Numerical Study of Transient Laminar Natural Convection Cooling of high Prandtl Number Fluids in a Cubical Cavity: Influence of the Prandtl Number
This paper presents and discusses the numerical simulations of transient laminar natural convection cooling of high Prandtl number fluids in cubical cavities, in which the six walls of the cavity are subjected to a step change in temperature. The effect of the fluid Prandtl number on the heat transfer coefficient is studied for three different fluids (Golden Syrup, Glycerin and Glycerin-water solution 50%). The simulations are performed at two different Rayleigh numbers (5·106 and 5·107) and six different Prandtl numbers (3 · 105 ≥Pr≥ 50). Heat conduction through the cavity glass walls is also considered. The propsed correlations of the averaged heat transfer coefficient (N u) showed that it is dependant on the initial Ra and almost independent on P r. The instantaneous flow patterns, temperature contours and time evolution of volume averaged temperature and heat transfer coefficient are presented and analyzed.
[1] W. K. George, S. P. Capp, A theory for natural convection turbulent
boundary layers next to heated vertical surfaces, International Journal of
Heat and Mass Transfer 22 (1979 ) 813-826.
[2] S. W. Armfield, J. C. Patterson, W. Lin, Scaling investigation
of the natural convection boundary layer on an evenly
heated plate. Int. J. Heat Mass Transfer (2006), (in press),
doi:10.1016/j.ijheatmasstransfer.2006.08.020.
[3] C. Y. Warner, V. S. Arpaci, An experimental investigation of turbulent
natural convection in air at low pressure along a vertical heated flat plate.
Int. J. Heat Mass Transfer 11 (1968) 397-406.
[4] R. Cheeswright, Turbulent natural convection from a plane vertical
surface. Journal of Heat Transfer 90 (1968) 1-8.
[5] G. S. H. Lock, F. J. D. Trotter, Observations on the structure of a turbulent
free convection boundary layer. Int. J. Heat Mass Transfer 11 (1968)
1225-1232.
[6] G. C. Vliet, C. K. Liu, An experimental study of turbulent natural
convection boundary layers. Journal of Heat Transfer 91 (1969) 517-531.
[7] T. Fuji, M. Takeuchi, M. Fuji, K. Suzaki, H. Uehara, Experiments on
natural-convection heat transfer from the outer surface of a vertical
cylinder to liquids. Int. J. Heat Mass Transfer 13 (1970) 753-787.
[8] S. S. Kutateladze, A. G. Kirdyashkin, V. P. Ivakin, Turbulent natural
convection on a vertical plate and in a vertical layer. Int. J. Heat Mass
Transfer 15 (1972) 193-202.
[9] K. Kitamura, M. Koike, I. Fukuoka, T. Saito, Large eddy structure and
heat transfer of turbulent natural convection along a vertical flat plate.
Int. J. Heat Mass Transfer 28 (1985) 837-850.
[10] J. C. Patterson, J. Imberger, Unsteady natural convection in a rectangular
cavity, Journal of Fluid mechanics 100 (1980) 65-86.
[11] J. E. B. Nelson, A. R. Balakrishnan, S. S. Murthy, Experimental on
stratified chilled-water tanks, International Journal of Refrigeration 22
(1999) 216-234.
[12] R. J. Shyu, J. Y. Lin, L. J. Fang, Thermal analysis of stratified storage
tanks, Journal of Solar Energy Engineering 111 (1989) 54-61.
[13] J. M. Hyun, Effect of the Prandtl number on heatup of stratified fluid
in an enclosure, ASME Journal of Heat Transfer 107 (1985) 982-984.
[14] Y. S. Lin, R. G. Akins, An experimental study of flow patterns and
heat transfer by natural convection inside cubical enclosures, ASME
conference,Seattle, Washington, USA, July1983.
[15] M.Ogawa, G. Schubert, A. Zebib, Numerical simulations of threedimensional
thermal convection in a fluid with strongly temperaturedependent
visocity, J. Fluid Mechanics 233 (1991) 299-328.
