Analytical solutions for heat conduction problems with three kinds of periodic boundary conditions and their applications

Abstract

In the present study, a general analytic expression for solving heat conduction problem in finite domain under periodic boundary conditions was suggested by using the variable separation method. Heat conduction problems under three kinds of periodic upper boundary conditions and constant temperature or zero-flux as bottom boundary conditions were solved respectively. By applying the analytical solutions, an equivalent method for transferring the periodic heat flux and convection combination boundary condition to the Dirichlet boundary condition was proposed. In addition, the proposed solution was generalized to solve the heat conduction problem infinite domain with periodic sine-like law boundary conditions. The present study can provide references for investigating the evolution law of temperature field under complex periodic boundary conditions.