LAUSR

This study proposed a promising analytical solution for transient heat conduction in an infinite geometry with general heat source under heterogeneous time-dependent boundary conditions of the third kind at both internal and external surfaces. Due to the inherent heterogeneity of the problem and its associated boundary conditions, the analytical solution is divided into two parts: (1) a linear part which is a linear function of space and satisfies the heterogeneous boundary conditions; (2) a nonlinear part which is formulated by the method of variable separation without heat source, leading to the introduction of a new series in terms of Bessel function. The heat source term is expanded using eigenfunctions of the series. Through the methods of superposition and variable separation, the spatiotemporal distribution of temperature is expressed in terms of a Bessel function. The same problem was also solved numerically employing implicit finite difference method to validate the derived analytical solution. The comparison between analytical and numerical results demonstrates that the derived analytical solution is accurate and applicable to efficient analysis of transient heat conduction in infinite geometries with general internal heat source under heterogeneous time-dependent boundary conditions of the third kind at internal and external surfaces.