[16] A. Davaille, C. Jaupart, Transient high Rayleigh number thermal convection
with large viscosity variation, J. Fluid Mechanics 25 (1993) 141-166.
[17] M. A. Cotter E. C. Michael, Transient cooling of petroleum by natural
convection in cylindrical storage tanks-II. Effect of heat transfer coefficient,
aspect ratio and temperature -dependent viscosity, International
Journal of Heat and Mass Transfer 36 (1993) 2175-2182.
[18] R.De. C. Oliveski,M. H. Macagnan, J. B. Copetti,A. M. Petroll, Natural
convection in a tank of oil: experimental validation of a numerical code
with prescribed boundary condition, Experimental Thermal and Fluid
Science 29 (2005) 671-680.
[19] O. younis, J. Pallares, F. X. Grau, Effect of the thermal boundary
conditions and physical properties variation on transient natural con-
vection of high Prandtl number fluids, 4th International Conference on
Computational Fluid Dynamics, Ghent, Belgium, 10-14 July, 2006.
[20] J. Pallares, F. X. Grau, F. Giralt, Flow Transitions in Laminar Rayleigh
Bénard Convection in a Cubical Cavity at Moderate Rayleigh Numbers,
Int. J. Heat Mass Transfer 42 (1999) 753-769.
[21] L. Valencia, J. Pallares, I. Cuesta, F. X. Grau, Rayleigh Bet-nard
Convection of water in a perfectly conducting cubical cavity : effects
of temperature -dependent physical properties in laminar and turbulent
regimes, J. Numerical Heat Transfer, part A 47 (2005) 333-352 .
[22] I. Cuesta, Estudi Numeric de Fluxos Laminars i Turbulents en una
Cavitat Cubica, Ph.D. thesis, Universitat Rovira i Virgili, Tarragona,
Spain, 1993.
[1] W. K. George, S. P. Capp, A theory for natural convection turbulent
boundary layers next to heated vertical surfaces, International Journal of
Heat and Mass Transfer 22 (1979 ) 813-826.
[2] S. W. Armfield, J. C. Patterson, W. Lin, Scaling investigation
of the natural convection boundary layer on an evenly
heated plate. Int. J. Heat Mass Transfer (2006), (in press),
doi:10.1016/j.ijheatmasstransfer.2006.08.020.
[3] C. Y. Warner, V. S. Arpaci, An experimental investigation of turbulent
natural convection in air at low pressure along a vertical heated flat plate.
Int. J. Heat Mass Transfer 11 (1968) 397-406.
[4] R. Cheeswright, Turbulent natural convection from a plane vertical
surface. Journal of Heat Transfer 90 (1968) 1-8.
[5] G. S. H. Lock, F. J. D. Trotter, Observations on the structure of a turbulent
free convection boundary layer. Int. J. Heat Mass Transfer 11 (1968)
1225-1232.
[6] G. C. Vliet, C. K. Liu, An experimental study of turbulent natural
convection boundary layers. Journal of Heat Transfer 91 (1969) 517-531.
[7] T. Fuji, M. Takeuchi, M. Fuji, K. Suzaki, H. Uehara, Experiments on
natural-convection heat transfer from the outer surface of a vertical
cylinder to liquids. Int. J. Heat Mass Transfer 13 (1970) 753-787.
[8] S. S. Kutateladze, A. G. Kirdyashkin, V. P. Ivakin, Turbulent natural
convection on a vertical plate and in a vertical layer. Int. J. Heat Mass
Transfer 15 (1972) 193-202.
[9] K. Kitamura, M. Koike, I. Fukuoka, T. Saito, Large eddy structure and
heat transfer of turbulent natural convection along a vertical flat plate.
Int. J. Heat Mass Transfer 28 (1985) 837-850.
[10] J. C. Patterson, J. Imberger, Unsteady natural convection in a rectangular
cavity, Journal of Fluid mechanics 100 (1980) 65-86.
