Green's Function for Heat Conduction in an Infinite Hollow Cylinder R50 with a Type 5 Boundary Condition

By Donald E. Amos

Sandia National Laboratories, Retired



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The Green's function is the principal tool in construction of the general solution to the classical heat conduction problem. The solution is presented in terms of the internal heat generation, initial temperature and integrals which reflect the physical influence of the boundary. In the current literature ( ) the common boundary conditions are presented as Types 1,2,3,4, and 5 ranging from specified temperature (Type 1) to the most general form (Type 5) where input energy (flux), heat loss to the surroundings, heat storage in a boundary layer and conduction into the material are considered. Since the driving energy for the Green's function is internal, the homogeneous form of the boundary condition is used to define the Green's function. The thrust of this work is to derive the Green's function, labeled R50, for an external hollow cylinder, r>a, with a Type 5 boundary condition on the surface r=a. Specializing the parameters reduces the Green's function to known results.


This work was supported by NSF Award 1250625, Exact Analytical Conduction Toolbox, administered by the University of Nebraska, Kevin Cole, Director


  1. Cole, KD, Beck, JV, et. al. (2010), Heat Conduction Using Green's Functions, 2nd Ed., CRC Press Boca Raton, 643pp
  2. Amos, DE (2014) Theory of Heat Conduction With Type 5 Boundary Condition,
  3. Amos, DE, (2014) Heat Conduction in a Hollow Cylinder R55T0 and Sub-cases,
  4. Carslaw, HS, Jaeger, JC (1948) Conduction of Heat in Solids, Oxford Univ Press, London, 386pp

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Researchers should cite this work as follows:

  • Donald E. Amos (2014), "Green's Function for Heat Conduction in an Infinite Hollow Cylinder R50 with a Type 5 Boundary Condition,"

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