A Mathematical Study of Rectangular and Triangular Fins with Variable Thermal Conductivity Through Local Thermal Equilibrium and Local Thermal Non-Equilibrium Fluid Models by Means of Artificial Neural Network

Abstract

A mathematical approach is employed to examine the heat transmission capabilities of rectangular and triangular porous fins in both Local Thermal Equilibrium (LTE) and Local Thermal Non-Equilibrium (LTNE) scenarios. To provide a more accurate depiction of the thermal interaction between the solid and fluid phases, the LTNE model uses two coupled energy equations to represent their respective temperature fields. In contrast, the LTE model is controlled by a single energy equation and assumes a constant temperature throughout the phases. In order to ascertain the temperature distribution and overall thermal performance of the fin system, the governing equations are developed using the basic concepts of heat conduction and convection. To achieve enhanced heat transmission ability and greater thermal conductivity, the fluid phase is blended with Ag, Au, and TiO₂ as nanoparticles. These formulated equations have been turned into dimensionless nonlinear ordinary differential equations, and then Runge-Kutta Fehlberg fourth-fifth order (RKF-45) approach is adopted to solve them numerically. The credibility and accuracy of the results are ensured by benchmarking with previously established findings. The influence of important parameters on the thermal behavior of porous fins is visually examined by graphical analysis. Additionally, an Artificial Neural Network (ANN) method is employed to precisely evaluate and forecast the rate of heat transmission. It attains a high regression coefficient R = 1, indicating that the predictions are highly reliable. The analysis shows that the Nusselt number for the LTNE model is about 26.19% higher than that of the LTE model, indicating enhanced heat transfer performance.