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Computational Thermal Sciences: An International Journal
ESCI SJR: 0.249 SNIP: 0.434 CiteScore™: 1.4

ISSN Druckformat: 1940-2503
ISSN Online: 1940-2554

Computational Thermal Sciences: An International Journal

DOI: 10.1615/ComputThermalScien.2020028420
pages 179-189

IMPROVED TRANSVERSAL METHOD OF LINES (ITMOL) FOR UNIDIRECTIONAL, UNSTEADY HEAT CONDUCTION IN REGULAR SOLID BODIES WITH HEAT CONVECTION EXCHANGE TO NEARBY FLUIDS

Antonio Campo
Department of Mechanical Engineering, The University of Texas at San Antonio, San Antonio, Texas 78249, USA
Diego Celentano
Departamento de Ingenieria Mecánica y Metalurgica, Pontificia Universidad Católica de Chile, Santiago, Chile

ABSTRAKT

The present paper addresses unidirectional, unsteady, heat conduction in regular solid bodies (large plane wall, long cylinder and sphere) with uniform initial temperature, thermophysical properties invariant with temperature and heat convection exchange with a neighboring fluid. A novel analytical/numerical procedure named the improved transversal method of lines (ITMOL) has been implemented to transform the one-dimensional, unsteady heat conduction equations along with the uniform initial temperature and the convection boundary conditions in rectangular, cylindrical and spherical coordinates into equivalent one-dimensional, "quasi-steady" heat conduction equations. The transformed "quasi-steady" heat conduction equations are nonlinear ordinary differential equations of second order with linear boundary conditions, which can be solved with any numerical method. The singular feature of this kind of "quasi-steady" heat conduction equations is that time appears embedded into them. In this work, the temperature profiles in the regular solid bodies are determined by a suitable combination of ITMOL and the finite-difference method. The center, surface and mean temperature profiles, as well as the total heat transfer in the large plane wall, long cylinder and sphere exhibit excellent quality for the full spectrum of mean convective coefficients h (0 < h < ∞) over the entire time domain 0 < t < ∞.

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