A New Numerical Approach for the Laminar Boundary Layer Flow and Heat Transfer along a Stretching Cylinder Embedded in a Porous Medium with Variable Thermal Conductivity

S Shateyi,G T Marewo

doi:10.1155/2013/576453

Abstract

The study presents an axisymmetric laminar boundary layer flow of a viscous incompressible fluid and heat transfer over a stretching cylinder embedded in a porous medium. A suitable similarity transformation is employed to transform the partial differential equations corresponding to the momentum and heat equations into nonlinear ordinary differential equations. The resultant ordinary differential equations are then solved using a successive relaxation method (SRM). The effects of significant parameters on the velocity and temperature profiles have been analyzed graphically. The obtained results are also compared with previously published results in some special cases and were found to be in excellent agreement. The skin friction as well as the heat transfer rate at the surface are increased as the values of the curvature parameter increase.

Highlights

The study of boundary layer flow and heat transfer due to stretching flat plates or cylinders has gained considerable attention due to its applications in fibre technology and extrusion processes, as well as theoretical interest
Sakiadis [1, 2] pioneered the study of boundary layer flow on a moving continuous solid surface
Mukhopadhyay [17] presented an axisymmetric laminar boundary layer mixed convection flow of a viscous incompressible fluid and heat transfer towards a stretching cylinder embedded in a porous medium

Summary

Introduction

The study of boundary layer flow and heat transfer due to stretching flat plates or cylinders has gained considerable attention due to its applications in fibre technology and extrusion processes, as well as theoretical interest. Mukhopadhyay [17] presented an axisymmetric laminar boundary layer mixed convection flow of a viscous incompressible fluid and heat transfer towards a stretching cylinder embedded in a porous medium. Elbashbeshy et al [20] discussed laminar boundary layer flow of an incompressible viscous fluid along a stretching horizontal surface embedded in a porous medium in the presence of a heat source or sink with suction/injection. Varjravelu et al [21] presented numerical solutions to the unsteady convective boundary layer flow of a viscous fluid at a vertical stretching surface with variable transport properties and thermal radiation. Mukhopadhyay and Gorla [26] presented an axisymmetric laminar boundary layer flow of a viscous incompressible fluid and heat transfer towards a stretching cylinder. The rest of the paper is outlined as follows: in Section 2 we give the model formulation of the problem; in Section 3, the successive relaxation method is given in detail; in Section 4, the results and discussion are given; and Section 5 gives the conclusions based on the findings

Mathematical Formulation

Solution Using the Successive Relaxation Method

Results and Discussion

Conclusion