Analysis of heat and mass transfer of a non-linear convective heat generating fluid flow in a porous medium with variable viscosity

Abstract

The present study addresses the significance of analyzing the heat and mass transfer characteristics of a non-linear convective fluid flow featuring variable viscosity within a porous medium. Our focus lies on understanding the impact of varying viscosity on the hydromagnetic coupling stress, particularly in the presence of internal heat generation. The fluid is confined within a porous medium, and convection cooling takes place at both wall of the fluid. A key assumption in our investigation is the nonlinearity nature of the buoyancy force, specifically when there is a substantial difference in temperature and concentration within the fluid and its surroundings, the buoyancy force becomes quadratic. The exploration of couple stress fluids, alongside considerations of temperature-dependent internal heat generation and mass transfer, contributes to advancing our understanding of thermal system performance. By accounting for nonlinearity in density, temperature, and concentration, the research aims to provide more accurate results than previous linear models, crucial for optimizing energy consumption in practical applications such as nuclear reactors and heat exchangers. Dealing with this type of problem often pose significant challenges, as they often lack analytical solutions, necessitating the use of more advanced numerical methods or approximation techniques. We employ Spectral Quasilinearisation Method (SQLM) to solve the coupled non-linear boundary value problems (PDE) arising from the model, momentum equation, energy equation, concentration equation, and entropy generation. The obtained results are then validated using the Runge–Kutta method and a good agreement is achieved. The findings for the dimensionless velocity, temperature, mass concentration and entropy generation are presented in graphics and in table manner, and effects of controlling parameters are extensively explained. The results highlight that an increase in variable viscosity leads to an enhancement in the velocity profile, while simultaneously reducing the temperature in the system. Furthermore, increments in the non-linear convection parameter and coupling stress parameter result in an appreciation of the velocity profile, temperature profile, and entropy generation rate.