Energy performance assessment of functionally graded metal foams using a finite element approach

Abstract Open-cell metal foams hold significant potential as functionally graded porous media for heat transfer applications such as solar thermal collectors; however, manufacturing constraints often limit the use of idealized, smoothly graded materials. While multiple uniform-layer foams present a pragmatic alternative, their thermohydraulic performance across moderate-to-high porosities remains under-researched. This study evaluates the energy performance of fluid flow through a parallel channel embedded with step-gradient metal foams. The Finite Element Method (FEM) was utilized to solve the normalized mass, momentum, and energy conservation equations under the Local Thermal Non-Equilibrium (LTNE) condition, examining constant, double, triple, and linear configurations at average porosities ($\overline{\phi}$) of 0.7, 0.8, and 0.9. Fluid dynamically redistributes to maintain a uniform longitudinal pressure decrease, yielding steep velocity gradients near boundaries and layer interfaces. An analysis of the non-equilibrium parameter ($\Delta \mathrm{NE}$) justifies the LTNE approach, demonstrating that thermal equilibrium is compromised near heated walls and porosity-variation interfaces. Thermally, deliberate foam stacking steepens near-wall temperature gradients and reduces the plate-to-fluid temperature difference. Notably, equal-thickness triple-layer configurations (model T2) exhibited an increase in the Performance Evaluation Criterion (PEC) of approximately 10--11\% compared to the constant-porosity case at $\overline{\phi} = 0.8$ and $0.9$. These results suggest that strategically stacked discrete-porosity open-cell metal foams provide a highly practical approach for optimizing energy performance in convective heat exchange devices.