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TECHNICAL PAPERS: Natural and Mixed Convection

Laminar Natural Convection Heat Transfer in a Differentially Heated Square Cavity Due to a Thin Fin on the Hot Wall

[+] Author and Article Information
Xundan Shi, J. M. Khodadadi

Mechanical Engineering Department, Auburn University, 201 Ross Hall, Auburn, AL 36849-5341

J. Heat Transfer 125(4), 624-634 (Jul 17, 2003) (11 pages) doi:10.1115/1.1571847 History: Received August 12, 2002; Revised March 05, 2003; Online July 17, 2003
Copyright © 2003 by ASME
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References

Ostrach,  S., 1988, “Natural Convection in Enclosures,” ASME J. Heat Transfer, 110, pp. 1175–1190.
Gebhart, B., Jaluria, Y., Mahajan, R. L., and Sammakia, B., 1988, Buoyancy-Induced Flows and Transport, Hemisphere Pub. Co., New York, NY.
Shakerin,  S., Bohn,  M., and Loehrke,  R. I., 1988, “Natural Convection in an Enclosure with Discrete Roughness Elements on a Vertical Heated Wall,” Int. J. Heat Mass Transf., 31(7), pp. 1423–1430.
Frederick,  R. L., 1989, “Natural Convection in an Inclined Square Enclosure with a Partition Attached to its Cold Wall,” Int. J. Heat Mass Transf., 32(1), pp. 87–94.
Frederick,  R. L., and Valencia,  A., 1989, “Heat Transfer in a Square Cavity with a Conducting Partition on its Hot Wall,” Int. Commun. Heat Mass Transfer, 16, pp. 347–354.
Scozia,  R., and Frederick,  R. L., 1991, “Natural Convection in Slender Cavities with Multiple Fins Attached on an Active Wall,” Numer. Heat Transfer, Part A, 20, pp. 127–158.
Facas,  G. N., 1993, “Natural Convection in a Cavity with Fins Attached to Both Vertical Walls,” J. Thermophys. Heat Transfer, 7(4), pp. 555–560.
Nag,  A., Sarkar,  A., and Sastri,  V. M. K., 1993, “Natural Convection in a Differentially Heated Square Cavity with a Horizontal Partition Plate on the Hot Wall,” Comput. Methods Appl. Mech. Eng., 110, pp. 143–156.
Lakhal,  E. K., Hasnaoui,  M., Bilgen,  E., and Vasseur,  P., 1997, “Natural Convection in Inclined Rectangular Enclosures with Perfectly Conducting Fins Attached on the Heated Wall,” Heat Mass Transfer, 32, pp. 365–373.
Bilgen,  E., 2002, “Natural Convection in Enclosures with Partial Partitions,” Renewable Energy, 26, pp. 257–270.
Shi,  X., and Khodadadi,  J. M., 2002, “Laminar Fluid Flow and Heat Transfer in a Lid-Driven Cavity Due to a Thin Fin,” ASME J. Heat Transfer, 124(6), pp. 1056–1063.
Patankar, S. V., 1980, Numerical Heat Transfer and Fluid Flow, Hemisphere Pub. Co., Washington, DC.
Hayase,  T., Humphrey,  J. A. C., and Grief,  R., 1992, “A Consistently Formulated QUICK Scheme for Fast and Stable Convergence Using Finite-Volume Iterative Calculation Procedures,” J. Comput. Phys., 98, pp. 108–118.
De Vahl Davis,  G., and Jones,  L. P., 1983, “Natural Convection in a Square Cavity: A Comparison Exercise,” Int. J. Numer. Methods Fluids, 3, pp. 227–248.
De Vahl Davis,  G., 1983, “Natural Convection of Air in a Square Cavity: A Bench Mark Numerical Solution,” Int. J. Numer. Methods Fluids, 3, pp. 249–264.
Shi, X., 2003, “Forced and Natural Convection Heat Transfer within Enclosures with Fixed and Moving Fins and Partitions,” Ph.D. thesis, Department of Mechanical Engineering, Auburn University.

Figures

Grahic Jump Location
Natural convection in a square cavity with a thin fin
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The absolute value of the stream function at the center of primary vortex, ψmin, as a function of the grid size (Ra=105,Sp=0.5, and Lp=0.5)
Grahic Jump Location
Natural convection in a square cavity: (a) streamlines and (b) temperature contours [contour level increment of 0.1]
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Flow fields for Ra=104 with fins at different positions: (a) Lp=0.2, (b) Lp=0.35, and (c) Lp=0.5
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Flow fields for Ra=107 with fins at different positions: (a) Lp=0.2, (b) Lp=0.35, and (c) Lp=0.5
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Variation of the absolute value of ψmin with the position of the fin: (a) Ra=104, (b) Ra=105, (c) Ra=106, and (d) Ra=107
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Temperature fields for Ra=107 with fins at different positions: (a) Lp=0.2, (b) Lp=0.35, and (c) Lp=0.5 [contour level increment of 0.05]
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Variation of the local Nusselt number along the left and right walls of the cavity with fins at different positions (Ra=104): (a) Lp=0.2, (b) Lp=0.35, and (c) Lp=0.5
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Variation of the NNR along the left and right walls of the cavity with fins at different positions: (a) Ra=104 and (b) Ra=107
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Curve fitting for the mean Nusselt number: (a) Ra=104 and 105, (b) Ra=106 and 107

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