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Variable Thermal Conductivity Heat Transfer With Symbolic Algebra

[+] Author Affiliations
A. Aziz

Gonzaga University

Paper No. IMECE2005-79119, pp. 197-203; 7 pages
doi:10.1115/IMECE2005-79119
From:
  • ASME 2005 International Mechanical Engineering Congress and Exposition
  • Innovations in Engineering Education: Mechanical Engineering Education, Mechanical Engineering/Mechanical Engineering Technology Department Heads
  • Orlando, Florida, USA, November 5 – 11, 2005
  • Conference Sponsors: Mechanical Engineering Education
  • ISBN: 0-7918-4232-0 | eISBN: 0-7918-3769-6
  • Copyright © 2005 by ASME

abstract

This paper deals with the analysis of heat transfer in media with variable thermal conductivity. The tool employed is the symbolic algebra package Maple. The specific problems considered are (1) steady conduction in a heat generating plane wall with thermal conductivity increasing as the square of the coordinate, (2) steady conduction in a circular rod with axially varying thermal conductivity exposed to a cross flow stream, (3) steady conduction in a hollow cylindrical shell with simultaneous coordinate and temperature dependent thermal conductivity, (4) steady conduction in a two-layered hollow cylindrical shell with the thermal conductivity of the inner shell varying linearly with the radial coordinate and the thermal conductivity of the outer shell varying linearly with temperature, (5) two-dimensional steady conduction in an orthotropic plate with different thermal conductivities along the two axes, and (6) transient conduction in a plane wall with coordinate dependent thermal conductivity. The paper demonstrates the effectiveness of the software that is capable of producing analytical solutions for problems that are very cumbersome to solve by hand, and at the same incorporates powerful numerical and graphical capabilities for solving problems that are analytically intractable. The paper should not be perceived as a commercial endorsement of Maple.

Copyright © 2005 by ASME

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