Magnetohydrodynamic reactive flow of a third-grade fluid between horizontal plates with variable properties including thermal radiation and convective cooling

Abstract

The temperature-dependent nature of viscosity and thermal conductivity, combined with thermal radiation and convective boundary conditions, creates a complex yet realistic problem that requires advanced analytical techniques to solve. This study explores the flow of a magnetohydrodynamic (MHD) viscous fluid of third-grade reactivity, sandwiched between horizontal plates and undergoing convective cooling, with varying thermal conductivity, viscosity, and pre-exponential force. The fluid's thermal conductivity and viscosity are represented through a temperature-dependent non-linear relationship, accurately mirroring real-world conditions. The fluid is treated as optically thin, and thermal radiation is accounted for using the Cogley model, while chemical reactions follow the Arrhenius law. Using the boundary layer approximation, the governing equations become steady, incompressible momentum equations and energy equations. These equations result in nonlinear coupled regular differential equations that can't be solved precisely. Thus, the Homotopy Analysis Technique, a recent perturbation technique, is utilized to solve these equations after they have been non-dimensionalized with suitable variables. Temperature-dependent viscosity shows contrasting behaviors for gases and liquids, with the Frank-Kamenetskii parameter exhibiting critical behavior in controlling reaction rates and thermal runaway conditions. Radiation effects contribute significantly to heat transfer enhancement, while convective boundary conditions provide realistic heat transfer scenarios that bridge the gap between isothermal and adiabatic conditions in industrial applications. The study explores the effects of key parameters on reaction rates, including Arrhenius, biomolecular, and sensitized reactions. Moreover, the temperature and velocity profiles are displayed and illustrated graphically for different flow conditions, with the results highlighting the impact on skin friction.