A numerical simulation of the turbulent transport from an isolated heat source in a square cavity with side openings is presented in this work. The openings allow an externally induced air stream at ambient temperature to flow through the cavity and, thus, mixed convection arises. Results for the turbulent regime are obtained, by employing a suitable, high-Reynolds-number from of the K–E turbulence model. A stream function-vorticity mathematical formulation is used, along with the kinetic energy and dissipation rate equations and an expression for the eddy viscosity. A time-marching scheme is employed, using the ADI method. The values of the Reynolds number Re, associated with the external flow, and the Grashof number Gr, based on the heat flux from the source, for which turbulent flow sets in are sought. Two typical values of the Reynolds number are chosen, Re = 1000 and Re = 2000, and turbulent results are obtained in the range Gr = 5 × 107 – 5 × 108. For both values of Re, the average Nusselt number over the surface of the source is found to vary with Gr in a fashion consistent with previous numerical and experimental results for closed cavities, while the effect of Re in the chosen range of values was small.

1.
Abrous, A., and Emery, A. F., 1989, “Turbulent Free Convection in Square Cavities With Mixed Boundary Conditions,” in: Heat Transfer in Convective Flows, R. K. Shah, ed., ASME HTD-Vol. 107, pp. 117–130.
2.
Arpaci, V. S., and Larsen, P. S., 1984, Convection Heat Transfer, Prentice-Hall, Englewood Cliffs, NJ.
3.
Cha
 
C. K.
, and
Jaluria
 
Y.
,
1984
, “
Effect of Thermal Buoyancy on the Recirculating Flow in a Solar Pond for Energy Extraction and Heat Rejection
,”
ASME Journal of Solar Energy Engineering
, Vol.
106
, pp.
428
437
.
4.
Fraikin
 
M.-P.
,
Portier
 
J. J.
, and
Fraikin
 
C. J.
,
1982
, “
Application of a k–ε Turbulence Model to an Enclosed Buoyancy Driven Recirculating Flow
,”
Chem. Eng. Commun.
, Vol.
13
, pp.
289
314
.
5.
Hanjalic, K., and Vasic, S., 1990, “Numerical Simulation of Free Convection in Single- and Multiple-Zone Rectangular Cavities,” Proc. 9th Int. Heat Transfer Conf., Jerusalem, Israel, Vol. 2, pp. 579–584.
6.
Henkes, R. A. W. M., 1990, “Natural Convection Boundary Layers,” Ph.D. Thesis, Delft University, Delft, The Netherlands.
7.
Hjertager, B. H., and Magnussen, B. F., 1977, “Numerical Predicition of Three-Dimensional Turbulent Buoyant Flow in a Ventilated Room,” in: Heat Transfer and Turbulent Buoyant Convection, D. B. Spalding and N. Afgan, eds., Vol. II, pp. 429–442, Hemisphere, Washington DC.
8.
Hoogendoorn, C. J., 1985, “The Flow of Stratified Air Layers in Horizontal Channels,” in: Natural Convection: Fundamentals and Applications, S. Kakac, W. Aung, and R. Viskanta, eds., pp. 443–460, Hemisphere, Washington DC.
9.
Humphrey
 
J. A. C.
, and
To
 
W. M.
,
1986
, “
Numerical Simulation of Buoyant, Turbulent Flow—II. Free and Mixed Convection in a Heated Cavity
,”
Int. J. Heat Mass Transfer
, Vol.
29
, pp.
593
610
.
10.
Launder
 
B. E.
, and
Spalding
 
D. B.
,
1974
, “
The Numerical Computation of Turbulent Flows
,”
Comp. Meth. Appl. Mech, Eng.
, Vol.
3
, pp.
269
289
.
11.
Markatos
 
N. C.
, and
Pericleous
 
K. A.
,
1984
, “
Laminar and Turbulent Natural Convection in an Enclosed Cavity
,”
Int. J. Heat Mass Transfer
, Vol.
27
, No.
5
, pp.
755
772
.
12.
Mokhtarzadeh-Dehghan
 
