Application of Lévêque Analogy to Open Cellular Solids

Porous materials are widely used for electronics cooling and heat exchangers owing to their enhanced heat transfer characteristics, which need to be estimated for such applications. In situations where pressure drop results are already available, heat transfer data can be predicted with the application of the Lévêque analogy or its modified version. To investigate this type of analogy, four different unit cell geometries representing periodic cellular structure with 75%-95% porosity is considered in the current work, where Reynolds number is varied between 1 and 100. Periodic flow and heat transfer simulations performed in ANSYS Fluent provide pressure drop and heat transfer results. Permeability and inertial coefficient are estimated, and permeability is correlated successfully with porosity and fiber diameter of the unit cell geometries. Lévêque's analogy in the original form is explored using the pressure drop coefficient and Nusselt number, which provides a 44% frictional contribution to the total pressure drop. The correlation for the current geometries is further improved using a modified version of the Lévêque analogy, where the exponent is estimated using best-fit instead of fixing at 1/3.