EFFECT OF INNER BOUNDARIES GEOMETRY ON NATURALCONVECTION HEAT TRANSFER IN HORIZONTAL ANNULI

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Kadhum A. Jehhef
Faris A. Badawy

Abstract

 An analytical modeling of natural convection in physically-based analysis is developed for investigate free convective heat transfer in horizontal eccentric annulus between a circular outer cylinder and heated different shape inner envelope with used four models of the shapes of the inner cross section of (circular, triangular, square and hexagon inner boundary). The main objective of this paper was taking a composite model based on asymptotic solutions for three limiting cases: pure conduction, laminar boundary layer convection and transition flow convection. Laminar conditions up to Rayleigh number RaPi of 5×104 were investigated. By using data from MATLAB simulations for a wide range of two cylinder temperature difference in order to study the effects of annulus diameter ratio, Rayleigh number, and the cross section geometries of inner cylinder on the Nusslte number and the ratio of thermal conductivity. The numerical result illustrated for the circular the increasing the Rayleigh number leading to slightly increasing the non-dimensional Nusslte number with various value of annulus diameter ratio and when used the high annulus perimeter ratio (Po/Pi( about (4.5,2.6,1.6 and 1.175). There is rapid increasing in the non-dimensional ratio of thermal conductivity with increasing the Rayleigh number at the high values of (Po/Pi(, and the result showed that the non-dimensional ratio of thermal conductivity and the Nusslte number values of the (triangular, square and hexagon) less than in the case of circular inner boundary, but the hexagon model showed the Nusslte number more that than in the (triangular and square). the mathematical results compared with model developed by pervious numerical the model and data are in good agreement, with an average RMS difference of 10.6% for the circular annulus of dimensional Nusselt number (NuPi) and less than 4.9 % and 9.8% for the square inner geometry non-dimensional ratio thermal conductivity. 

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“EFFECT OF INNER BOUNDARIES GEOMETRY ON NATURALCONVECTION HEAT TRANSFER IN HORIZONTAL ANNULI” (2024) Journal of Engineering, 16(04), pp. 6048–6063. doi:10.31026/j.eng.2010.04.24.
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How to Cite

“EFFECT OF INNER BOUNDARIES GEOMETRY ON NATURALCONVECTION HEAT TRANSFER IN HORIZONTAL ANNULI” (2024) Journal of Engineering, 16(04), pp. 6048–6063. doi:10.31026/j.eng.2010.04.24.

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References

Alshahrani, D. and Zeitoun, O., 2005 “Natural Convection in Horizontal

Cylindrical Annuli”, submitted for publication in Alexandria Engineering Journal,

Alexandria, Egypt.

 Beckmann, W., 1931."Die Warmeubertragung in Zylindrischen Gasschichten bei

Naturlicher Konvection", Forsch. Geb. d. Ingenieurwesen, Vol. 2, No. 5, pp 165-178,

 Churchill, S.W. and Usagi, R., 1972. “A General Expression for the Correlation of

Rates of Transfer and Other Phenomenon,” A.I.Ch.E. Journal, Vol. 18, pp. 1121 – 1128.

 Churchill, S. W., and Churchill, R. U., 1975, “A Comprehensive Correlating

Equation for Heat and Component Heat Transfer by Free Convection,” AIChE J., 21, pp.

–606.

 Char, M.I. and Y.H. Hsu, 1998. "Comparative Analysis of Linear and Nonlinear

Low-Reynolds Number Eddy Viscosity Models to Turbulent Natural Convection in

Horizontal Cylindrical Annuli," Numerical Heat Transfer, Part A, 33: 191-206.

 Char, M.I. and G.C. Lee, 1998. "Maximum Density Effects on Natural Convection

of Micropolar Fluids between Horizontal Eccentric Cylinders," Int. J. Engng. Sci., 36(2):

-169.

 Chang, K.S., Won, Y.H. and Cho, C.H., “Patterns of Natural Convection around a

Square Cylinder PlacedConcentrically in a Horizontal Circular Cylinder,” Jour-nal of

Heat Transfer, Vol. 105, 1983, pp. 273 - 280.

 D. Alshahran, O. Zeitoun 2006. "Natural Convection in Horizontal Annulus With

Fins Attached to Inner Cylinder". Graduate student, King Saud University, Riyadh, Saudi

Arabia.

ElSherbiny, S. M. and Moussa, A. R., 2004 “Natural Convection in Air Layers between

Horizontal Concentric Isothermal Cylinders”, Alexandria Engineering Journal, Vol. 43, pp.

-311.

 Glakpe, E.K. and Asfaw, A., “Prediction of Two-Dimensional Natural Convection

in Enclosures with Inner Bodies of Arbitrary Shapes" Numerical Heat Transfer, Part A:

Applications, vol. 20, 1987, pp. 279-296.

 H. L. Zhang1, W. Q. Tao1 and Q. J. Wu1 2007"Numerical simulation of natural

convection in circular enclosures with inner polygonal cylinders, with confirmation by

experimental results" Department of Power Machinery Engineering, Xi’an Jiaotong

University, 710049 Xi’an, Shanxi, China, pp.249-258.

 P. Teertstra, 2004."Comprehensive Review of Natural Convection in Horizontal

Circular Annuli" Microelectronics Heat Transfer Laboratory Department of Mechanical

Engineering University of Waterloo, Waterloo, Ontario, CANADA N2L 3G1.

 P. Teertstra , M. M. Yovanovich and J. R. Culham 2005. "Analytical Modeling of

Natural Convection in Horizontal Annuli" Microelectronics Heat Transfer Laboratory

Microelectronics Department of Mechanical Engineering University of Waterloo,

Ontario, Canada Waterloo, 12 January,

 Peter Teertstra, M. Michael Yovanovich, J. Richard Culham. 2006, " Modeling of

Natural Convection in Electronic Enclosures" Microelectronics Heat Transfer

Laboratory, Department of Mechanical Engineering, University of Waterloo, Waterloo,

Ontario, N2L 3G1, Canada Journal of Electronic Packaging JUNE Vol. 128 / 165.

 Shahraki, F., 2002. "Modeling of Buoyancy-Driven Flow and Heat Transfer for Air

in a Horizontal Annulus: Effects of Vertical Eccentricity and Temperature Dependent

Properties," Numerical Heat Transfer, Part A, 42: 603-621.

 Teertstra, P.M., , 2003, "Models and Experiments for Laminar Natural Convection

from Heated Bodies in Enclosures", Ph.D. Thesis, Department of Mechanical

Engineering, University of Waterloo, Waterloo, Ontario, Canada.

 Teertstra, P.M., Yovanovich, M.M. and Culham, J.R., 2004. “Analytical Modeling

of Natural Convection in Concentric Spherical Enclosures,” 42nd Aerospace Sciences

Meeting and Exhibit Conference, Reno, NV, Jan. 5 – 7.

 Yoo, J-S, 1996 “Dual Steady Solutions in Natural Convection between Horizontal

Concentric Cylinders,” International Journal of Heat and Fluid Flow, Vol. 17, pp. 587 -