim, “Combined Effects of Viscous Dissipation and Temperature Dependent Thermal Conductivity on MHD Free Convection Flow with Conduction and Joule Heating along a Vertical Flat Plate”, Journal of Naval Architecture and Marine Engineering, Vol. 6, No. 1, pp. 30-40, (2009).

[7] N. C. Mahanti and P. Gaur, “Effects of Varying Viscosity and Thermal Conductivity on Steady Free Convective Flow and Heat Transfer Along an Isothermal Vertical Plate in the Presence of Heat Sink”, Journal of Applied Fluid Mechanics, Vol. 2, No. 1, pp. 23-28, (2009).

[8] I. J. Uwanta and H. Usman, “Effect of Variable Thermal Conductivity on Heat and Mass Transfer Flow over a Vertical Channel with Magnetic Field Intensity Applied and Computational Mathematics”, Applied and Computational Mathematics, Vol. 3, No. 2, pp. 48-56, (2014).

[9] V. G. Gupta, A. Jain and A. K. Jha, “The Effect of Variable Thermal Conductivity and the Inclined Magnetic Field on MHD Plane Poiseuille Flow Past Non-Uniform Plate Temperature”, Global Journal of Science Frontier Research: F Mathematics and Decision Sciences, Vol. 15, No. 10, pp. 21-28, (2015).

[10] J. C. Umavathi, Ali J. Chamkha, A. Mateen and A. Al-Mudhaf, “Unsteady Oscillatory Flow and Heat Transfer in a Horizontal Composite Porous Medium Channel” Nonlinear Analysis: Modelling and Control, Vol. 14, No. 3, pp. 397-41, (2009).

[11] A. Kumar Jhankal and M. Kumar, “Magnetohydrodynamic (MHD) Plane Poiseuille Flow with Variable Viscosity and Unequal Wall Temperatures” Iranian Journal of Chemical Engineering, Vol. 11, No. 1, pp. 63-68, (2014).

[12] X. Yu, J. X. Qiu, Q. Qin and Z. F. Tian, “Numerical investigation of natural convection in a rectangular cavity under different directions of uniform magnetic field”, International Journal of Heat and Mass Transfer, Vol. 67, pp. 1131-1144, (2013).

[13] W. A. Manyange, D. W. Kiema and C. C. W. Iyaya, “Steady poiseuille flow between two infinite parallel porous plates in an inclined magnetic field”, International journal of pure and applied mathematics, Vol. 76, No. 5, pp. 661-668 (2012).

[14] C. Ceasar Muriuki , E. Mwenda and D. M. Theuri, “Investigation of MHD Flow and Heat Transfer of a Newtonian Fluid Passing through Parallel Porous Plates in Presence of an Inclined Magnetic Field” Australian Journal of Basic and Applied Sciences, Vol. 8, No. 10, pp. 121-128, (2014).

[15] D. R. Kuiry and S. Bahadur, “Effect of an Inclined Magnetic Field on Steady Poiseuilleflow between Two Parallel Porous Plates”, IOSR Journal of Mathematics, Vol. 10, No. 5, pp. 90-96, (2014).

[16] K. M. Joseph, P. Ayuba, L. N. Nyitor and S. M. Mohammed, “Effect of heat and mass transfer on unsteady MHD Poiseuille flow between two infinite parallel porous plates in an inclined magnetic field”, International Journal of Scientific Engineering and Applied Science,Vol. 1, No. 5, pp. 353-375, (2015).

[17] A. S. Idowu and J. O. Olabode, “Unsteady MHD Poiseuille Flow between Two Infinite Parallel Plates in an Inclined Magnetic Field with Heat Transfer”, IOSR Journal of Mathematics, Vol. 10, No. 3, pp. 47-53, (2014).

[18] K. M. Joseph, S. Daniel and G. M. Joseph, “Unsteady MHD Couette flow between Two Infinite Parallel Plates in an Inclined Magnetic Field with Heat transfer”, Inter. J. Math. Stat. Inv., Vol. 2, No. 3, pp. 103-110 (2014).

[19] Ali J. Chamkha, “Unsteady laminar hydromagnetic flow and heat transfer in porous channels with temperature-dependent properties”, International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 11, No. 5, pp. 430-448, (2001).

[20] A. S. Eegunjobi and O. D. Makinde, “Entropy Generation Analysis in a Variable Viscosity MHD Channel Flow with Permeable Walls and Convective Heating”, Mathematical Problems in Engineering, pp. 1-13, (2013).

[21] H. A. Attia, W. A. El-Meged, W. Abbas and M. A. M. Abdeen, “Unsteady flow in a porous medium between parallel plates in the presence of uniform suction and injection with heat transfer”, International

Journal of Civil Engineering, Vol. 12, No. 3, pp. 277-281, (2014).

[22] S. Das and R. N. Jana, “Effects of Hall currents on entropy generation in a porous channel with suction/injection”, International Journal of Energy &

Technology, Vol. 5, No. 25, pp. 1-11, (2013).

[23] S. Ganesh, S. Krishnambal, Unsteady MHD Stokes flow of viscous fluid between two parallel porous plates, Journal of Applied Sciences, Vol. 7, No. 3, pp. 374-379, (2007).

[25] K. S. Sai and B. Nageswara Rao, “Magnetohydrodynamic flow in a rectangular duct with suction and injection”, Acta Mechanica, Vol. 140, No. 1, pp. 57-64, (2000).

[26] S. Das, and R. N. Jana, “Entropy generation in MHD porous channel flow under constant pressure gradient.” Applied Mathematics and Physics, Vol.1, No. 3, pp. 78-89 (2013).

[27] H. Schlichting, Boundary Layer theory, McGraw - Hill Book Co, Inc., Network, (1960).

[28] J. H. Mathews and K. D. Fink, Numerical Methods using Matlab, PHI Learning Private Limited, New Delhi, (2009).

[29] M. J. Alkhawaja and M. Selmi, “Finite difference solutions of MFM square duct with heat transfer using Matlab Program”, Matlabmodeling programming and simulations, Sciyo, pp. 365-388, (2010).

[30] J. C. Umavathi and Ali J. Chamkha, “Steady natural convection flow in a vertical rectangular duct with isothermal wall boundary conditions”, International Journal of Energy & Technology, Vol. 5, pp. 1-14, (2013).