Numerical study of unsteady reactive third-grade fluid flow in a microchannel through a porous medium subject to exothermic reaction

The purpose of this study is to investigate the transient dynamics of a third-grade fluid, which can undergo exothermic reactions in a saturated porous microchannel. The adverse pressure gradient force constitutes the primary flow driver. In addition to exothermic reactions, the system is also subjected convective cooling at the microchannel boundaries. Newton’s law of cooling and Arrhenius kinetics are employed to model the boundary cooling and exothermic reactions, respectively. The temperature-dependent fluid viscosity is modelled via a Nahme-type law and the porous material between the parallel microchannels is assumed to have constant permeability. To account for this, the unsteady modified Darcy’s law is applied, effectively capturing the impact of porosity. Computational solutions are employed to solve the non-homogeneous partial differential equations (PDEs) for the flow temperature and velocity. These computational solutions are developed from efficient, convergent and unconditionally stable, semi-implicit finite difference (SIFD) methods. Examining the thermodynamic and fluid-dynamical consequences of variations in the numerical exponent \(\aleph \) $\aleph$ and exothermic reaction parameter \(\delta _2\) ${\delta }_2$ are the principal motives of the study. A comparative evaluation of the thermal runaway susceptibility of the numerical exponent parameter for two distinct types of fluids is outlined, indicating that the ranking of susceptibility ranges from most to least susceptible in the bimolecular case, the Arrhenius case and the sensitised case. Newtonian fluids are the most prone to non-Newtonian fluids. Additionally, the study systematically explores the sensitivity of field variables to changes in different flow parameters through graphical representations and shows that the fluid variables increase with the increase in Reynolds number, viscosity parameter and Brinkman number, while decrease for the third-order parameter and porous medium parameter. The obtained results are qualitatively discussed and compared with the published data.