M. R.
,
El Telbany
 
M. M. M.
, and
Reynolds
 
A. J.
,
1990
, “
Transfer Rates in Single-Sided Ventilation
,”
Building and Environment
, Vol.
25
, No.
2
, pp.
155
161
.
13.
Nielsen
 
P. V.
,
1975
, “
Predicition of Air Flow and Comfort in Air Conditioned Spaces
,”
ASHRAE Transactions
, Vol.
81
, part II, pp.
247
259
.
14.
Nobile, E., Sousa, A. C. M., and Barozzi, G. S., 1990, “Turbulent Buoyant Flows in Enclosures,” Proc. 9th Int. Heat Transfer Conf., Jerusalem, Israel, Vol. 2, pp. 543–548.
15.
Ozoe, H., Mouri, A., Hiramitsu, M., Churchill, S. W., and Lior, N., 1984, “Numerical Calculation of Three-Dimensional Turbulent Natural Convection in a Cubical Enclosure Using a Two-Equation Model,” in: Fundamentals of Natural Convection/Electronic Equipment Cooling, L. C. Witte and L. S. Saxena, eds., ASME HTD-Vol. 32, pp. 25–32.
16.
Ozoe
 
H.
,
Mouri
 
A.
,
Ohmuro
 
M.
,
Churchill
 
S. W.
, and
Lior
 
N.
,
1985
, “
Numerical Calculations of Laminar and Turbulent Natural Convection in Water in Rectangular Channels Heated and Cooled Isothermally on the Opposing Vertical Walls
,”
Int. J. Heat Mass Transfer
, Vol.
28
, No.
1
, pp.
125
138
.
17.
Ozoe, H., Miyachi, H., Hiramitsu, M., and Matsui, T., 1986, “Numerical Computation of Natural Convection in a Cubical Enclosure With Ventilation for Both a Laminar and a Two-Equation Turbulent Model,” Proc. 8th Int. Heat Transfer Conf., San Francisco, CA, Vol. 4, pp. 1489–1494.
18.
Paolucci
 
S.
, and
Chenoweth
 
D. R.
,
1989
, “
Transition to Chaos in a Differentially Heated Vertical Cavity
,”
J. Fluid Mech.
, Vol.
201
, pp.
379
410
.
19.
Papanicolaou
 
E.
, and
Jaluria
 
Y.
,
1990
, “
Mixed Convection From an Isolated Heat Source in a Rectangular Enclosure
,”
Num. Heat Transfer
, Part A, Vol.
18
, pp.
427
461
.
20.
Papanicolaou, E., 1991, “Mixed Convection From Isolated Heat Sources in a Cavity: a Study of Various Regimes and Configurations,” Ph.D. Thesis, Rutgers University, New Brunswick, NJ.
21.
Papanicolaou
 
E.
, and
Jaluria
 
Y.
,
1992
, “
Transition to a Periodic Regime in Mixed Convection in a Square Cavity
,”
J. Fluid Mech.
, Vol.
239
, pp.
489
509
.
22.
Patankar, S. V., 1980, Numerical Heat Transfer and Fluid Flow, Hemisphere, Washington DC.
23.
Roache, P. J., 1972, Computational Fluid Dynamics, Hermosa Publishers, Albuquerque, NM.
24.
Rodi, W., 1980, “Turbulence Models and Their Application in Hydraulics—A State of the Art Review,” International Association of Hydraulic Research, Delft, The Netherlands.
25.
Thompson, C. P., Wilkes, N. S., and Jones, I. P., 1985, “Numerical Studies of Buoyancy Driven Turbulent Flow in a Rectangular Cavity,” in: Numerical Methods in Thermal Problems, R. W. Lewis and K. Morgan, eds., Proc. 4th Int. Conf., Swansea, United Kingdom, pp. 353–364.
This content is only available via PDF.
You do not currently have access to this content.