Analytic solutions to heat transfer problems on a basis of determination of a front of heat disturbance

Abstract

With the use of additional boundary conditions in integral method of heat balance, we obtain analytic solution to nonstationary problem of heat conductivity for infinite plate. Relying on determination of a front of heat disturbance, we perform a division of heat conductivity process into two stages in time. The first stage comes to the end after the front of disturbance arrives the center of the plate. At the second stage the heat exchange occurs at the whole thickness of the plate, and we introduce an additional sought-for function which characterizes the temperature change in its center. Practically the assigned exactness of solutions at both stages is provided by introduction on boundaries of a domain and on the front of heat perturbation the additional boundary conditions. Their fulfillment is equivalent to the sought-for solution in differential equation therein. We show that with the increasing of number of approximations the accuracy of fulfillment of the equation increases. Note that the usage of an integral of heat balance allows the application of the given method for solving differential equations that do not admit a separation of variables (nonlinear, with variable physical properties etc.).