Numerical Study of Mixed Convection Coupled to Radiation in a Square Cavity with a Lid-Driven
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.
[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.
[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.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:71343", author = "Mohamed Amine Belmiloud and Nord Eddine Sad Chemloul", title = "Numerical Study of Mixed Convection Coupled to Radiation in a Square Cavity with a Lid-Driven", 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.", volume = "9", number = "10", pages = "1815-7", }
