Analysis on the heat transfer characteristics of a micro-channel type porous-sheets Stirling regenerator

To avoid the high flow frictional loss associated with conventional wire mesh Stirling regenerators, a micro-channel type stacked porous-sheets Stirling regenerator is investigated. An analytical solution is derived for the transient heat transfer characteristics of the fully developed reciprocating laminar flow under prescribed wall temperature profiles. The complex Nusselt number (Nu) is expressed as a function of kinetic Reynolds number (Reω) and Prandtl number (Pr). At low Reω of less than 10, the real part of Nu has an almost constant value of 6.0, approximately equal to the known real-valued Nu for the fully developed unidirectional laminar flow under constant wall heat flux, while the imaginary part is negligible, thus “scaling effect” can be utilized to enhance heat transfer. At higher Reω, both the real and imaginary parts of Nu increase with the increase of Reω and Pr, and the phase shift between the temperature difference and the heat flux gradually increases and approaches 45°. Approximate analytical solutions are also deduced for the entrance region from the integral boundary layer equations in both cases of “Thermally developing flow” and “Simultaneously developing flow”. The heat transfer is enhanced in the entrance region and the local Nu in the flow direction approaches the corresponding values of fully developed flow. The analytical results are confirmed by dynamic mesh CFD results, and the obtained Nu∼ Reω data and patterns generally agree with available analytical and experimental data from published literatures. Application of the analytical results to the design and optimization of Stirling regenerator are also shown.