TITLE:
Numerical Study of Natural Convection in Square Cavity with Inner Bodies Using Finite Element Method
AUTHORS:
Renato José Pinto, Paulo Mohallem Guimarães, Genésio José Menon
KEYWORDS:
Heat Transfer, Natural Convection, Square Cavity, Finite Element Method, Inner Body
JOURNAL NAME:
Open Journal of Fluid Dynamics,
Vol.6 No.2,
April
29,
2016
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.