[11] J. E. B. Nelson, A. R. Balakrishnan, S. S. Murthy, Experimental on
stratified chilled-water tanks, International Journal of Refrigeration 22
(1999) 216-234.
[12] R. J. Shyu, J. Y. Lin, L. J. Fang, Thermal analysis of stratified storage
tanks, Journal of Solar Energy Engineering 111 (1989) 54-61.
[13] J. M. Hyun, Effect of the Prandtl number on heatup of stratified fluid
in an enclosure, ASME Journal of Heat Transfer 107 (1985) 982-984.
[14] Y. S. Lin, R. G. Akins, An experimental study of flow patterns and
heat transfer by natural convection inside cubical enclosures, ASME
conference,Seattle, Washington, USA, July1983.
[15] M.Ogawa, G. Schubert, A. Zebib, Numerical simulations of threedimensional
thermal convection in a fluid with strongly temperaturedependent
visocity, J. Fluid Mechanics 233 (1991) 299-328.
[16] A. Davaille, C. Jaupart, Transient high Rayleigh number thermal convection
with large viscosity variation, J. Fluid Mechanics 25 (1993) 141-166.
[17] M. A. Cotter E. C. Michael, Transient cooling of petroleum by natural
convection in cylindrical storage tanks-II. Effect of heat transfer coefficient,
aspect ratio and temperature -dependent viscosity, International
Journal of Heat and Mass Transfer 36 (1993) 2175-2182.
[18] R.De. C. Oliveski,M. H. Macagnan, J. B. Copetti,A. M. Petroll, Natural
convection in a tank of oil: experimental validation of a numerical code
with prescribed boundary condition, Experimental Thermal and Fluid
Science 29 (2005) 671-680.
[19] O. younis, J. Pallares, F. X. Grau, Effect of the thermal boundary
conditions and physical properties variation on transient natural con-
vection of high Prandtl number fluids, 4th International Conference on
Computational Fluid Dynamics, Ghent, Belgium, 10-14 July, 2006.
[20] J. Pallares, F. X. Grau, F. Giralt, Flow Transitions in Laminar Rayleigh
Bénard Convection in a Cubical Cavity at Moderate Rayleigh Numbers,
Int. J. Heat Mass Transfer 42 (1999) 753-769.
[21] L. Valencia, J. Pallares, I. Cuesta, F. X. Grau, Rayleigh Bet-nard
Convection of water in a perfectly conducting cubical cavity : effects
of temperature -dependent physical properties in laminar and turbulent
regimes, J. Numerical Heat Transfer, part A 47 (2005) 333-352 .
[22] I. Cuesta, Estudi Numeric de Fluxos Laminars i Turbulents en una
Cavitat Cubica, Ph.D. thesis, Universitat Rovira i Virgili, Tarragona,
Spain, 1993.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:60223", author = "O. Younis and J. Pallares and F. X. Grau", title = "Numerical Study of Transient Laminar Natural Convection Cooling of high Prandtl Number Fluids in a Cubical Cavity: Influence of the Prandtl Number", abstract = "This paper presents and discusses the numerical simulations of transient laminar natural convection cooling of high Prandtl number fluids in cubical cavities, in which the six walls of the cavity are subjected to a step change in temperature. The effect of the fluid Prandtl number on the heat transfer coefficient is studied for three different fluids (Golden Syrup, Glycerin and Glycerin-water solution 50%). The simulations are performed at two different Rayleigh numbers (5·106 and 5·107) and six different Prandtl numbers (3 · 105 ≥Pr≥ 50). Heat conduction through the cavity glass walls is also considered. The propsed correlations of the averaged heat transfer coefficient (N u) showed that it is dependant on the initial Ra and almost independent on P r. The instantaneous flow patterns, temperature contours and time evolution of volume averaged temperature and heat transfer coefficient are presented and analyzed.
", keywords = "Transient natural convection, High Prandtl number, variable viscosity.", volume = "1", number = "12", pages = "758-6", }
