Thermal Analysis of Chemical Reactions with Exponential Heat Generation using Double Interpolation process

Abstract: This study focuses on the thermal analysis of chemical reactions characterized by exponential heat generation, modeled using a reaction-diffusion equation. The non-linear nature of the heat generation, driven by temperature, reflects the rapid acceleration of reaction rates at higher temperatures. A double interpolation process is used to improve the precision of temperature distribution solutions over space and time. Starting from the classical heat equation with a reaction term, the analysis employs Dirichlet boundary conditions and a Gaussian initial temperature profile. The double interpolation method enhances solution accuracy, particularly in capturing steep temperature gradients caused by exponential heat generation. This approach is especially valuable for high-temperature chemical reactions, such as combustion, where precise thermal control is essential. The study's results provide insights into the thermal behavior of reactive systems, making it useful for applications like industrial reactors and heat-sensitive processes.

Keywords: Thermal analysis, chemical reactions, exponential heat generation, double interpolation process, reaction kinetics