Exact solutions of nonlinear heat- and mass-transfer equations

Exact solutions of nonlinear heat- and mass-transfer equations

The method of generalized separation of variables for solving nonlinear steady and unsteady heat- and mass-transfer equations is outlined. New exact solutions of one-, two-, and three-dimensional heat equations are obtained. Anisotropic media with a nonlinear heat source of general form are consider...

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Bibliographic Details
Published in:Theoretical foundations of chemical engineering Vol. 34; no. 5; pp. 403 - 415
Main Authors: Polyanin, A. D., Zhurov, A. I., Vyaz’min, A. V.
Format: Journal Article
Language:English
Published: New York Springer Nature B.V 2000
Subjects:
Anisotropic media
Anisotropy
Exact solutions
Mass transfer
Mathematical analysis
Thermodynamics
Online Access:Get full text
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Summary:The method of generalized separation of variables for solving nonlinear steady and unsteady heat- and mass-transfer equations is outlined. New exact solutions of one-, two-, and three-dimensional heat equations are obtained. Anisotropic media with a nonlinear heat source of general form are considered for the case in which the main thermal diffusivities show a power or an exponential dependence on the spatial coordinates. Equations with a logarithmic heat source are analyzed in detail. The results obtained are applied to the problem of thermal explosion in an anisotropic medium.
ISSN:0040-5795
1608-3431
DOI:10.1007/BF02827383