The transversal method of lines (TMOL) is a general hybrid technique for determining approximate, semi-analytic solutions of parabolic partial differential equations. When applied to a one-dimensional (1D) parabolic partial differential equation, TMOL engenders a sequence of adjoint second-order ordinary differential equations, where in the space coordinate is the independent variable and the time appears as an embedded parameter. Essentially, the adjoint second-order ordinary differential equations that result are of quasi-stationary nature, and depending on the coordinate system may have constant or variable coefficients. In this work, TMOL is applied to the unsteady 1D heat equation in simple bodies (large plate, long cylinder, and sphere) with temperature-invariant thermophysical properties, constant initial temperature and uniform heat flux at the surface. In engineering applications, the surface heat flux is customarily provided by electrical heating or radiative heating. Using the first adjoint quasi-stationary heat equation for each simple body with one time jump, it is demonstrated that approximate, semi-analytic TMOL temperature solutions with good quality are easily obtainable, regardless of time. As a consequence, usage of the more involved second adjoint quasi-stationary heat equation accounting for two consecutive time jumps come to be unnecessary.
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November 2014
This article was originally published in
Journal of Heat Transfer
Research-Article
Transversal Method of Lines for Unsteady Heat Conduction With Uniform Surface Heat Flux
Antonio Campo,
Antonio Campo
1
Department of Mechanical Engineering,
College of Engineering,
e-mail: campanto@yahoo.com
College of Engineering,
The University of Texas at San Antonio
,San Antonio, TX 78249
e-mail: campanto@yahoo.com
1Corresponding author.
Search for other works by this author on:
José Garza
José Garza
Department of Mechanical Engineering,
College of Engineering,
College of Engineering,
The University of Texas at San Antonio
,San Antonio, TX 78249
Search for other works by this author on:
Antonio Campo
Department of Mechanical Engineering,
College of Engineering,
e-mail: campanto@yahoo.com
College of Engineering,
The University of Texas at San Antonio
,San Antonio, TX 78249
e-mail: campanto@yahoo.com
José Garza
Department of Mechanical Engineering,
College of Engineering,
College of Engineering,
The University of Texas at San Antonio
,San Antonio, TX 78249
1Corresponding author.
Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received November 13, 2013; final manuscript received July 21, 2014; published online August 26, 2014. Assoc. Editor: William P. Klinzing.
J. Heat Transfer. Nov 2014, 136(11): 111302 (7 pages)
Published Online: August 26, 2014
Article history
Received:
November 13, 2013
Revision Received:
July 21, 2014
Citation
Campo, A., and Garza, J. (August 26, 2014). "Transversal Method of Lines for Unsteady Heat Conduction With Uniform Surface Heat Flux." ASME. J. Heat Transfer. November 2014; 136(11): 111302. https://doi.org/10.1115/1.4028082
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