Identifiability, in the large, of a nonlinear heat-conduction equation and self-similar solutions

1983 ◽  
Vol 45 (2) ◽  
pp. 944-949
Author(s):  
M. R. Romanovskii
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Conduction Equation ◽  
Nonlinear Heat Conduction ◽  
Nonlinear Heat Conduction Equation ◽  
Self Similar ◽  
Similar Solutions

scholarly journals Approximate Solution of the Nonlinear Heat Conduction Equation in a Semi-Infinite Domain

2010 ◽  
Vol 2010 ◽  
pp. 1-24 ◽  
Author(s):  
Jun Yu ◽  
Yi Yang ◽  
Antonio Campo
Keyword(s):  
Heat Conduction ◽  
Energy Density ◽  
Approximation Method ◽  
Heat Conduction Equation ◽  
Boundary Energy ◽  
Approximate Solutions ◽  
Nonlinear Heat Conduction ◽  
Infinite Domain ◽  
Nonlinear Heat Conduction Equation ◽  
Self Similar

We use an approximation method to study the solution to a nonlinear heat conduction equation in a semi-infinite domain. By expanding an energy density function (defined as the internal energy per unit volume) as a Taylor polynomial in a spatial domain, we reduce the partial differential equation to a set of first-order ordinary differential equations in time. We describe a systematic approach to derive approximate solutions using Taylor polynomials of a different degree. For a special case, we derive an analytical solution and compare it with the result of a self-similar analysis. A comparison with the numerically integrated results demonstrates good accuracy of our approximate solutions. We also show that our approximation method can be applied to cases where boundary energy density and the corresponding effective conductivity are more general than those that are suitable for the self-similar method. Propagation of nonlinear heat waves is studied for different boundary energy density and the conductivity functions.

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