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Journal of Heat Transfer | Volume 128 | Issue 7 | Research Paper
RESEARCH PAPERS: Forced Convection

Convective Heat Transfer in Turbulent Flow Near a Gap

[+] Author and Article Information
D. Chang

Department of Mechanical Engineering, University of Ottawa, Ottawa, Ontario, K1N 6N5, Canada

S. Tavoularis

Department of Mechanical Engineering, University of Ottawa, Ottawa, Ontario, K1N 6N5, Canadatav@eng.uottawa.ca

J. Heat Transfer 128(7), 701-708 (Mar 08, 2006) (8 pages) doi:10.1115/1.2194039 History: Received May 31, 2005; Revised March 08, 2006
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Convective heat transfer in a rectangular duct containing a heated rod forming a narrow gap with a plane wall has been simulated by solving the unsteady Reynolds-averaged Navier-Stokes equations with a Reynolds stress model. Of particular interest is the role of quasi-periodic coherent structures in transporting fluid and heat across the gap region. It is shown that the local instantaneous velocity and temperature vary widely because of large-scale transport by coherent vortical structures forming in pairs on either side of the rod.
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Copyright © 2006 by American Society of Mechanical Engineers
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Grahic Jump Location
+Sketches of the computational geometry and mesh
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Sketches of the computational geometry and mesh
Figure 1

Sketches of the computational geometry and mesh

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+Predicted isocontours of (a) the dimensionless time-averaged temperature difference Θ¯=(T¯−T¯b)∕(T¯rod,m−T¯b); (b) the standard deviation of the normalized coherent temperature fluctuations ϑc2¯∕(T¯rod,m−T¯b); (c) the standard deviation of the normalized non-coherent temperature fluctuations ϑnc2¯∕(T¯rod,m−T¯b); and (d) the percent ratio of the variances of coherent and total temperature fluctuations ϑc2¯∕ϑ2¯×100; the left-side plots correspond to the uniform rod temperature case and the right-side plots to the uniform rod heat flux case
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Predicted isocontours of (a) the dimensionless time-averaged temperature difference Θ¯=(T¯−T¯b)∕(T¯rod,m−T¯b); (b) the standard deviation of the normalized coherent temperature fluctuations ϑc2¯∕(T¯rod,m−T¯b); (c) the standard deviation of the normalized non-coherent temperature fluctuations ϑnc2¯∕(T¯rod,m−T¯b); and (d) the percent ratio of the variances of coherent and total temperature fluctuations ϑc2¯∕ϑ2¯×100; the left-side plots correspond to the uniform rod temperature case and the right-side plots to the uniform rod heat flux case
Figure 2

Predicted isocontours of (a) the dimensionless time-averaged temperature difference Θ¯=(T¯−T¯b)∕(T¯rod,m−T¯b); (b) the standard deviation of the normalized coherent temperature fluctuations ϑc2¯∕(T¯rod,m−T¯b); (c) the standard deviation of the normalized non-coherent temperature fluctuations ϑnc2¯∕(T¯rod,m−T¯b); and (d) the percent ratio of the variances of coherent and total temperature fluctuations ϑc2¯∕ϑ2¯×100; the left-side plots correspond to the uniform rod temperature case and the right-side plots to the uniform rod heat flux case

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+Spanwise variations of the time-averaged (——) and representative instantaneous (- - -, −•−•−) dimensionless temperature differences on the bottom wall in (a) the uniform rod temperature case and (b) the uniform rod heat flux case
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Spanwise variations of the time-averaged (——) and representative instantaneous (- - -, −•−•−) dimensionless temperature differences on the bottom wall in (a) the uniform rod temperature case and (b) the uniform rod heat flux case
Figure 3

Spanwise variations of the time-averaged (——) and representative instantaneous (- - -, −•−•−) dimensionless temperature differences on the bottom wall in (a) the uniform rod temperature case and (b) the uniform rod heat flux case

