Back
 OJFD  Vol.6 No.2 , June 2016
Numerical Study of Natural Convection in Square Cavity with Inner Bodies Using Finite Element Method
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.
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.
References

[1]   Maliska, C.R. (2014) Transferência de Calor e Mecânica dos Fluidos Computacional. 2nd Edition, LTC—Livros Técnicos e Científicos Editora Ltda, Rio de Janeiro.

[2]   Valencia, A. and Frederick, R.L. (1989) Heat Transfer in Square Cavities with Partially Active Vertical Walls. International Journal of Heat and Mass Transfer, 32, 1567-1574.
http://dx.doi.org/10.1016/0017-9310(89)90078-1

[3]   Ghaddar, N.K. (1992) Natural Convection Heat Transfer between a Uniformly Heated Cylindrical Element and Its Rectangular Enclosure. International Journal of Heat and Mass Transfer, 35, 2327-2334.
http://dx.doi.org/10.1016/0017-9310(92)90075-4

[4]   Kurokawa, F.Y., Zaparoli, E.L. and Andrade, C.R. (2005) Conjugate Natural Convection Applied to the Electronic Component Cooling. Proceedings of the 18th International Congress of Mechanical Engineering, Ouro Preto, 6-11 November 2005, 1-8.

[5]   Jaikrishna, C.R., Rathan, R.B., Aswatha and Seetharamu, K.N. (2010) Effect of Discrete Heat Sources on Natural Convection in a Square Cavity. Proceedings of the 37th National & 4th International Conference on Fluid Mechanics and Fluid Power, Chennai, 16-18 December, 1-10.

[6]   Saravanan, S. and Sivaraj, C. (2011) Natural Convection in an Enclosure with a Localized Nonuniform Heat Source on the Bottom Wall. International Journal of Heat and Mass Transfer, 54, 2820-2828.
http://dx.doi.org/10.1016/j.ijheatmasstransfer.2011.02.058

[7]   Goldstein, R.J., et al. (2010) Heat Transfer—A Review of 2004 Literature. International Journal of Heat and Mass Transfer, 53, 4343-4396.
http://dx.doi.org/10.1016/j.ijheatmasstransfer.2010.05.004

[8]   Goldstein, R.J., et al. (2010) Heat Transfer—A Review of 2005 Literature. International Journal of Heat and Mass Transfer, 53, 4397-4447.
http://dx.doi.org/10.1016/j.ijheatmasstransfer.2010.05.005

[9]   Siddique, M., Khaled, A.R.A., Abdulhafiz, N.I. and Boukhary, A.Y. (2010) Recent Advances in Heat Transfer Enhancements: A Review Report. International Journal of Chemical Engineering, 2010, 1-28.
http://dx.doi.org/10.1155/2010/106461

[10]   Pinto, R.J. (2007) Análise Numérica da Convecção Natural em Cavidade Quadrada com Corpos Internos Utilizando o Método de Elementos Finitos. M.S. Thesis, Federal University of Itajubá, Itajubá.

[11]   Segerlind, L.J. (1984) Applied Finite Element Analysis. 2nd Edition, John Wiley & Sons Inc., New York.

[12]   Menon, G.J. (1984) Convecção Natural no Interior de Coletores Solares Concentradores de Parábolas Compostas. Ph. D. Thesis, Technological Institute of Aeronautics, São José dos Campos.

[13]   Ozoe, H., Yamamoto, K., Sayama, H. and Churchill, S.W. (1974) Natural Circulation in an Inclined Rectangular Channel Heated on One Side and Cooled on the Opposing Side. International Journal of Heat and Mass Transfer, 17, 1209-1217.
http://dx.doi.org/10.1016/0017-9310(74)90121-5

[14]   Tabarrok, B. and Lin, R.C. (1977) Finite Element Analysis of Free Convection Flows. International Journal of Heat and Mass Transfer, 20, 945-952.
http://dx.doi.org/10.1016/0017-9310(77)90065-5

[15]   Figueredo, J.R., Ganzarolli, M.M. and Almeida, P.I.F. (1986) Convecção Natural em Cavidades Retangulares – Solução Numérica. II Congresso Latino-Americano de Transferência de Calor e Matéria, São Paulo, 5-10 October 1986, 62-73.

[16]   Wong, H.H. and Raithby, G.D. (1979) Improved Finite-Difference Methods Based on a Critical Evaluation of the Approximation Errors. Numerical Heat Transfer, 2, 139-163.
http://dx.doi.org/10.1080/10407787908913404

[17]   Souza, J.J. (2006) Simulação Numérica da Transferência de Calor por Convecção Forçada, Natural e Mista numa Cavidade Retangular. M. S. Thesis, Federal University of Itajubá, Itajubá.

[18]   Brito, R.F. (1999) Simulação Numérica da Transferência de Calor e do Escoamento de Fluidos. M. S. Thesis, Federal University of Itajubá, Itajubá.

 
 
Top