Stagnation-point flow and heat transfer over an exponentially shrinking/stretching sheet in porous medium with heat generation

This study seeks to examine the fluid flow at the stagnation point over an exponentially shrinking and stretching sheet in a porous medium.  This study also investigates the heat transfer rate in the presence of heat generation.  By using the appropriate similarity transformation, we obtained ordinary differential equations (ODEs) that are reduced from the governing system of partial differential equations (PDEs).  These resulting equations are subjected to new boundary conditions and solved numerically by using BVP4C in MATLAB software.  The effects of the parameters involved in this study are summarized and thoroughly discussed: the skin friction coefficient, local Nusselt number, velocity profile, and temperature profile obtained.  The analysis is done by using graphical and tabular data.  The observed parameters are the permeability parameter $K$ and the heat generation parameter $Q$ towards shrinking/stretching parameter $\lambda$.  It is found that a dual solution exists for $\lambda<0$ (shrinking case), whereas the solution is unique for $\lambda>0$ (stretching case).  The analysis reveals that with heat generation being increased, the skin friction coefficient is constant. However, it increases when permeability increases.  The local Nusselt number decreases with heat generation being increased. However, it increases when the permeability increases.