Numerical Study of Mixed Convection Coupled to Radiation in a Square Cavity with a Lid-Driven
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32799
Numerical Study of Mixed Convection Coupled to Radiation in a Square Cavity with a Lid-Driven

Authors: Mohamed Amine Belmiloud, Nord Eddine Sad Chemloul

Abstract:

In this study, we investigated numerically heat transfer by mixed convection coupled to radiation in a square cavity; the upper horizontal wall is movable. The purpose of this study is to see the influence of the emissivity ε and the varying of the Richardson number Ri on the variation of average Nusselt number Nu. The vertical walls of the cavity are differentially heated, the left wall is maintained at a uniform temperature higher than the right wall, and the two horizontal walls are adiabatic. The finite volume method is used for solving the dimensionless Governing Equations. Emissivity values used in this study are ranged between 0 and 1, the Richardson number in the range 0.1 to 10. The Rayleigh number is fixed to Ra=104 and the Prandtl number is maintained constant Pr=0.71. Streamlines, isothermal lines and the average Nusselt number are presented according to the surface emissivity. The results of this study show that the Richardson number Ri and emissivity ε affect the average Nusselt number.

Keywords: Numerical study, mixed convection, square cavity, wall emissivity, lid-driven.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1109928

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2194

References:


[1] B. Gebhart, Y. Jaluria, R. L. Mahajan and B. Sammakia, Buoyancy induced flows and transport, Hemisphere, New York (1988) 699-723.
[2] M. Hasnaoui, E. Bilgen and P. Vasseur, Natural convection above an array of open cavities heated from below, AIAA J. Thermophys. Heat Transfer, 6 (1990) 255-264
[3] R. Iwatsu, J. M. Hyun and K. Kuwahara, Numerical simulation of flows driven by a torsionally oscillating lid in a square cavity, J. Fluids Eng., 114 (1992) 143-151.
[4] R. Iwatsu, J. M. Hyun and K. Kuwahara, Mixed convection in a driven cavity with a stable vertical temperature gradient, Intl. J. Heat Mass Transfer, (36) (1993) 1601-1608.
[5] R. Iwatsu and J. M. Hyun, Three-dimensional driven cavity flows with a vertical temperature gradient, Intl. J. Heat Mass Transfer, (38) (1995) 3319-3328.
[6] S. C. Lee and C. K. Chen, Finite element solutions of laminar and turbulent mixed convection in a driven cavity, Int. J. Numer. Methods Fluids, 23 (1996) 47-64.
[7] N. Moraga and S. López, Numerical simulation of three dimensional mixed convection in an air-cooled cavity, Numerical Heat Transfer, Part A, 45 (8) (2004) 811-824.
[8] M. A. R. Sharif, Laminar mixed convection in shallow inclined driven cavities with hot moving lid on top and cooled from bottom, Applied Thermal Engineering, 27 (2007) 1036-1042.
[9] W.-A. Khan and R. S. R. Gorla, Mixed convection of power-law fluids along a vertical wedge with convective boundary condition in a porous medium, Journal of Mechanical Science and Technology, 24 (9) (2010) 1313-1325
[10] W. Aich, I. Hajri and A. Omri, Numerical analysis of natural convection in a prismatic enclosure, Thermal science, 15 (2) (2011) 437-446.
[11] T. Fusegi, K. Ishii, B. Farouk, and K. Kuwahara, Natural Convection- Radiation Interactions in a Cube Filled with a Nongray Gas, Numer. Heat Transfer A, vol. 19, pp. 207–217, 1991.
