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Research Papers: Conduction

Analytical Solutions for Anisotropic Heat Conduction Problems in a Trimaterial With Heat Sources

[+] Author and Article Information
Ming-Ho Shen1

Department of Automation Engineering, Nan Kai University of Technology, 568 Chung Cheng Road, Tsao Tun, Nantou County 542, Taiwanmhshen@nkut.edu.tw

Fu-Mo Chen

Department of Mechanical Engineering, Nan Kai University of Technology, 568 Chung Cheng Road, Tsao Tun, Nantou County 542, Taiwan

Shih-Yu Hung

Department of Automation Engineering, Nan Kai University of Technology, 568 Chung Cheng Road, Tsao Tun, Nantou County 542, Taiwan

1

Corresponding author.

J. Heat Transfer 132(9), 091302 (Jun 28, 2010) (8 pages) doi:10.1115/1.4001613 History: Received July 01, 2009; Revised March 04, 2010; Published June 28, 2010; Online June 28, 2010

In this work, the analytical solution of a fundamental problem of heat conduction in anisotropic medium is derived. The steady-state temperature field in an anisotropic trimaterial subject to an arbitrary heat source is analyzed. “Trimaterial” denotes an infinite body composed of three dissimilar materials bonded along two parallel interfaces. The method of analytical continuation is applied across the two parallel interfaces in order to derive the trimaterial solution in a series form from the corresponding homogeneous solution. A variety of problems, e.g., bimaterial, a finite thin film on a semi-infinite substrate, and a finite strip, can be analyzed as special cases of the present study. The numerical results of the temperature distributions for some practical examples are provided in graphic form and discussed in details.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

A trimaterial with a singularity located in Sb

Grahic Jump Location
Figure 2

Temperature distribution in an anisotropic trimaterial for a concentrated heat source applied within the middle layer (k11a=k11c=2k11b, k22a=k22c=4k11b, k22b=2k11b)

Grahic Jump Location
Figure 3

Temperature distribution in an anisotropic trimaterial for a concentrated heat source applied within the middle layer (k11a=k11c=0.5k11b, k22a=k22c=k11b, k22=2k11)

Grahic Jump Location
Figure 4

Temperature distribution for a concentrated heat source applied at (0, h/2) of a strip under isothermal boundary conditions (k22b=k11b, k12b=0)

Grahic Jump Location
Figure 5

Temperature distribution for a concentrated heat source applied at (0, h/4) of a strip under isothermal boundary conditions (k22b=0.5k11b, k12b=0.25k11b)

Grahic Jump Location
Figure 6

Temperature distribution for a concentrated heat source applied at (0, h/2) of a strip under adiabatic boundary conditions (k22b=k11b, k12b=0)

Grahic Jump Location
Figure 10

Temperature distributions in a film-substrate with a concentrated heat source applied within the substrate under adiabatic boundary conditions (k11b=2k11c, k22b=4k11c, k22c=2k11c)

Grahic Jump Location
Figure 9

Temperature distributions in a film-substrate with a concentrated heat source applied within the substrate under isothermal boundary conditions (k11c, k12c, k22c=83.6, 18.1, 20.8, k11b, k12b, k22b=76.5, 20.6, 52.7)

Grahic Jump Location
Figure 8

Temperature distribution in an anisotropic trimaterial for a concentrated heat source applied within the bottom layer (k11a=k11c, k11b=0.5k11c, k22a=k22c=2k11c, k22b=k11c)

Grahic Jump Location
Figure 7

Temperature distribution in an anisotropic trimaterial for a concentrated heat source applied within the bottom layer (k11a=k11c, k11b=2k11c, k22a=k22c=2k11c, k22b=4k11c)

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