An analytical study of local thermal equilibrium in porous heat sinks using fin theory

This work presents an algorithm model for estimating the heat transfer by forced convection of the porous heat sink in a channel by applying the fin theory and the concept of the thermal network. The proposed algorithm model is simpler and more convenient than numerical analysis. By comparison with numerical calculations and other experiments, the model was verified to predict accurately heat transfer in various porous channels, such as metal foam channels and sintered porous channels. The inlet thermal boundary condition is also examined. The finding reveals that the effect of the inlet thermal boundary condition on the numerical calculations becomes weaker as the interstitial heat transfer coefficient increases. Additionally, a parameter Ω in terms of hv, image and H∗ is postulated to determine the local thermal equilibrium (LTE) in porous channels. Analytical results reveal some criteria for LTE in various porous channels. For instance, the criterion for LTE in aluminum foam channels is: if ε = 0.91 and H = 45 mm, Re ⩾ 4700; if ε = 0.95/10PPI and H = 45 mm, Re ⩾ 1600; if ε = 0.95/10PPI and H = 25.4 mm, then Re ⩾ 6600. Besides, the scope of LTE in sintered copper bead porous channels with ε = 0.38/d = 1.59 mm and H = 10 mm is about Re ⩾ 6600. Accordingly, the one-equation model, which is simpler than the two-equation model, can be used to analyze heat transfer through porous media in the applicable regions.