Numerical Study of Natural Convection in Square Cavity with Inner Bodies Using Finite Element Method

Renato José  Pinto; Paulo Mohallem  Guimarães; Genésio José  Menon

doi:10.4236/ojfd.2016.62007

Renato José Pinto, Paulo Mohallem Guimarães, Genésio José Menon

Abstract: A numerical study of heat transfer problem by natural convection of a fluid inside a square cavity with two inner bodies is presented. This subject is of great interest in the engineering area, mainly in applications involving development of heat exchangers and cooling or heating systems of bodies by natural convection mechanism. Two cases have been studied. The inner bodies are square in case 1 and circular in case 2. In both cases, the bodies are solid and thermally conductive, the cavity lower and upper horizontal surfaces are isothermal with high temperature Th and low temperature Tc, respectively. Both vertical surfaces are adiabatic. A FORTRAN code using Finite Element Method (FEM) is developed to simulate the problem and solve the governing equations. The distributions of stream function, ψ, dimensionless temperature, θ, and vorticity, ω, are determined. Heat transfer is evaluated by analyzing the behavior of the average Nusselt number. The Grashof number and thermal diffusivity ratio are considered in range from 2 × 104 to 105 and from 0.1 to 100, respectively. The fluid is air with Prandtl number fixed in 0.733.

Keywords: Heat Transfer, Natural Convection, Square Cavity, Finite Element Method, Inner Body

Cite this paper: Pinto, R. , Guimarães, P. and Menon, G. (2016) Numerical Study of Natural Convection in Square Cavity with Inner Bodies Using Finite Element Method. Open Journal of Fluid Dynamics, 6, 75-87. doi: 10.4236/ojfd.2016.62007.

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