An Exact Solution of Stikker’s Nonlinear Heat Equation

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.