Effects of thermal radiation and slip on unsteady stagnation-point flow and heat transfer past a permeable shrinking sheet: A stability analysis

Abstract

This paper solves the problem of unsteady viscous fluid flow and heat transfer near the stagnation-point over a permeable stretching/shrinking surface. The effects of thermal radiation, velocity and thermal slip conditions are considered in this study. The problem modelled in the form of partial differential equations, subjected to the respective boundary conditions, and transformed to a system of nonlinear ordinary differential equations by applying the right similarity transformations. The MATLAB solver bvp4c function produces every numerical solution with the variation in pertinent parameters. Excellent agreement in comparison with previous literature is presented. The presences of dual solutions are noticeable when the permeable sheet is stretching or shrinking. Stability of the dual solutions is checked by obtaining the lowest eigenvalues of the governing linearized boundary value problem. The effects of the governing parameters on the reduced skin friction coefficients, reduced local Nusselt number, dimensionless velocity and temperature profiles are given in the form of graphs and discussed in detail. Results from the stability analysis proved that the upper branch solution is stable and physically realizable whereas the lower branch solution is unstable.