Cattaneo–Christov model for Marangoni convection in Casson fluid with thermal radiation and activation energy under dual-phase heat transfer

This study investigates the effect of local thermal non-equilibrium (LTNE) conditions on the flow of Casson fluid under elastic deformation along a stretched boundary. The Cattaneo–Christov flux framework is used to model thermal and mass diffusion, incorporating non-classical effects of thermal and concentration relaxation phenomena. Furthermore, the model accounts for thermal radiation, activation energy, and an internal heat source, offering a more comprehensive representation of energy transfer in non-Newtonian fluid systems. These physical effects are particularly relevant in technical applications that require precise heat transfer control between fluid and solid phases, such as heat exchangers, geothermal systems, and thermal control devices. The model is also applicable in industrial processes that involve viscoplastic or yield-stress fluids, such as polymer extrusion, oil recovery, and food processing. By applying similarity transformations, the governing partial differential equations are reduced to a set of coupled ordinary differential equations, which are numerically solved using MATLAB’s bvp4c solver. The results reveal that increasing the interphase heat transfer coefficient $\left(N_h\right)$ from 1.0 to 5.0 causes a 23.7% reduction in the fluid-phase temperature and a 31.4% reduction in the solid-phase temperature at a fixed location. Furthermore, the presence of thermal radiation ($Rd=2$) and internal heat generation ($Q=1.5$) amplifies this cooling effect by an additional 12.5% compared to the case without these effects. These findings emphasize the critical role of the LTNE parameters and energy transport mechanisms in optimizing thermal performance in engineering systems.