Time-dependent solution for natural convection in a porous enclosure using the Darcy–Lapwood–Brinkman model

Natural convection (NC) in high permeable porous media is usually investigated using the Darcy–Lapwood–Brinkman model (DLB). The problem of squared cavity widely used as a common benchmark case for NC media. solutions to this with DLB are limited steady-state conditions. In paper, we developed time-dependent accurate solution based on Fourier–Galerkin method (FG). derived considering two configurations dealing unsteady and transient modes. governing equations reformulated stream function. Temperature functions expended unknowns space Fourier series which appropriately substituted equations. then projected spectral trigonometric trial functions. obtained form nonlinear differential algebraic system An appropriate technique integrate time ensure accuracy. results FG compared finite element different Rayleigh Darcy numbers values. feasible low computational cost. paper provides useful benchmarking numerical models efficient gain physical insight into processes.