Abstract:
We consider a heat conduction problem for an infinite plate with a mismatch between initial and boundary conditions. Using the method of integral relations, we obtain an approximate analytic solution to this problem by determining the temperature perturbation front. The solution has a simple form of an algebraic polynomial without special functions. It allows us to determine the temperature state of the plate in the full range of the Fourier numbers ($0\le\mathsf F<\infty$) and is especially effective for very small time intervals.
Keywords:approximate analytic solution, integral relation method, temperature disturbance front, variable initial condition.