The exterior unsteady viscous flow and heat transfer due to a porous expanding stretching cylinder

• The model of the flow over the porous stretching expanding pipe is new.
• The heat transfer of the flow is considered simultaneously.
• Dual solutions exist and the interval of the existence for different parameter also is different.
• The solutions are obtained by a combined analytical/numerical method.

This paper presents a numerical solution of the flow and heat transfer outside a stretching expanding porous cylinder. Under this special boundary condition, the governing system of partial differential equations is converted to a set of coupled ordinary differential equations by using suitable similarity transformations, which are solved by a collocation method equivalent to the fourth order mono-implicit-Runge–Kutta method with MATLAB. The main purpose of the present study is to investigate the effects of the different physical parameters, namely the stretching Reynolds number, the permeability Reynolds number,the expansion ratio and the Prandtl number on the velocity and temperature distribution. The results are shown graphically.