Heat Transfer Characteristics and Variable Thermophysical Properties of Naturally Convective Flow of Viscous Fluid Inside a Porous Square Cavity

The primary purpose of our work is to investigate and quantify the influence of temperature-dependent thermophysical properties on the behavior of natural convection with a porous medium. Recognizing that the properties of real fluids vary significantly with temperature, especially under the large thermal gradients common in porous media, we aim to understand how this variation affects flow patterns and heat distribution, moving beyond simplified models that assume constant properties. To achieve this, we specially examine spontaneous convection in a viscous fluid inside a square cavity where the vertical walls undergo sinusoidal oscillation and the horizontal walls are adiabatic. Fluid flow is simulated using the Boussinesq approximation and Darcy's law. Using similarity transformations, the governing equations are transformed into dimensionless form and then numerically solved using the Peaceman–Rachford alternating direction implicit technique and Gauss–Jordan elimination. The results demonstrate that taking temperature-dependent characteristics into consideration greatly increases convection, leading to more robust rolls, improved circulation, and densely packed streamlines. The distribution of temperatures is significantly changed, with isotherms smoothing/expanding with more conduction and sharpening close to heat sources under low conduction. The shifting interaction between convection and diffusion is also reflected in the isoconcentration patterns, which seem more uniformly distributed with higher diffusivity and more localized with low diffusivity.