Numerical modeling of natural convection in a square cavity filled with air: fractional derivative formalism

Abstract

This paper presents a numerical study of natural convection using the fractional derivative formalism. The model adopts nonlinear axis transformations and applies the finite difference method for spatial and temporal discretization in a square cavity filled with an incompressible fluid with a Prandtl number of $Pr = 0.71$. The configuration consists of four rigid walls, subject to a temperature gradient, which serves as the driving force behind the convection. No-slip and constant temperature conditions are applied on the walls. The governing equations are solved using fractional-order operators. Isotherms and streamlines are used to visualize the results, and the influence of varying the order of the fractional derivatives is analyzed to capture fine-scale flow and heat transfer features.