Convective Heat Transfer in Brinkman–Darcy–Kelvin–Voigt Fluid with Variable Gravity and Generalized Maxwell–Cattaneo Law

Abstract

This article investigates thermal convection in Kelvin–Voigt fluids saturating a Brinkman–Darcy-type porous medium under variable gravity effects. The stability analysis encompasses linear, nonlinear conditional, and nonlinear unconditional regimes, leveraging the generalized Maxwell–Cattaneo law for heat flux. Normal mode technique is applied for linear analysis, while nonlinear governing equations for conditional and unconditional stability are derived using energy methods. The compound matrix method is utilized to compute critical Rayleigh numbers and corresponding wave numbers. Numerical computations are performed in MATLAB to determine all critical values, with graphical results illustrating stability trends. Six gravity variation profiles are examined, revealing that the gravity modulation parameter \(\epsilon\) influences stability depending on the gravity profile, either promoting or suppressing convection. Additionally, the parameter \(\xi\) consistently enhances stability by increasing the critical Rayleigh numbers across all cases. These findings highlight the role of gravity variations and material parameters in shaping convection onset, contributing to a deeper understanding of thermal stability in viscoelastic porous systems.