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Research Papers: Natural and Mixed Convection

Correlation Equations for Natural Convective Heat Transfer From Two Inclined Vertically Spaced Narrow Isothermal Flat Plates

[+] Author and Article Information
Abdulrahim Kalendar

Mem. ASME
Department of Mechanical Power
and Refrigeration,
College of Technological Studies-PAAET,
Shuwaikh 13092, Kuwait
e-mail: ay.kalendar1@paaet.edu.kw

Ahmed Kalendar

Department of Mechanical Power
and Refrigeration,
College of Technological Studies-PAAET,
Shuwaikh 13092, Kuwait
e-mail: a_kalendar@yahoo.com

Sayed Karar

Department of Mechanical Power
and Refrigeration,
College of Technological Studies-PAAET,
Shuwaikh 13092, Kuwait
e-mail: karar1952@hotmail.com

Patrick H. Oosthuizen

Mem. ASME
Department of Mechanical
and Materials Engineering,
Queen's University,
Kingston, ON K7L 3N6, Canada
e-mail: oosthuiz@queensu.ca

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received March 11, 2014; final manuscript received December 31, 2014; published online February 10, 2015. Assoc. Editor: Wei Tong.

J. Heat Transfer 137(5), 052501 (May 01, 2015) (10 pages) Paper No: HT-14-1123; doi: 10.1115/1.4029594 History: Received March 11, 2014; Revised December 31, 2014; Online February 10, 2015

Natural convective flow over narrow plates induces an inward flow near the edges of the plate causing the flow to be three-dimensional near the edges of the plate. This influences the heat transfer rate near the edges of the plate and is referred to as the edge effect. The primary objective of this paper is to numerically study this edge effect and the interaction of the flows over two inclined vertically separated narrow heated plates of the same size embedded in a plane adiabatic surface. The cases where the plates and surrounding adiabatic surface are inclined at positive or negative angles to the vertical have been considered. Results were obtained by numerically solving the full three-dimensional form of governing equations using the commercial finite volume based software Fluent©. Results have only been obtained for a Prandtl number of 0.7; this being the value existing in the application which involved airflow that originally motivated this study. The results presented here cover Rayleigh numbers between 103 and 107, at all values of W considered, plate width-to-height ratios between 0.2 and 1.2, gap, at all values of W considered, to the plate height ratios of between 0 and 1.5, and, at all values of W considered, angles of inclination of between −45 deg and +45 deg. The effects of the Rayleigh number, dimensionless plate width, dimensionless gap between plates, and inclination angle on the heat transfer rate have been studied in detail. Empirical correlations defining the effect of these parameters on the heat transfer rate have been derived.

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References

Kalendar, A., Oosthuizen, P. H., and Kalandar, B., 2009, “An Interaction of Natural Convective Heat Transfer From Two Adjacent Isothermal Narrow Vertical and Inclined Flat Plates,” Proceedings of the ASME Summer Heat Transfer Conference, San Francisco, CA, July 19–23, pp. 97–105.
Kalendar, A., and Oosthuizen, P. H., 2009, “Natural Convective Heat Transfer From Two Vertically Spaced Narrow Isothermal Flat Plates,” Proceedings of the 17th Annual Conference of the CFD Society of Canada, Ottawa, ON, May 3–5.
Oosthuizen, P. H., and Kalendar, A., 2013, “Natural Convective Heat Transfer From Narrow Plates,” Springer Briefs in Applied Science and Technology, Thermal Engineering and Applied Science, Springer, New York.
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Figures

Grahic Jump Location
Fig. 1

Flow situation considered

Grahic Jump Location
Fig. 3

Comparison of the variation of numerical values of the mean Nusselt number for bottom heated plate surface with Rayleigh numbers for VGap = 1.5, W = 1.2, and φ = 0 deg with the variation given by correlation equation

Grahic Jump Location
Fig. 4

Variation of mean Nusselt number for the top and bottom heated plate surfaces with the dimensionless gap between the heated plates for various Rayleigh numbers for W = 0.6 and φ = −45 deg

Grahic Jump Location
Fig. 5

Variation of mean Nusselt number for the top and bottom heated plate surfaces with the dimensionless gap between the heated plates for various Rayleigh numbers for W = 0.6 and φ = +45 deg

Grahic Jump Location
Fig. 6

Variation of mean Nusselt number for the top and bottom heated plate surfaces with the dimensionless gap between the heated plates for various Rayleigh numbers for W = 0.3 and φ = −45 deg

Grahic Jump Location
Fig. 7

Variation of mean Nusselt numbers for the top and bottom heated plate surfaces with the dimensionless gap between the heated plates for various Rayleigh numbers for W = 0.3 and φ = +45 deg

Grahic Jump Location
Fig. 8

Variation of total mean Nusselt number for the top and bottom heated plate surfaces with the dimensionless gap between the heated plates for various Rayleigh numbers and dimensionless plate width W for φ = −45 deg

Grahic Jump Location
Fig. 9

Variation of average mean Nusselt number for the top and bottom heated plate surfaces with the dimensionless gap between the heated plates for various Rayleigh numbers and dimensionless plate width W for φ = +45 deg

Grahic Jump Location
Fig. 10

Variation of the total mean Nusselt number for top and bottom heated plate surfaces with dimensionless plate width for various dimensionless gaps, VGap, and Rayleigh numbers and for φ = −45 deg

Grahic Jump Location
Fig. 11

Variation of mean Nusselt number for top heated plate surface with dimensionless plate width for various dimensionless gaps, VGap, and Rayleigh numbers for φ = −45 deg

Grahic Jump Location
Fig. 12

Variation of the total mean Nusselt number for both top and bottom heated plate surfaces with dimensionless plate width for various dimensionless gaps, VGap, and Rayleigh numbers and for φ = +45 deg

Grahic Jump Location
Fig. 13

Variation of mean Nusselt number for top heated plate surface with dimensionless plate width for various dimensionless gaps, VGap, and Rayleigh numbers for φ = +45 deg

Grahic Jump Location
Fig. 14

Variation of the mean Nusselt number for top heated plate surface with angle of inclination for various dimensionless gaps and Rayleigh numbers for dimensionless plate width of W = 0.3

Grahic Jump Location
Fig. 15

Variation of the local Nusselt number based on h over the top and bottom heated plate surfaces with different angles of inclination for Ra = 1 × 106, VGap = 0.1, and W = 0.3

Grahic Jump Location
Fig. 16

Variation of the local Nusselt number based on h for the top and bottom heated plate surfaces with different dimensionless gaps for Ra = 1 × 106, φ = +45 deg, and W = 0.3

Grahic Jump Location
Fig. 17

Comparison of the Nusselt number values for the top surface given by the correlation equation Eq. (21) with the numerically obtained values for an angle of inclination of φ = 0 deg

Grahic Jump Location
Fig. 18

Comparison of the Nusselt number values given by the correlation equation Eq. (23) for two narrow heated plates separated by a gap with the numerical results for angle of inclination of φ = −45 deg

Grahic Jump Location
Fig. 19

Comparison of the Nusselt number values for the top heated plate surface given by the correlation equation Eq. (24) with the numerically obtained values for angle of inclination of φ = −45 deg

Grahic Jump Location
Fig. 20

Comparison of the Nusselt number values given by the correlation equation Eq. (25) for two narrow heated plates separated by a gap with the numerical results for an angle of inclination of φ = +45 deg

Grahic Jump Location
Fig. 21

Comparison of Nusselt number values for the top heated plate surface given by the correlation equation Eq. (26) with the numerically obtained values for an angle of inclination of φ = +45 deg

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