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

#### Abstract

This paper presents the derivation of the Green's function for composite cylinders 0<r<a and r>a in perfect contact on the surface r=a. 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 temperature and 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 are in perfect contact, but may have non-zero initial conditions and/or possibly a distribution of internal heat sources. The Green's function approach and a direct approach agree when applied to three problems with known solutions. A fourth problem illustrates a complication where the Laplace transform of the general solution is more useful.

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

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

#### Cite this work

Researchers should cite this work as follows:

• Donald E. Amos (2013), "Green's Function For Radial Heat Conduction in Two-Region Composite Cylinders With Perfect Boundary Contact," http://nanohub.org/resources/16482.