• FLOW AND HEAT TRANSFER AT A NONLINEARLY SHRINKING POROUS SHEET IN A THERMALLY STRATIFIED MEDIUM

Abstract

An analysis is carried out to study the laminar, boundary layer flow and heat transfer of a viscous fluid over shrinking permeable sheet with a power-law velocity in a thermally stratified environment. The sheet is assumed to shrink in its own plane with power-law velocity proportional to the distance from the stagnation point. The governing partial differential equations are first transformed into coupled non-linear ordinary differential equation using a similarity transformation. From here, we are able to compute several classes of exact solutions for certain values of the physical parameters. For other values of the physical parameters, the coupled non-linear boundary value problem is solved numerically by a second order finite difference scheme known as Keller Box method. Numerical computations are performed for two different cases namely, impermeable () and permeable () cases to get the effects of the thermally stratified environment on the velocity and temperature fields, at several physical situations. Numerical results for the skin-friction coefficient and the Nusselt number are tabulated for different values of the pertinent parameters. This is the first time such results for power-law nonlinearly shrinking sheets have been discussed in the context of a thermally stratified medium.