Analytical solution of the transpiration on the boundary layer flow and heat transfer over a vertical slender cylinder

Abstract

An analysis is carried out to study the effects that blowing/injection and suction on the steady mixed convection or combined forced and free convection boundary layer flows over a vertical slender cylinder with a mainstream velocity and a wall surface temperature proportional to the axial distance along the surface of the cylinder. Both cases of buoyancy forces aid and oppose the development of the boundary layer are considered. For the investigated problem, the governing non-linear partial differential equations and their associated boundary conditions are transformed into coupled non-linear ordinary differential equations by using similarity transformations. This equation is solved both by a newly developed analytic technique, namely homotopy analysis method (HAM) and by a numerical method employing the shooting method. The convergence of the obtained series solutions is carefully checked. The physical significance of interesting parameters on the velocity profile and the temperature profile are shown through graphs and discussed in detail. The values of the skin friction coefficient, the local Nusselt number, curvature parameter, buoyancy or mixed convection parameter and Prandtl number are tabulated. Comparison is also made with the corresponding results of viscous fluid with no mixed convection and an excellent agreement is noted.

Keywords: Vertical slender cylinder, boundary layer, suction/injection, HAM, shooting method

Quaestiones Mathematicae 36(2013), 353–380