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+Streamwise variations of the time-averaged (——) and representative instantaneous (- - -, −•−•−) dimensionless temperature differences along the bottom wall at z∕D=0 in (a) the uniform rod temperature case and (b) the uniform rod heat flux case
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Streamwise variations of the time-averaged (——) and representative instantaneous (- - -, −•−•−) dimensionless temperature differences along the bottom wall at z∕D=0 in (a) the uniform rod temperature case and (b) the uniform rod heat flux case
Figure 4

Streamwise variations of the time-averaged (——) and representative instantaneous (- - -, −•−•−) dimensionless temperature differences along the bottom wall at z∕D=0 in (a) the uniform rod temperature case and (b) the uniform rod heat flux case

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+Circumferential variations of the time-averaged (——) and representative instantaneous (- - -, −•−•−) Nusselt numbers around the rod in (a) the uniform rod temperature case and (b) the uniform rod heat flux case; the values have been normalized by the corresponding circumferential averages
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Circumferential variations of the time-averaged (——) and representative instantaneous (- - -, −•−•−) Nusselt numbers around the rod in (a) the uniform rod temperature case and (b) the uniform rod heat flux case; the values have been normalized by the corresponding circumferential averages
Figure 5

Circumferential variations of the time-averaged (——) and representative instantaneous (- - -, −•−•−) Nusselt numbers around the rod in (a) the uniform rod temperature case and (b) the uniform rod heat flux case; the values have been normalized by the corresponding circumferential averages

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+Streamwise variations of the time-averaged (——) and representative instantaneous (- - -, −•−•−) Nusselt numbers along the rod on the symmetry plane and facing the bottom wall in (a) the uniform rod temperature case and (b) the uniform rod heat flux case; the values have been normalized by the corresponding streamwise averages
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Streamwise variations of the time-averaged (——) and representative instantaneous (- - -, −•−•−) Nusselt numbers along the rod on the symmetry plane and facing the bottom wall in (a) the uniform rod temperature case and (b) the uniform rod heat flux case; the values have been normalized by the corresponding streamwise averages
Figure 6

Streamwise variations of the time-averaged (——) and representative instantaneous (- - -, −•−•−) Nusselt numbers along the rod on the symmetry plane and facing the bottom wall in (a) the uniform rod temperature case and (b) the uniform rod heat flux case; the values have been normalized by the corresponding streamwise averages

Grahic Jump Location
+Predicted isocontours of the dimensionless instantaneous temperature difference Θ on the equidistant plane in (a) the uniform rod temperature case and (b) the uniform rod heat flux case; coherent structures identified by the Q criterion are also shown in both plots, which represent a flow area that is 7.5D long
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Predicted isocontours of the dimensionless instantaneous temperature difference Θ on the equidistant plane in (a) the uniform rod temperature case and (b) the uniform rod heat flux case; coherent structures identified by the Q criterion are also shown in both plots, which represent a flow area that is 7.5D long
Figure 7

Predicted isocontours of the dimensionless instantaneous temperature difference Θ on the equidistant plane in (a) the uniform rod temperature case and (b) the uniform rod heat flux case; coherent structures identified by the Q criterion are also shown in both plots, which represent a flow area that is 7.5D long

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+(a) Computed (—) and measured (7) (- - - -) smoothened power spectra of the spanwise velocity in the center of the gap; (b) computed smoothened spectra of the resolved temperature in the constant rod temperature case (—) and the constant rod heat flux case (- - - -)
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(a) Computed (—) and measured (7) (- - - -) smoothened power spectra of the spanwise velocity in the center of the gap; (b) computed smoothened spectra of the resolved temperature in the constant rod temperature case (—) and the constant rod heat flux case (- - - -)
Figure 8

(a) Computed (—) and measured (7) (- - - -) smoothened power spectra of the spanwise velocity in the center of the gap; (b) computed smoothened spectra of the resolved temperature in the constant rod temperature case (—) and the constant rod heat flux case (- - - -)

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