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Green's Function For Radial Heat Conduction in Two-Region Composite Cylinders With Imperfect Boundary Contact

Sandia National Laboratories, Retired

Abstract

This paper presents the derivation of the Green's function for composite cylinders 0a with contact resistance on the surface r=a. This imperfect contact is expressed by taking the flux proportional to the temperature difference across the boundary where the constant of proportionality is called the heat transfer coefficient h. Because the source function can be in either region, there are two pairs of functions which define the Green's function. Each pair is the solution to a two-region conduction problem with zero initial temperatures and continuity of flux on the cylinder r=a. These pairs are used in conjunction with a general formula to get the solution to other problems where the cylinders have contact resistance, but may have non-zero initial conditions and/or possibly a distribution of internal heat sources. The case of perfect contact is obtained by taking h to infinity and the case of perfect insulation on r=a for both regions ra is obtained by taking h to zero.

Keywords Two Regions Heat Conduction Unsteady State Laplace Transform

References

[1] Abramowitz S, Stegun IA (1965) Handbook of Mathematical Functions, AMS 55, Dover Publications Inc., New York, 1046pp

[2] Amos DE (2006) Handbook of Integrals Related to Heat Conduction and Diffusion, http://nanohub.org/resources/13874

[3] Amos DE, Beck JV, de Monte F (2011) Transient Heat Conduction in Adjacent Quadrants Separated by a Thermal Resistance, http://nanohub.org/resources/12465

[4] Amos DE (2011) Transient Heat Conduction in Adjacent Materials Heated on Part of the Common Boundary, http://nanohub.org/resources/12390

[5] Amos, DE (2012), Green's Functions For Heat Conduction in Adjacent Materials, http://nanohub.org/resources/12856

[6] Amos, DE (2012), Theory of Heat Conduction for Two-region Problems Using Green's Functions, http://nanohub.org/resources/13671

[7] Amos, DE (2012), 1-D Green's Functions For Heat Conduction Between Semi-infinite Slabs With Perfect and Imperfect Boundary Contact, http://nanohub.org/resources/15237

[8] Amos, DE (2013), Green's Function For Radial Heat Conduction in Two-Region Composite Cylinders With Perfect Boundary Contact, http://nanohub.org/resources/16482

[9] Cole DC, Beck JV, Haji-SheikhA, Litkouhi B (2010) Heat Conduction Using Green's Functions, 2nd Ed., CRC Press, 643p.

[10] Carslaw HS, Jaeger JC (1948) Conduction of Heat in Solids, Oxford Univ Press, London, 386pp

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