The effects of variable porosity and cell size on the thermal performance of functionally-graded foams

The thermal performance of several engineering devices, such as heat exchangers, volumetric solar receivers and thermal energy storage systems, is improved by open-cell metal or ceramic foams. Among them functionally-graded foams, through which morphological characteristics are variable, look promising. Heat transfer and pressure drop in a functionally-graded foam, with a uniform heat flux entering one of its sides, are investigated numerically in this paper. Porosity and cell size variable in the direction of the entering heat flux according to different power-law functions are considered; their maximum and minimum values are constrained at the opposite upper and lower sides of the foam. Governing equations, written with reference to a Representative Elementary Volume (REV) of the foam, are solved with a Local Thermal Non Equilibrium (LTNE) model by means of a finite element scheme; the code is validated with experimental data from the literature. The thermal performance of the foam is expressed by a Performance Evaluation Criterion (PEC), referred to the average morphological characteristics of foams with the same surface area. Nusselt numbers, friction factors and Performance Evaluation Criteria (PECs), for different power-laws, are predicted. A 38% higher PEC than in foams with uniform porosity is found in foams with variable-porosity while a 14% larger PEC is exhibited in foams with variable cell size. A 42% increase in PEC is found in foams that account for both variable porosity and cell size.