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Technical Briefs

Effortless Application of the Method of Lines for the Inverse Estimation of Temperatures in a Large Slab With Two Different Surface Heating Waveforms

[+] Author and Article Information
Antonio Campo1

Mechanical Engineering Department, The University of Vermont, 33 Colchester Avenue, Burlington, VT 05405campanto@yahoo.com

John Ho

Mechanical Engineering Department, The University of Vermont, 33 Colchester Avenue, Burlington, VT 05405

1

Corresponding author.

J. Heat Transfer 131(2), 024501 (Dec 11, 2008) (5 pages) doi:10.1115/1.2993141 History: Received September 07, 2007; Revised July 13, 2008; Published December 11, 2008

The boundary inverse heat conduction problem (BIHCP) deals with the determination of the surface heat flux or the surface temperature from measured transient temperatures inside a conducting body where the initial temperature is known. This work addresses a BIHCP related to the spatiotemporal heat conduction in a large slab when a time-variable heat flux is prescribed at an exposed surface and the other surface is thermally insulated. Two different heating waveforms are studied: a constant heat flux and a time-dependent triangular heat flux. The numerical temperature-time history at the insulated surface of the large slab provides the “temperature-time measurement” with one temperature sensor. Framed in the theory of the method of lines (MOL) first and employing rudimentary concepts of numerical differentiation later, the main objective of this paper is to develop a simple computational methodology to estimate the temporal evolution of temperature at the exposed surface of the large slab receiving the two distinct heat fluxes. In the end, it is confirmed that excellent predictions of the surface temperatures versus time are achievable for the two cases tested while employing the smallest possible system of two heat conduction differential equations of first-order.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Computational domain with three lines: Lines 0, 1, and 2

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Figure 2

Surface temperature estimates for constant surface heat flux

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Figure 3

Relative errors produced by the forward and central finite-difference approximations in Fig. 2

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Figure 4

Surface temperature estimates for a triangular surface heat flux

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Figure 5

Relative errors produced by the forward and central finite-difference approximations in Fig. 4

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