ISSN:
0029-5981
Keywords:
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
An analysis is presented for the steady state free convective flow and heat transfer from an axisymmetric heat-generating body that is embedded in a fluid-saturated, semi-infinite, porous medium. The porous medium is assumed to be rigid, homogeneous and isotropic, and be in thermal equilibrium with the fluid. The fluid is assumed to be incompressible, with the density changes contributing only towards the buoyancy forces via the Boussinesq approximation. The governing equations for the fluid consist of the equation of continuity, Darcy's law and the equation of energy. After introducing the stream function concept, the equations governing the stream function and pressure are derived. Using the non-dimensional variables, the non-dimensional equations governing the non-dimensional forms of the temperature, stream function and pressure are dervied and the appropriate boundary conditions are stated. The mathematical formulation contains two parameters; D, the non-dimensional depth of the body from the surface of the porous medium, and a product Raθs of Rayleigh number (Ra) and the non-dimensional surface temperature of the body (θs). The Galerkin finite element method, with linear, isoparametric, quadrilateral elements, is used to reduce the mathematical formulation into a set of algebraic equations. The expressions to calculate the non-dimensional surface temperature and Nusselt number of the body, and the non-dimensional velocity of the fluid, are derived. A computer code has been developed to solve the algebraic equations, using Gauss elimination procedure, in a banded matrix form. The computer code, in addition to the non-dimensional temperature, stream function and pressure, calculates the isothermal lines, non-dimensional surface temperature of the body, Nusselt number of the body, velocity field and isobars.To demonstrate the application of the code, a spherical heat-generating body is considered as an example. Numerical results are obtained for D = 3 and 6, and Raθs = 0.001, 0.1, 1 and 5, and presented.
Additional Material:
11 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/nme.1620260213
