Thermal conductivity at variable in time relative to the heat transfer coefficient

Abstract

The practically important problem of unsteady heat conduction with time-varying relative coefficient of heat transfer is considered. Systematization of different approaches for finding the analytical solution of the problem is shown: the method of splitting the generalized Fourier integral; expanding the desired temperature function in a power series; reduction of the problem to an integral Voltaire equation of the second kind. It is shown that in all cases the solution is reduced to an infinite series of successive approximations of various functional forms, and the main goal of each approach is to find the more successful of the first approximations. Particular cases of the time dependence of the relative heat transfer coefficient are considered: linear, exponential, degree, root. The analytical solutions and numerical experiments, the peculiarities of the temperature curves for a number of specified dependencies are given. It was established that in case of the time-linear heat transfer coefficient the temperature curve changes significantly differ in comparison with the classical case of constant coefficient, while exponential dependence makes no substantive difference.

Keywords

• transient heat transfer, time-varying relative heat transfer coefficient, analytical methods for solving boundary value problems with variable coefficients, successive approximations, illustrative examples.