**ABSTRACT**

This paper is focused on the study of effects of thermal radiation on the natural convective heat and mass transfer of a viscous, incompressible, gray absorbing-emitting fluid flowing past an impulsively started moving vertical plate with viscous dissipation. The governing boundary-layer equations are formulated in an (x, y, t) coordinate system with appropriate boundary conditions. The Rosseland diffusion approximation is used to analyze the radiative heat flux in the energy equation, which is appropriate for non-scattering media. The dimensionless governing equations are solved using an implicit finite-difference method of Crank-Nicolson type. The influence of Prandtl number, radiation-conduction parameter, thermal Grashof number, species Grashof number, Schmidt number, and Eckert number on the dimensionless velocity, temperature and concentration are studied. In addition the variation of the local and average skin-friction, Nusselt number, and Sherwood number for selected thermophysical parameters are computed and shown graphically. Increasing the Eckert number is seen to accelerate the flow. Thermal radiation reduces both velocity and temperature in the boundary layer. This model finds applications in solar energy collection systems, geophysics and astrophysics, aero space and also in the design of high temperature chemical process systems.

**KEYWORDS**

PAPER SUBMITTED: 2008-06-06

PAPER REVISED: 2009-02-17

PAPER ACCEPTED: 2009-02-27

**THERMAL SCIENCE** YEAR

**2009**, VOLUME

**13**, ISSUE

**2**, PAGES [171 - 181]

- Stokes, G. G., On the Effect of Internal Friction of Fluids on the Motion of Pendulums, Camb. Phil. Trans IX (1851), 2, pp. 8-106
- Stewartson, K., On the Impulsive Motion of a Flat Plate in a Viscous Fluid, Quarterly Journal of Mechanics and Applied Mathematics, IV (1951), 2, pp.182-198
- Hall, M. G., The Boundary Layer over an Impulsively Started Flat Plate, Proc. Roy. Soc. A, 310 (1969), 1502, pp .401-414
- Soundalgekar, V. M., Free Convection Effects on the Stokes Problem for Infinite Vertical Plate, ASME, J. Heat Transfer, 99c (1977), 6, pp. 499-501
- Muthucumaraswamy, R., Natural Convection on Flow Past an Impulsively Started Vertical Plate with Variable Surface Heat Flux, Far East Journal of Applied Mathematics, 14 (2004), 1, pp. 99-109
- Das, U. N., Deka, R. K., Soundalgekar, V. M., Effects of Mass Transfer on Flow Past an Impulsively Started Infinite Vertical Plate with Constant Heat Flux and Chemical Reaction, Forschung im Ingenieurwesen, 60 (1994), 10, pp. 284-287
- Muthucumaraswamy, R., Ganesan, P., Unsteady Flow Past an Impulsively Started Vertical Plate with Heat and Mass Transfer, Heat and Mass Transfer, 14 (1998), 2, pp. 187-193
- Huges, W. F., Young, F. J., The Electro-Magneto-Dynamics of Fluids, John Wiley & Sons, New York, USA, 1966
- Sacheti, N. C., Chandran, P., Singh, A. K., An Exact Solution for Unsteady MHD Free Convection Flow with Constant Heat Flux, Int. Comm, Heat Mass Transfer, 21 (1994), 1, pp. 131-142
- Shankar, B., Kishan, N., The Effect of Mass Transfer on the MHD Flow Past an Impulsively Started Inifinite Vertical Plate with Variable Temperature or Constant Heat Flux, Journal of Energy, Heat and Mass Transfer, 19 (1997), 3, pp. 273-278
- Chang, L. C., Yang, K. T., Lloyd, J. R., Radiation Natural Convection Interactions in Two Dimensional Complex Enclousers, ASME J. Heat Transfer, 105 (1983), 1, pp. 89-95
- Hossain, M. A., Takhar, H. S., Radiation Effects on Mixed Convection along a Vertical Plate with Uniform Surface Temperature, J. Heat and Mass Transfer, 31 (1996), 4, pp. 243-248
- Mosa, M. F., Radiative Heat Transfer in Horizontal MHD Channel Flow with Buoyancy Effects and an Axial Temperature Gradient, Ph. D. thesis, Mathematics Department, Bradford University, Bradford, U. K., 1979
- Takhar, H. S., Gorla, R. S. R., Soundalgekar, V. M., Radiation Effects on MHD Free Convection Flow of a Radiating Fluid Past a Semi-Infinite Vertical Plate, Int. J. Numerical Methods for Heat and Fluid Flow, 6 (1996), 1, pp.77-83
- Abd El-Naby, M. A., et al., Finite Difference Solution of Radiation Effects on MHD Free Convection Flow over a Vertical Plate with Variable Surface Temperature, J. Appl. Math., 2 (2003), 2, pp. 65-86
- Ramachandra Prasad, V., Bhaskar Reddy, N., Muthucumaraswamy, R., Radiation and Mass Transfer Effects on Two-Dimensional Flow Past an Impulsively Started InfiniteVertical Plate, Int. J. Thermal Sciences, 46 (2007), 12, pp. 1251-1258
- Mahajan, R. L, Gebhart, B. B., Viscous Dissipation Effects in Buoyancy-Induced Flows, Int. J. Heat Mass Transfer, 32 (1989), 7, pp. 1380-1382
- Israel-Cookey, C., Ogulu, A., Omubo-Pepple, V. M., Influence of Viscous Dissipation on Unsteady MHD Free Convection Flow Past an Infinite Vertical Plate in Porous Medium with Time-Dependent Suction, Int. J. Heat Mass Transfer, 46 (2003), 13, pp. 2305-2311
- Soundalgekar, V. M., Hiremath, S. V., Finite Difference Analysis of Mass Transfer Effects on Flow Past an Impulsively Started Infinite Isothermal Vertical Plate in Dissipative Fluid, Astro Physics and Space Science, 95 (1983), 2, pp.163-173
- Zueco Jordan, J., Network Simulation Method Applied to Radiation and Dissipation Effects on MHD Unsteady Free Convection over Vertical Porous Plate, Appl. Math., Modelling, 31 (2007), 20, pp. 2019-2033
- Brewster, M. Q., Thermal Radiative Transfer and Properties, John Wiley & Sons, New York, USA, 1992
- Carnahan, B., Luther, H. A., Willkes, J. O., Applied Numerical Methods, John Wiley & Sons, New York, USA, 1969