Physics-informed Hermite neural networks for wetted porous fin under the local thermal non-equilibrium condition: application of clique polynomial method

The proposed investigation highlights the thermal variation and heat transmission behavior of a wetted porous fin under a local thermal non-equilibrium state (LTNE). The fluid–solid interaction is governed by the Darcy formulation. The two-equation model of LTNE is utilized to depict the energy transfer for both the solid and fluid phases. The pertinent thermal distribution problems are represented as highly nonlinear ordinary differential equations (ODEs) with boundary conditions for both solid and fluid phases. The governing heat equations have been transformed into a non-dimensional form by employing dimensionless variables. The application of the clique polynomial method with Laplace–Pade approximant (CPMLPA) for these modified governing equations is the unique objective of the present research endeavor. Furthermore, physics-informed Hermite neural network (PIHNN) is employed to solve the resulting non-dimensional heat equations of the wetted porous fin. An explanation and visual demonstration of the impact of embedded thermal variables on the temperature profiles are provided. As the values of the convection–conduction and surface-ambient radiation parameters rise, the thermal profile diminishes. Augmentation of the Rayleigh number diminishes temperature dispersion in the fin. The upsurge in values of the radiation parameter intensifies the temperature profile. This study compares the temperature values of PIHNN, CPMLPA, and the clique polynomial method and reveals a strong correlation.