Closed form dual nature solutions of fluid flow and heat transfer over a stretching/shrinking sheet in a porous medium

The aim of this work is to investigate the dual nature solutions of the fluid flow due to stretching/shrinking permeable surface saturated in a porous medium. Heat transfer analysis has been carried out in the presence of convective boundary conditions. Compatible transform are utilized to rehabilitate the system of nonlinear partial differential equations into the nonlinear ordinary differential equations. Closed form dual solutions are obtained for each unknown velocity and temperature profiles in terms of Gamma functions. Graphical interpretation of the possible dual solutions of dimensionless velocity, temperature, skin-friction coefficient, local Nusselt number as well as for stream lines and isotherms are analyzed under the influence of different physical parameters. It is finally concluded that all the obtained results against each velocity profile depicts the both increasing and decreasing behavior according the upper and lower solution. However, temperature profile shows the same behavior of two different solutions for each parameter. Isotherms behavior in the entire domain of the model shows the significant variation for three different fluids (air, water and kerosene oil).