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Group method solution for solving nonlinear heat diffusion problems
Faculty
Science
Year:
2006
Type of Publication:
Article
Pages:
930-940
Authors:
Helal, Medhat M, Abd-el-Malek, Mina B
DOI:
10.1016/j.apm.2005.06.006
Journal:
APPLIED MATHEMATICAL MODELLING ELSEVIER SCIENCE INC
Volume:
30
Research Area:
Engineering; Mathematics; Mechanics
ISSN
ISI:000239357600010
Keywords :
group method, transient heat diffusion, nonlinear problems
Abstract:
The linear transformation group approach is developed to simulate heat diffusion problems in a media with the thermal conductivity and the heat capacity are nonlinear and obeyed a striking power law relation, subject to nonlinear boundary conditions due to radiation exchange at the interface according to the fourth power law. The application of a one-parameter transformation group reduces the number of independent variables by one so that the governing partial differential equation with the boundary conditions reduces to an ordinary differential equation with appropriate corresponding conditions. The Runge-Kutta shooting method is used to solve the nonlinear ordinary differential equation. Different parametric studies are worked out and plotted to study the effect of heat transfer coefficient, density and radiation number on the surface temperature. (c) 2005 Elsevier Inc. All rights reserved.
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