Theory of Heat Conduction for Two Region Problems Using Green's Functions

Sandia National Laboratories, Retired

Abstract

This paper derives equations which describe transient temperature distributions in adjacent regions which share a common boundary. These regions consist of materials with distinct, constant physical properties. The theory is developed for two types of boundary contact. The first formula is developed for perfect contact where there is continuity of both temperature and flux. The second formula allows for a thermal resistance at the boundary which retains continuity of flux, but causes a temperature drop across the boundary. As an example, the two-region theory is applied to quadrants 1 and 2 which are separated by an infinitely thin resistive layer on the y-axis and are heated along the x-axis. This problem was solved by a direct approach in a previous paper and the two-region Green's function approach gives the same results. Keywords Two Regions Heat Conduction Unsteady State Laplace Transform

References

References

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

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

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

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

 Amos DE (2012) Handbook of Integrals Related to Heat Conduction and Diffusion, http://nanohub.org/resources/13874

 Beck JV, Cole KD, Haji-Sheikh A, Litkouhi B (2010) Heat Conduction Using Green's Functions, 2nd Ed., CRC Press, Boca Raton, 643 pp

 Morse PM, Feshbach H (1953) Methods of Theoretical Physics, Part I, McGraw-Hill, New York, 997 pp

 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 (2012), "Theory of Heat Conduction for Two Region Problems Using Green's Functions," https://nanohub.org/resources/13671.