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RESEARCH PAPERS: Conduction

Steady-Periodic Green’s Functions and Thermal-Measurement Applications in Rectangular Coordinates

[+] Author and Article Information
Kevin D. Cole

Mechanical Engineering Department,  University of Nebraska–Lincoln, Lincoln, NE 68588-0656kcole1@unl.edu

J. Heat Transfer 128(7), 709-716 (Nov 28, 2005) (8 pages) doi:10.1115/1.2194040 History: Received June 06, 2005; Revised November 28, 2005

Methods of thermal property measurements based on steady-periodic heating are indirect techniques, in which the thermal properties are deduced from a systematic comparison between experimental data and heat-transfer theory. In this paper heat-transfer theory is presented for a variety of two-dimensional geometries applicable to steady-periodic thermal-property techniques. The method of Green’s functions is used to systematically treat rectangles, slabs (two dimensional), and semi-infinite bodies. Several boundary conditions are treated, including convection and boundaries containing a thin, high-conductivity film. The family of solutions presented here provides an opportunity for verification of numerical results by the use of distinct, but similar, geometries. A second opportunity for verification arises from alternate forms of the Green’s function, from which alternate series expressions may be constructed for the same unique temperature solution. Numerical examples are given to demonstrate both verification techniques for the steady-periodic response to a heated strip.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Geometries under discussion include (a) rectangles, (b) semislabs, and (c) slabs

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Figure 2

Slab heated over a small area and cooled by convection

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Figure 3

Amplitude (a) and phase (b) of the temperature on the heated surface of a slab with Ba=1 and W∕a=1 for three heating frequencies

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Figure 4

Amplitude (a) and phase (b) of the temperature on the heated surface of a slab with heating frequency ω+=1 and W∕a=1 for three Biot values

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Figure 5

Amplitude (a) and phase (b) of the temperature on the heated surface of a slab with Ba=1 and ω+=1 for three slab thicknesses

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Figure 6

Thin film on a thick substrate, heated over a small area and cooled by convection

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Figure 7

Amplitude (a) and phase (b) of the spatial average temperature on the heater for a thick substrate with no surface film as a function of frequency for three convection values

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Figure 8

Amplitude (a) and phase (b) of the spatial average temperature on the heater as a function of frequency at Ba=1 for various thicknesses of films on a large substrate. For the films, (ρc)1∕(ρc)=1.

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