This paper presents an axi-symmetric laminar boundary layer flow of a viscous incompressible fluid and heat transfer towards a stretching cylinder embedded in a porous medium. The partial differential equations corresponding to the momentum and heat equations are converted into highly nonlinear ordinary differential equations with the help of similarity transformations. Numerical solutions of these equations are obtained by shooting method. It is found that the velocity decreases with increasing permeability parameter. The skin friction as well as the heat transfer rate at the surface is larger for a cylinder compared to a flat plate.

The study of hydrodynamic flow and heat transfer over a stretching cylinders or flat plates has gained considerable attention due to its applications in industries and important bearings on several technological processes. Crane [

Flow over cylinders is considered to be two-dimensional if the body radius is large compared to the boundary layer thickness. On the other hand for a thin or slender cylinder, the radius of the cylinder may be of the same order as that of the boundary layer thickness. Therefore, the flow may be considered as axi-symmetric instead of two-dimensional [

The study of hydrodynamic flow and heat transfer in porous medium becomes much more interesting due to its vast applications on the boundary layer flow control. Heat removal from nuclear fuel debris, underground disposal of radioactive waste material, storage of food stuffs and exothermic and/or endothermic chemical reactions and dissociating fluids in the packed-bed reactors, and so forth are some porous media applications. It is well known that Darcy’s law is an empirical formula relating the pressure gradient, the bulk viscous fluid resistance and the gravitational force for a forced convective flow in a porous medium. Deviations from Darcy’s law occur when the Reynolds number based on the pore diameter is within the range of 1 to 10 (Ishak et al. [

No attempt has been made yet to analyze the flow and thermal characteristics of boundary layer axi-symmetric flow and heat transfer along a stretching cylinder in a porous medium. Therefore, an attempt is made to study the steady forced convection flow and heat transfer past a stretching cylinder placed in a fluid-saturated porous medium using the Darcy model. Using similarity transformation, a third order ordinary differential equation corresponding to the momentum equation and a second-order ordinary differential equation corresponding to heat equation are derived. Using shooting method, numerical calculations up to desired level of accuracy were carried out for different values of dimensionless parameters of the problem under consideration for the purpose of illustrating the results graphically. The results obtained are then compared with those of Grubka and Bobba [

Consider the steady axi-symmetric flow of an incompressible viscous fluid along a stretching cylinder embedded in a porous medium. The continuity, momentum, and energy equations governing such type of flow are written as

The appropriate boundary conditions for the problem are given by

The continuity equation is automatically satisfied by the introduction of stream function

One can note that if

The above equations (

Taking the series of values for

In order to analyse the results, numerical computation has been carried out using the method described in the previous section for various values of the curvature parameter (

(a) Variation of velocity

For the verification of accuracy of the applied numerical scheme, a comparison of the present results corresponding to the heat transfer coefficient

Values of

Ishak and Nazar [ | Grubka and Bobba [ | Ali [ | Present study | |
---|---|---|---|---|

0 | 0.5820 | 0.5820 | 0.5801 | 0.5821 |

1 | 1.0000 | 1.0000 | 0.9961 | 1.0000 |

2 | 1.3333 | 1.3333 | 1.3269 | 1.3332 |

Let us first concentrate on the effects of curvature parameter

Effects of curvature parameter on the temperature distribution are presented in Figure

Now, the velocity profiles are presented for the variation of permeability parameter for flat plate and stretching cylinder, respectively. Figures

(a) Variation of velocity

Figures

(a) Variation of temperature

Figures

(a) Variation of skin friction coefficient

(a) Variation of temperature

It is noted that temperature decreases with increasing Pr. An increase in Prandtl number reduces the thermal boundary layer thickness. It is also observed that the effects of Pr is much more prominent for flat plate (Figure

The present study gives the numerical solutions for steady boundary layer flow and heat transfer along a stretching cylinder embedded in porous medium. The rate of transport is considerably reduced with increasing values of curvature parameter

It is hoped that, the physics of flow over the stretching cylinder can be utilized as the basis for many engineering and scientific applications with the help of the present model. The results pertaining to the present study may be useful for the different model investigations. The findings of the present problem are also of great interest in different areas of science and technology where the surface layers are being stretched.