Analytic Optimization of Porous Medium Heat Sinks for Energy Efficiency and Minimum Mass

Abstract

Use of microchannel heat sinks for high heat flux applications is substantial for thermal management and it is also critical for scalable power generation. For both applications, the energy efficiency consideration of the pump power is crucial. A number of models have been created that predict the performance as a function of the geometrical parameters, taking into account, the pressure loss over the length and volume constraints. Most of the approaches either involve sophisticated calculations incorporating fluid dynamics in channels, or have an analogy with the pin-fin model, which gives simpler calculations but considers only a single laminar flow regime for optimization. Even with the simplified models available, the geometrical impact on mass and pumping power is nonlinear and not apparent for optimization. We propose an optimization of porous medium heat sinks with respect to the heat transfer rate, mass, and pumping power. These are functions of the simplest geometric parameters, i.e. porosity, pore density, and length of the porous medium. Considering large production, mass (cost of raw material) is nearly proportional to the cost of the heat sink, we consider minimizing the mass for indirectly minimizing the overall cost. The other factor for saving energy considered here is the pumping power. This connects to both the heat transfer rate and the power consumption to drive the fluid through the porous medium. The optimization is performed for a specific value of porosity and length of the heat sink. The model considers the effect of flow through the porous medium and the effective thermal conduction as a function of combined conductivity of the solid ligaments and the fluid in pores. An optimum coefficient of performance (COP) is found at over 90% of porosity for minimum mass, pumping work and maximum heat transfer. This mathematical expression of the model will give a quantifiable figure-of-merit to take into account the impact of the mass and the pumping power on the performance to cost ratio.

Performance and mass optimization of thermoelectric microcoolers

“…In separate studies, the impact of heat sink design on the performance is reported [39] and further potential for a cost effective heat sink for energy systems is theoretically analyzed and reported in Ref. [40]. This extensive study of heat sinks based on porous material could yield the theoretical upper limit of COP of the heat sink itself.…”