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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Effortless Application of the Method of Lines for the Inverse Estimation of Temperatures in a Large Slab With Two Different Surface Heating Waveforms
Antonio Campo,
Antonio Campo
Mechanical Engineering Department,
e-mail: campanto@yahoo.com
The University of Vermont
, 33 Colchester Avenue, Burlington, VT 05405
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John Ho
John Ho
Mechanical Engineering Department,
The University of Vermont
, 33 Colchester Avenue, Burlington, VT 05405
Search for other works by this author on:
Antonio Campo
Mechanical Engineering Department,
The University of Vermont
, 33 Colchester Avenue, Burlington, VT 05405e-mail: campanto@yahoo.com
John Ho
Mechanical Engineering Department,
The University of Vermont
, 33 Colchester Avenue, Burlington, VT 05405J. Heat Transfer. Feb 2009, 131(2): 024501 (5 pages)
Published Online: December 11, 2008
Article history
Received:
September 7, 2007
Revised:
July 13, 2008
Published:
December 11, 2008
Citation
Campo, A., and Ho, J. (December 11, 2008). "Effortless Application of the Method of Lines for the Inverse Estimation of Temperatures in a Large Slab With Two Different Surface Heating Waveforms." ASME. J. Heat Transfer. February 2009; 131(2): 024501. https://doi.org/10.1115/1.2993141
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