Thermal-Hydraulic Optimization of Open-Cell Metallic Foams Used as Extended Surfaces

A one-dimensional analytical validated model for predicting temperature distribution, heat transfer, pressure drop, and fluid pumping power in an open-cell metal foam (OCMF) fin is developed. A foam length optimization technique based on its performance factor (PF) is proposed. Every optimized foam's efficiency is shown to be 33.2%, regardless of its pores per inch (PPI) or porosity. Although it can be applied to other porous materials, the model has been illustrated for aluminum foams with 5–40 PPI and 0.88–0.96 porosity (ε). The highest PPI, lowest porosity foam gives the best unit area goodness factor $φu=jH/f$⁠, heat transfer, and heat transfer per unit volume $Q˙V$⁠, while the greatest goodness factor $φ$ (heat transfer rate to fluid pumping power) is achieved by the lowest PPI, lowest porosity foam. The highest PPI, highest porosity foam yields the best heat transfer per unit mass$Q˙M$⁠. Thus, optimum foam selections strongly depend on the application. An often-used fin optimization criterion recommends that the fin effectiveness should equal or exceed 2. This study shows that the effectiveness of any optimized foam always exceeds 2. However, the converse, i.e., requiring the foam effectiveness to at least equal 2, does not guarantee an optimal foam, which implies that the PF-based optimization criterion is an inclusive one. It is also proved that a previously suggested optimization criterion of maximizing a foam's geometric mean efficiency will result in a suboptimal foam design.