Unsteady boundary layer flow and heat transfer over a stretching sheet: heat flux case

Abstract

Unsteady two-dimensional boundary layer flow and heat transfer over a stretching flat plate in a viscous and incompressible fluid of uniform ambient temperature is investigated in this paper. It is assumed that the velocity of the stretching sheet and the heat flux from the surface of the plate vary inverse proportionally with time. Two equal and opposite forces are impulsively applied along the plate so that the plate is stretched keeping the origin fixed. Using appropriate similarity variables, the basic partial differential equations are transformed into a set of two ordinary differential equations. These equations are solved numerically for some values of the governing parameters using the Runge-Kutta method of fourth order. Flow and heat transfer characteristics are determined and represented in some tables and figures. It is found that the structure of the boundary layer depends on the ratio of the velocity of the potential flow near the stagnation point to that of the velocity of the stretching surface. In addition, it is shown that the heat transfer from the plate increases when the Prandtl number increases. The present results include also the steady situation as a special case considered by other authors. Comparison with known results is very good.

Keywords

• heat transfer
• unsteady flow
• stretching surface
• boundary layer
• stagnation point flow
• numerical results