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An Exact Solution of Stikker's Nonlinear Heat Equation
Allan R. Willms
SIAM Journal on Applied Mathematics
Vol. 55, No. 4 (Aug., 1995), pp. 1059-1073
Published by: Society for Industrial and Applied Mathematics
Stable URL: http://www.jstor.org/stable/2102638
Page Count: 15
You can always find the topics here!Topics: Steels, Heat equation, Boundary conditions, Temperature gradients, Conductive heat transfer, Annealing, Boundary value problems, Heat conductivity, Mathematical problems, Conductivity
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Exact solutions are derived for a nonlinear heat equation where the conductivity is a linear fractional function of (i) the temperature gradient or (ii) the product of the radial distance and the radial component of the temperature gradient for problems expressed in cylindrical coordinates. It is shown that equations of this form satisfy the same maximum principle as the linear heat equation, and a uniqueness theorem for an associated boundary value problem is given. The exact solutions are additively separable, isolating the nonlinear component from the remaining independent variables. The asymptotic behaviour of these solutions is studied, and a boundary value problem that is satisfied by these solutions is presented.
SIAM Journal on Applied Mathematics © 1995 Society for Industrial and Applied Mathematics