Unsteady mixed convection flow in the stagnation region of a heated vertical plate due to impulsive motion Rajeswari Seshadri a , Nalini Sreeshylan b , G. Nath c, * a Fluid Dynamics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560 064, India b Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India c B-20, Mahadeo Nagar Colony, Sarang Talab, P.O. Tapovan Ashram, Via Saranath, Varanasi, UP 221 007, India Received 14 February 2000 Abstract The unsteady mixed convection in the stagnation flow on a heated vertical plate is studied where the unsteadiness is caused by the impulsive motion of the free stream velocity and by sudden increase in the surface temperature (heat flux). The short time as well as the long time solutions are included in the analysis. Both prescribed surface temperature and prescribed surface heat flux conditions are considered. The partial differential equations governing the flow and the heat transfer have been solved numerically using an implicit finite difference scheme. Also, the asymptotic behaviour of the solution for large value of the independent variable is examined when the flow becomes steady. There is a smooth transition from the small-time solution to the large-time solution. The surface shear stress and the heat transfer increase with time and buoyancy parameter. The heat transfer increases with the Prandtl number, but the surface shear stress decreases. Ó 2002 Elsevier Science Ltd. All rights reserved. 1. Introduction The combined forced and free convection flow (mixed convection flow) is encountered in many tech- nical and industrial applications which include solar central receivers exposed to wind currents, electronic devices cooled by fans, nuclear reactors cooled during emergency shutdown and heat exchangers placed in a low-velocity-environment. The two-dimensional stag- nation flow in a forced convection refers to the flow in the vicinity of a stagnation line that results from a two- dimensional flow impinging on a surface at right angles and flowing there after symmetrically about the stag- nation line. Hiemenz [1] studied the two-dimensional stagnation flow and Eckert [2] considered the corre- sponding heat transfer problem. The mixed convection in stagnation flow is important when the buoyancy forces due to the temperature difference between the surface and the free stream become large. Consequently, both the flow and thermal fields are significantly affected by the buoyancy forces. Ramachandran et al. [3] have investigated the mixed convection flow in the stagnation region of a vertical plate. The above studies deal with steady flows. In several problems the flow may be un- steady which might be caused by the change in the free stream velocity or in the surface temperature (surface heat flux) or in both. When there is an impulsive change in the velocity field, the inviscid flow is developed instantaneously, but the flow in the viscous layer near the wall is developed slowly which becomes fully developed steady flow after sometime. For small time the flow is dominated by the viscous forces and the unsteady acceleration, but for large time it is dominated by the viscous forces, the pressure gradient and the convective acceleration. For small time the flow is generally independent of the conditions far upstream and at the leading edge or at the stagnation point and for large time the flow depends on these conditions. The mathematical problem for short time is governed by the Rayleigh type of equation and for large time by the Falkner–Skan type of equation. The boundary layer flow development of a viscous fluid on a semi-infinite flat plate due to the impulsive International Journal of Heat and Mass Transfer 45 (2002) 1345–1352 www.elsevier.com/locate/ijhmt * Corresponding author. 0017-9310/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII:S0017-9310(01)00228-9