(A Peer Review Journal)
e–ISSN: 2408–5162; p–ISSN: 2048–5170


Pages: 320-333
Sanjib Sengupta*and Bishnu Ram Das

keywords: Newtonian fluid, mixed convection, heat transfer, heat absorption, Darcian


The present paper deals with the study of a mixed convective flow of Newtonian, incompressible, viscous fluid past a porous vertical plate embedded in heat absorbing Darcian porous media in presence of viscous dissipation and thermal radiation. A system of non-linear, coupled partial differential equations has been developed based on the basic conservation principles of physics such as conservation of mass, conservation of momentum and conservation of energy. Multi – parameter regular perturbation technique has been used to solve the governed system of equations subject to a set of favourable boundary conditions. The exact closed form of solutions for the velocity, temperature as well as skin – friction and Nusselt number have been obtained in terms of some governed physical parameters. Numerical simulations in terms of graphs and table have been made to investigate the effects of pertinent parameters. It is observed that, an increase in Reynolds number decreases the temperature as well as the velocity while the presence of Reynolds number increases the Nusselt number as well as skin- friction. Again the fluid velocity and temperature are found to increase due to increase in Eckert number but a reversed effect has observed in case of Nusselt number and skin – friction.


Abdollahzadeh J & Hyun PJ 2014. Thermal radiation Joule heating and viscous dissipation effects on MHD forced convection flow with uniform surface temperature. Open J. of Fluid Dynamics, 4: 125-132.; Ahmed S, Muhammad A & Syed KS 2011. Effects of thermal radiation on MHD axisymmetric stagnation-point flow and heat transfer of a Micro polar fluid over a shrinking sheet. World Applied Sci. J., 15(6): 835-848.; Babu SM, Narayana S PV, Reddy ST & Reddy UD 2011. Radiation and chemical reaction effects on unsteady MHD convection flow past a vertical moving porous plate embedded in a porous medium with viscous dissipation. Advances in Applied Sci. Res., 2(5): 226-239.; Barletta A 1998. Laminar mixed convection with viscous dissipation in a vertical channel. Int. J. of heat and Mass Trans., 41:3501-3513.; Chen CH 1998. Mixed convection cooling of a heated, continuously stretching surfaces. Heat Mass Trans., 36: 79-86.; Christoph H & Johannes W 2014. Numerical investigation of heat transfer with thermal radiation in an enclosure in case of buoyancy driven flow. Smart Sci., 2(3): 116-125.; Das K 2014. Influence of chemical reaction and viscous dissipation on MHD mixed convection flow. J. Mechanical Sci. & Technology, 28(5): 1881-1885.; Devi Renuka RLV, Neeraja NA & Reddy B 2016. Effect of radiation on an unsteady MHD mixed convective flow past an accelerated vertical porous plate with suction and chemical reaction. Int. J. of Technical and Applications, 4(2):1-8.; Dawood HK, Mohammed HA, Sidik NA, Monogamy KM & Wahid MA 2015. Forced, natural and mixed-convection heat transfer and fluid flow in annulus: A review. Int. common in Heat and Mass trans., 62:45-57.; Elsayed MA, Elbashbeshy TG & Emam KMA 2012. Effects of thermal radiation and magnetic field on unsteady mixed convection flow and heat transfer over an exponentially stretching surface with suction in the presence of internal heat generation/absorption..J. Egyp. Maths. Society, 20(3): 215-222.; Fand RM & Brucker J 1983. A correlation for heat transfer by natural convection from horizontal cylinder that accounts for viscous dissipation, Int. J. of Heat and Mass Trans., 26:709-726.; Gebhart B 1962. Effect of viscous dissipation in natural convection. J. of Fluid Mechan., 14: 225-235.; Gireesha BJ, Chamkha AJ, Manjunatha S & Begewadi CS 2013. Mixed convective flow of a dusty fluid over a vertical stretching sheet with non-uniform heat source/sink and radiation. Int. J. Numerical Methods Heat Fluid Flow, 23(4): 598-612.; Hadhrami AK, Elliott L & Ingharm DB 2001. Combined free and forced convection in vertical channels of porous media. Transport Porous Med., 49: 265-289.; Hung YM & Tao CP 2009. Effects of viscous dissipation on fully developed forced convection in porous media. Int. Communications in Heat Mass Trans., 36(6): 597-603.; Khan S, Wahiduzzaman M & Islam S 2014. Heat generation effects on unsteady mixed convection flow from a vertical porous plate with induced magnetic field. 10th Int. Confe.on Mecha. Eng. ICME 2013, 90: 238-244.; Mahajan RL & Gebhart BB 1989. Viscous dissipation effects in buoyancy induced flows. Int. J. Heat Mass Trans., 32(7): 1380-1382.; Mahmud S & Fraser RA 2003. Mixed convection radiation interaction in a vertical porous channel.Entropy generation. Energy, 28: 1557-1577.; Manjunatha S & Gireesha BJ 2012. Effects of thermal radiation on boundary layer flow and heat transfer of dusty fluid over an unsteady stretching sheet. Int. J. of Eng. Sci. and Techno., 4(4): 36-48.; Nield DA, Kuznetsov AV & Xiong M 2003. Thermally developing forced convection in a porous medium: parallel plate channel with walls at uniform temperature with axial conduction and viscous dissipation effects. Int. J. Heat and Mass Trans., 46(4): 643-651. Ostrich S 1954. Combined natural and forced convection laminar flow and heat transfer of fluid with and without heat source in channels with linearly varying wall temperature NACA, TN, 3441.; Pal DR & Samad MA 2015. Combined effects of viscous dissipation and thermal radiation on non-Newtonian fluid along a surface with heat generation and uniform surface heat flux. Dhaka Univ. J. Sci., 63(2): 97-104.; Pantokratoras A 2005. Effects of viscous dissipation in natural convection along a heated vertical plate. Applied Mathematical Modeli., 29: 553-564.; Reddy GVR, Reddy BA & Reddy NB 2013. Thermal radiation and magnetic field effects on unsteady mixed convection flow and mass transfer over a porous stretching surface with heat generation. Int. J. of Appli. Mecha. & Eng., 18(4): 1151-1164 .; Sahoo S, Kuchhal A, Vineeth S & Chesham V 2016. Thermal radiation heat transfer model and its application for automobile exhaust components. SAE Technical Paper, DOI: 10, 4271/2016-28-0051.; Sengupta S 2015. Free convective chemically absorption fluid past an impulsively accelerated plate with thermal radiation with variable wall temperature and concentrations. Applications and Appl. Maths., 10(1): 328 -348.; Shit GC & Halder R 2011. Effects of thermal radiation and MHD viscous fluid flow and heat transfer over non-linear shrinking porous sheet. Appl. Maths. Mecha. Eng. Ed., 32(6): 677-688.