Local Similarity Solution of the Free Convection from a Long Vertical Cylinder Embedded in a Darcian Fluid-Saturated Porous Medium.

Document Type : Research Studies

Author

Mechanical Power Engineering Department., Faculty of Engineering., El--Mansoura University., Mansoura., Egypt.

Abstract

In this work , local similarity solution is obtained for free convection from along cylinder embedded in afluid-saturated porous medium. The cylinder wall is maintained constant. The free convection along the cylinder is described by continuity equation, momentum equation in axial direction, momentum equation in radial direction and energy equation . these governing equations are expressed in cylindrical coordinates. Defining new proper independent and dependent variables , the governing equations are transformed to dimensionless form. Since the proposed solution is restricted to the case of long cylinders, the derived dimensionless governing equations are ordinary differential equations of the boundary value problems type. They are solved numerically using Runge - Kutta method accompanied with shooting technique. Newton-raphson method of non-algebraic equation is used to carry out the shooting technique . solving these equations at different positions along the cylinder, temperature and velocity distributions are obtained and hence the values of local nusselt number are calculated for rayeigh number of 1,5 ,10 and 20. Because of the application of darcian model. In this work, the obtained results are valid only for the case of porous medium of small permeability.

Main Subjects

MEJ- Mansoura Engineering Journal
Volume 23, Issue 2
VOL 23 has two issues issue 1 consists of two parts (from March to June)
June 1998
Pages 16-25

Files

Share

How to cite

Statistics