The method of lines with numerical differentiation of the sequential temperature–time histories for a facile solution of 1D inverse heat conduction problems
 Antonio Campo,
 Mohammad R. Salimpour,
 John Ho
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This work addresses an inverse heat conduction problem (IHCP) in a large planar slab receiving a certain heat flux at one surface while the other surface is thermally insulated. The two different heating conditions to be studied are: (1) constant heat flux and (2) a timedependent triangular heat flux. For the IHCP, the temperature–time variations at the insulated surface of the large planar slab are obtained with a single temperature sensor. The two temperature–time histories are generated from the solutions of the direct heat conduction problem. The central objective of the paper is to implement the method of lines for the descriptive 1D heat equation combined with numerical differentiation of: (1) the “measured” temperature–time history at the insulated surface and (2) the temperature–time history at other subsurface locations. In the end, it is confirmed that excellent predictions of the temperature–time variations at the directly heated surface are obtainable for the two dissimilar heating conditions. This is accomplished with small systems of firstorder differentialdifference equations, one with two equations and the other with four equations.
Inside
Within this Article
 Introduction
 Direct heat conduction problem
 Inverse heat conduction problem
 Theory of the method of lines
 Practical applications
 Numerical calculation procedure
 Presentation of numerical results
 Concluding remarks
 References
 References
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 Title
 The method of lines with numerical differentiation of the sequential temperature–time histories for a facile solution of 1D inverse heat conduction problems
 Journal

Heat and Mass Transfer
Volume 49, Issue 3 , pp 369379
 Cover Date
 20130301
 DOI
 10.1007/s0023101210885
 Print ISSN
 09477411
 Online ISSN
 14321181
 Publisher
 SpringerVerlag
 Additional Links
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 Authors

 Antonio Campo ^{(1)}
 Mohammad R. Salimpour ^{(2)}
 John Ho ^{(3)}
 Author Affiliations

 1. Department of Mechanical Engineering, The University of Texas at San Antonio, San Antonio, TX, 78249, USA
 2. Department of Mechanical Engineering, Isfahan University of Technology, 8415683111, Isfahan, Iran
 3. Department of Mechanical Engineering, University of Vermont, Burlington, VT, 05405, USA