Radiative heat transfer analysis of a concave porous fin under the local thermal non-equilibrium condition: application of the clique polynomial method and physics-informed neural networks

The heat transfer through a concave permeable fin is analyzed by the local thermal non-equilibrium (LTNE) model. The governing dimensional temperature equations for the solid and fluid phases of the porous extended surface are modeled, and then are nondimensionalized by suitable dimensionless terms. Further, the obtained non-dimensional equations are solved by the clique polynomial method (CPM). The effects of several dimensionless parameters on the fin's thermal profiles are shown by graphical illustrations. Additionally, the current study implements deep neural structures to solve physics-governed coupled equations, and the best-suited hyperparameters are attained by comparison with various network combinations. The results of the CPM and physics-informed neural network (PINN) exhibit good agreement, signifying that both methods effectively solve the thermal modeling problem.