One-Dimensional Quasilinear Heat Flow with Boundary Conditions Periodic in Time.

摘要

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.