One-Dimensional Quasilinear Heat Flow with Boundary Conditions Periodic in Time
JOHNS HOPKINS UNIV BALTIMORE MD
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If thermal conductivity and specific heat are taken as linear functions of temperature, a nonlinear heat-conduction equation results. For small nonlinearities an approximate first-order analytical solution may be obtained in certain cases. The present analysis deals with one-dimensional problems with periodic boundary conditions. Only the steady-state solution i.e. , one which is periodic in time is considered. Solutions are obtained for the following cases 1 Semi-infinite solid with sinusoidal boundary temperature, 2 thick slab with sinusoidal temperature at one boundary and constant temperature at the other, and 3 thick slab with prescribed heat flux a constant term plus a sinusoidal term at one boundary, constant temperature at the other. The effects of the nonlinearities are discussed they are found to be surprisingly small.