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For this article, an analytical study has been conducted on the flow and energy transfer of unsteady compressible oscillating flow through channels filled with porous medium representing stack in thermoacoustic engines/refrigerators. The flow in the porous material is described by the Darcy momentum equation. Analytical expressions for oscillating velocity, temperature in the porous layer, complex Nusselt number, and energy flux density are obtained after simplifying and solving the governing differential equations with reasonable approximations (such as long wave, short stack, small amplitude oscillation, etc.). The result for heat transfer between the porous medium and the channel wall is expressed as a dimensionless Nusselt number. For the limiting case of nonporous medium, the Nusselt number obtained in the present study matches quantitatively with the expression available in the existing literature. The results reveal that the Nusselt number in oscillating flow is significantly enhanced (almost an order of magnitude) by employing sufficiently large thermal conductivity of porous media in a channel. The system of equations developed in the present study is a helpful tool for thermal engineers to design porous stacks for thermoacoustic devices.