Experimental Estimate of the Continuous One-Dimensional Kernel Function in a Rectangular Duct With Forced Convection

[+] Author and Article Information
Jinny Rhee

Mechanical and Aerospace Engineering Department, San Jose State University, One Washington Square, San Jose, CA 95192-0087jrhee@email.sjsu.edu

Robert J. Moffat

Mechanical Engineering Department, Stanford University, Stanford, CA 94305-3030rmoffat@stanford.edu

The adiabatic heat transfer coefficient and the unpowered component temperature are actually extensions of the DKF. In the limit as the component size approaches zero in the streamwise direction, all that remains is the continuous one-dimensional (1D) kernel function. Both the DKF and the 1D kernel are used in the appropriate sum/integral to evaluate the surface temperature rise above the inlet temperature.

J. Heat Transfer 128(8), 811-818 (Jan 17, 2006) (8 pages) doi:10.1115/1.2227039 History: Received July 08, 2005; Revised January 17, 2006

The continuous, one-dimensional kernel function in a rectangular duct subject to forced convection with air was experimentally estimated using liquid crystal thermography techniques. Analytical relationships between the kernel function for internal flow and the temperature distribution resulting from a known heat flux distribution were manipulated to accomplish this objective. The kernel function in the hydrodynamically fully developed region was found to be proportional to the streamwise temperature gradient resulting from a constant heat flux surface. In the hydrodynamic entry region of the rectangular duct, a model for the kernel function was proposed and used in its experimental determination. The kernel functions obtained by the present work were shown to be capable of predicting the highly nonuniform surface temperature rise above the inlet temperature resulting from an arbitrary heat flux distribution to within the experimental uncertainty. This is better than the prediction obtained using the analytically derived kernel function for turbulent flow between parallel plates, and the prediction obtained using the conventional heat transfer coefficient for constant heat flux boundary conditions. The latter prediction fails to capture both the quantitative and qualitative nature of the problem. The results of this work are relevant to applications involving the thermal management of nonuniform temperature surfaces subject to internal convection with air, such as board-level electronics cooling. Reynolds numbers in the turbulent and transition range were examined.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 2

Cross-sectional view of test section assembly

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Figure 3

Top view of two test plates used for present work: constant heat flux on entire surface (35cm in the streamwise direction); and constant heat flux on two strips only (4.6–9.7cm and 12.2–14.8cm in the streamwise direction)

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Figure 4

Temperature calibration of liquid crystal paint verified by concurrent thermocouple measurements

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Figure 7

Continuous one-dimensional kernel function in the hydrodynamically developing section of rectangular duct flow for a Reynolds number of 8070

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Figure 8

Comparison of one-dimensional kernel functions for hydrodynamically fully developed flow at various Reynolds numbers

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Figure 9

Weighting function, f(ξ), in the hydrodynamically developing section of rectangular duct flow at various Reynolds numbers

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Figure 10

Convective heat flux pattern in the streamwise direction for test plate with strip heaters

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Figure 12

Comparison of temperature predictions resulting from application of present kernel function, analytical kernel function by Hatton and Quarmby (see Ref. 3), and the heat transfer coefficient with the mean temperature as the reference temperature

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Figure 11

Comparison of surface temperature data for arbitrary heat flux distribution with temperature prediction using present kernel function

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Figure 6

Nusselt and Reynolds numbers from present work compared to analytical solution of flow between parallel plates with constant heat flux on one side (see Ref. 3)

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Figure 5

Centerline temperature measurements on constant heat flux surface as a function of distance from onset of heating

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Figure 1

Schematic of wind tunnel and experimental setup



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