[01] Oyelami Funmilayo Helen, Department of Mathematical and Physical Sciences, Afe Babalola University, Ado Ekiti, Nigeria.

This work examines the heat transfer analysis of a convective flow over a vertical plate under the combined influence of viscous dissipation and thermal radiation in the presence of heat source/sink with the plate being subjected to a variable surface temperature. The governing boundary layer equations are formulated, simplified and non-dimensionalised. The dimensionless equations were solved by employing Crank Nicolson’s implicit finite difference scheme. The effects of dimensionless numbers affecting the flow are shown graphically on the dimensionless temperature profile. Increasing thermal radiation reduces temperature profile while there was an increase on temperature profile with an increase in dissipation parameter.

Heat Transfer, Convective Flow, Radiation, Viscous Dissipation, Heat Source, Magnetic Field

[01] B. Gebhart. (1962). Effects of viscous dissipatton in natural convection, J. Fluid Mech. 14, 225-5235. [02] B. Gebhatt and J. Mollendorf. (1969). Viscous dissipation in external natural convection flows. J. FIuid Mech. 38. 97-108. [03] V. M. Soundalgekar, H. S. Takhar, and N. V. Vighnesam (1960). The combined free and forced convection flow past a semi-infinite plate with variable surface temperature, Nuclear Eng. Design, 110, 95–98. [04] B. C. Sakiadis. (1961). Boundary layer behavior on continuous solid surface, II. The boundary layer on a continuous flat surface, A. I. Ch. E. J., 7, 221–225. [05] E. M. Sparrow and R. D. Cess. (1961). Effect of magnetic field on free convection heat transfer, Int. J. Heat Mass Transf., 3, 267–274. [06] M. Romig (1964). The influence of electric and magnetic field on heat transfer to electrically conducting fluids, Adv. Heat Transf., 1, 268–352. [07] K. Vajravelu, A. Hdjinicolaou, (1993): Heat transfer in a viscous fluid over a streching sheet with viscous dissipation and internal heat generation, Int. Comm. Heat Mass Transfer 20, 417-430. [08] R. Muthucumaraswamy, P. Ganesan, (2001), Effect of the chemical reaction and injection on flow characteristics in an unsteady motion of an isothermal plate, J. Appl. Mech. Tech. Phys. 42, 65-667. [09] Gnaneshwara Reddy M and Bhaskar Reddy N (2009): Radiation and mass transfer effect on an unsteady MHD free convection flow past a heated vertical porous plate with viscous dissipation, Int. J. of Appl. Math and Mech, 6 (6): 96-110. [10] Alam M. S, Rahman M. M and sattar M. A, (2009): Transient magnetohydrodynamic free convective heat and mass transfer flow with thermophoresis past a radiate inclined permeable plate in the presence of variable chemical reaction and temperature dependent viscosity, Nonlinear Analysis: Modelling and control (14): 3-20. [11] S. P. Anjali Devi and B. Ganga. (2010). Dissipation effect on MHD flow and heat transfer past a Porous surface with prescribed heat flux. Journal of Applied flux Mechanics, 3, 1-6. [12] H. Kumar. (2009). Radiative Heat transfer with hydromagnetic flow and viscous dissipation over a stretching surface in the presence of variable heat flux. Thermal Science, 13 (2), 163-169. [13] R. J. Gribben. (1965). The magnetohydrodynamic boundary layer in the presence of a pressure Gradient. Proc. Royal. Soc London 287, pp. 123-141. [14] K. A. Helmy. (1998). MHD unsteady free convection flow past a vertical porous plate. ZAMM 78, pp. 255-270. [15] M. A. Hossain, H. S. Takhar. (1996). Radiation effect on mixed convection along a vertical plate with uniform surface temperature, Heat Mass Transfer 31, 243–248. [16] A. J. Chamkha, H. S. Takhar and V. M. Soundalgekar. (2001) Radiation effects on free convection flow past a semi-infinite vertical plate with mass transfer, Chem. Engrg. J. 84, 335–342. [17] M. H. Mansour. (1990). Radiative and free convection effects on the oscillatory flow past a vertical plate, Astrophys. Space Sci. 166, 26–75. [18] A. Raptis and C. Perdikis. (1999). Radiation and free convection flow past a moving plate, Appl. Mech. Eng. 4, 817–821. [19] G. A. Gregantopoulos, J. Koullias, C. L. Goudas and C. Courogenis. (1981). Free convection and mass transfer effects on the hydromagnetic oscillatory flow past an infinite vertical porous plate. Astrophysics and space science 74, pp. 357-389. [20] Oyelami F. H., Dada M. S., (2018). Unsteady magnetohydrodynamic flow of some non-Newtonian fluids with slip in a porous channel, International Journal of Heat and Technology, vol. 36, no. 2, pp. 709-713. [21] Carnahan B., Luther H. A., and Willkes J. O (1969). Applied Numerical Method. John Wiley and Sons, New York, USA.