Heat Conduction in a Square Plate Involving Multivariable H-Function

A rigorous mathematical paradigm incorporating the multivariable H-function is devised to elucidate heat conduction phenomena in square plates. This innovative framework facilitates the derivation of a precise temperature field model, thereby enabling a comprehensive examination of the interplay between plate geometry and heat propagation characteristics. The analytical solution is substantiated through meticulous numerical simulations, underscoring the multivariable H-function's exceptional capability in capturing intricate heat conduction dynamics under disparate boundary conditions. This investigation substantially enhances the theoretical foundations of thermal analysis in square plates, unlocking novel avenues for interdisciplinary applications in engineering and physical sciences.