Abstract
Plane thermal waves in a heat conducting and radiating (emitting and absorbing) medium that occupies the half-spacex>0 are investigated. The governing equations for a gray medium are linearized with regard to small perturbations of the radiative equilibrium. Solutions are given for the thermal wave that is due to harmonic oscillations of either the wall temperature or the radiative energy flux produced by an outer source. The behaviour of the thermal wave is then discussed for the asymptotic cases of weak, strong, optical thin and optical thick radiation, respectively, and also for the special case that the Bouguer numberBu and the radiation-conduction parameterK as defined in the text are equal to one. Then the equations and their solutions are generalized in order to apply to certain models of frequency-dependent absorption coefficients (non-gray media). Finally it is shown that nonlinear terms, although being small of higher order in the differential equations, cause the perturbation solution to be not uniformly valid as the distance from the boundary surface goes to infinity.
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