Eigenfunction-based solution for solid-liquid phase change heat transfer problems with time-dependent boundary conditions

• Considers phase change problems with time-dependent boundary conditions. Derives an eigenfunction expansion based solution for Cartesian, cylindrical and spherical problems. Results are in good agreement numerical simulations past work. correctly reduce to Stefan Neumann solutions special cases. improve the understanding of practical engineering systems. Solid-liquid heat transfer appear a broad variety systems, such as thermal management latent energy storage. Boundary conditions systems often vary time, example, due sinusoidal heating, or step changes externally applied temperature flux. Unfortunately, do not generally admit exact solution, therefore, approximate analytical much interest. This paper presents technique solving one-dimensional flux The field is expressed series appropriate eigenfunctions, coefficients, which determined by deriving ordinary differential equation that accounts nature condition. Solutions derived. found be excellent work simulations. effect problem on propagation studied. Two involving function also solved analyzed detail. In addition improving fundamental transfer, this may contribute towards design optimization transfer.