Natural convection in rectangular enclosures heated from below and symmetrically cooled from the sides

Steady natural convection in an enclosure heated from below and symmetrically cooled from the sides is studied numerically, using a streamfunction-vorticity formulation. The Allen discretization scheme is adopted and the discretized equations were solved in a line by line basis. The Rayleigh number based on the cavity height is varied from 103 to 107. Values of 0.7 and 7.0 for the Prandtl number are considered. The aspect ratio LH (length to height of the enclosure) is varied from 1 to 9. Boundary conditions are uniform wall temperature and uniform heat flux. For the range of the parameters studied, a single cell is observed to represent the flow pattern. Numerical values of the Nusselt number as a function of the Rayleigh number are reported, and the Prandtl number is found to have little influence on the Nusselt number. A scale analysis is presented in order to better understand the phenomenon.

[1]  V. G. Jenson.  Viscous flow round a sphere at low Reynolds numbers (<40) , 1959, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[2]  S. Ostrach.  Natural convection in enclosures , 1988 .

[3]  A. Bejan.  Convection Heat Transfer , 1984 .

[4]  M. Nansteel,et al.  Natural convection in rectangular enclosures heated from below and cooled along one side , 1987 .

[5]  R. Pletcher,et al.  Computational Fluid Mechanics and Heat Transfer. By D. A ANDERSON, J. C. TANNEHILL and R. H. PLETCHER. Hemisphere, 1984. 599 pp. $39.95. , 1986, Journal of Fluid Mechanics.

[6]  Dimos Poulikakos,et al.  Natural Convection in a Confined Fluid-Filled Space Driven by a Single Vertical Wall With Warm and Cold Regions , 1985 .

[7]  P. M. Ku.  ASME winter annual meeting , 1978 .

[8]  Guy Lauriat,et al.  THE HORIZONTAL NATURAL CONVECTION BOUNDARY LAYER REGIME IN A CLOSED CAVITY , 1986 .

[9]  V. Carey,et al.  Proceedings of the eighth international heat transfer conference , 1986 .

[10]  D. N. De G. Allen,et al.  RELAXATION METHODS APPLIED TO DETERMINE THE MOTION, IN TWO DIMENSIONS, OF A VISCOUS FLUID PAST A FIXED CYLINDER , 1955 .

[11]  A. Bejan,et al.  Natural convection in a differentially heated corner region , 1985 .

[12]  A. Bejan,et al.  Penetration of free convection into a lateral cavity , 1981, Journal of Fluid Mechanics.

[13]  Effect of Stabilizing Thermal Gradients on Natural Convection in Rectangular Enclosures , 1979 .