[12] J. E. Hutchison and R. F. Richards, Effect of Non-gray Gas Radiation on Thermal Stability in Carbon Dioxide, J. Thermophys. Heat Transfer, vol. 13, pp. 25–32, 1999.
[13] A. Yucel and S. Acharya, Natural Convection of a Radiating Fluid in a Partially Divided Square Enclosure, Numer. Heat Transfer A, vol. 19, pp. 471–485, 1991.
[14] C. Mesyngier and B. Farouk, Turbulent Natural Convection-Nongray Gas Radiation Analysis in a Square Enclosure, Numer. Heat Transfer A, vol. 29, pp. 671–687, 1996.
[15] E. Yu and Y. Joshi, Effects of Orthotropic Thermal Conductivity of Substrates in Natural Convection Cooling of Discrete Heat Sources, Numer. Heat Transfer A, vol. 32, pp. 575– 593, 1997
[16] C. I. Baek and K. S. Lee, Study of Combined Heat Transfer in a Three- Dimensional Enclosure with a Protruding Heat Source, Numer. Heat Transfer A, vol. 32, pp. 733–747, 1997
[17] D. C. Kuo, J. C. Morales, and K. S. Ball, Combined Natural Convection and Volumetric Radiation in a Horizontal Annulus: Spectral and Finite Volume Predictions, J. Heat Transfer, vol. 121, pp. 610–615, 1999
[18] W.-M. Yan and H.-Y. Li, Radiation Effects on Mixed Convection Heat Transfer in a Vertical Square Duct, Int. J. Heat Mass Transfer, vol. 44, pp. 1401–1410, 2001.
[19] C. G. Rao, C. Bamaji, and S. P. Venkateshan, Effect of Surface Radiation on Conjugate Mixed Convection in a Vertical Channel with a Discrete Heat Source in Each Wall, Int. J. Heat Mass Transfer, vol 45, pp. 3331–3347, 2002.
[20] B. Straughan, Global Stability for Convection Induced by Absorption of Radiation, Dynam. Atmos. Oceans, vol. 35, pp. 351–361, 2002.
[21] C. H. Lan, O. A. Ezekoye, J. R. Howell, and K. S. Ball, Stability Analysis for Three Dimensional Rayleigh-Be´nard Convection with Radiatively Participating Medium Using Spectral Methods, Int. J. Heat Mass Transfer, vol. 46, pp. 1371–1383, 2003.
[22] K. A. R. Ismail and C. S. Salinas, Application of Multidimensional Scheme and the Discrete Ordinate Method to Radiative Heat Transfer in a Two-Dimensional Enclosure with Diffusely Emitting and Reflecting Boundary Walls, J. Quant. Spectrosc. Radiat. Transfer, vol. 88, pp. 407– 422, 2004.
[23] S. N. Singh and S. P. Venkateshan, Numerical Study of Natural Convection with Surface Radiation in Side-Vented Open Cavities, Int. J. Thermal Sci., vol. 43, pp. 865–876, 2004
[24] X. Cui and B. Q. Li, A Discontinuous Finite-Element Formulation for Radiative Transfer in Axisymmetric Finite Cylindrical Enclosure and Couping with Other Mode Heat Transfer, Numer. Heat Transfer B, vol. 48, pp. 317–344, 2005.
[25] S. V. Patankar, Numerical heat transfer and fluid flow, Hemisphere/McGraw-Hill, Washington D.C. (1980).
[26] T. Hayase, J. C. Humphrey and R. Greif, A consistently formulated quick scheme for fast and stable convergence using finite-volume iterative calculation procedures, J. Comput. Phy, 98 (1992) 118-18.
[27] Akiyama M, Chong QP. Numerical analysis of natural convection with surface radiation in a square enclosure. Numer Heat Transfer Part A 1997; 31:419–33.
[28] M. K. Moallemi and K. S. Jang, Prandtl number effects on laminar mixed convection heat transfer in a lid-driven cavity, Intl. J. Heat Mass Transfer, 35 (1992) 1881-1892
[29] J. C. Roy; T. Boulard; C. Kittas; S. Wang, Convective and Ventilation Transfers in Greenhouses, Part 1: the Greenhouse considered as a Perfectly Stirred Tank, Biosystems Engineering (2002) 83 (1), 1–20.