Non-Darcian Effects on Buoyancy-Induced Heat Transfer in a Partially Divided Square Enclosure with Internal Heat Generation

• Published in: Transport in porous media Vol. 84; no. 3; pp. 663 - 683
• Main Authors: Marafie, Alia, Khanafer, Khalil, Pop, Ioan
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.09.2010; Springer; Springer Nature B.V
• Subjects: Buoyancy; Civil Engineering; Classical and Continuum Physics; Computational fluid dynamics; Darcy number; Earth and Environmental Science; Earth Sciences; Earth, ocean, space; Enclosure; Enclosures; Engineering and environment geology. Geothermics; Exact sciences and technology; Finite element method; Fluid flow; Galerkin method; Galerkin methods; Geotechnical Engineering & Applied Earth Sciences; Heat generation; Heat transfer; Hydrocarbons; Hydrogeology; Hydrology. Hydrogeology; Hydrology/Water Resources; Industrial Chemistry/Chemical Engineering; Mathematical analysis; Mathematical models; Parameters; Pollution, environment geology; Sedimentary rocks; Viscosity; Galerkin numerical method; Non-Darcian effects; Buoyancy-induced flow; Square enclosure; models; isotherms; transport; finite element analysis; buoyancy; Galerkin method; equilibrium; porous media; heat transfer; methodology
• ISSN: 0169-3913; 1573-1634
• DOI: 10.1007/s11242-010-9531-x

The present investigation addresses non-Darcian effects on the buoyancy-induced heat transfer in a partially divided square enclosure with internal heat generation. The generalized model of the momentum equation, which is also known as the Forchheimer–Brinkman extended Darcy model, which takes into account boundary and inertia effects, was used in representing the fluid motion inside the porous layer. The local thermal equilibrium condition was assumed to be valid for the range of the thermophysical parameters considered in the present investigation. The transport equations were solved using the finite element formulation based on the Galerkin method of weighted residuals. The validity of the numerical code used was ascertained by comparing our results with previously published results. Results were obtained in terms of streamlines, isotherms, and Nusselt number for various geometrical parameters specifying the height and width of the partition. In addition, the effects of external and internal Rayleigh numbers and Darcy number were highlighted in the proposed study.