Abstract 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 ( http://Exact.unl.edu ) 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 transfer 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 R55Phi00, for an annulus with radial and angular variation and Type 5 boundary conditions on both surfaces. Types 2, 3, and 4 are special cases which can be obtained by setting an appropriate parameter to zero. The Type 1 case can be obtained by taking the heat transfer coefficient to infinity.

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

References [1] Cole, KD, Beck, JV, et. al. (2010), Heat Conduction Using Green’s Functions, 2^nd Ed., CRC Press,      Boca      Raton, 643pp

[2] Amos, DE (2014) Theory of Heat Conduction With Type 5 Boundary Condition,

       http://nanohub.org/resources/20365

[3] Amos, DE, (2014) Heat Conduction in a Hollow Cylinder R55T0 and Sub-cases,       http://nanohub.org/resources/20535

[4] Amos, DE, (2014) Green’s Function for Heat Conduction in a Hollow Cylinder R55        with Type 5 Boundary Conditions, http://nanohub.org/resources/20661 [5] Amos, DE, (2014) Heat Conduction in a Slab X55T0 and Sub-cases,       http://nanohub.org/resources/20381

Researchers should cite this work as follows:

• Donald E. Amos (2014), "Green's Function for Heat Conduction in an Annulus R55Phi00 with Type 5 Boundary Conditions," https://nanohub.org/resources/21621.

  BibTex | EndNote

1. Annulus
2. heat conduction heat transfer
3. Type5 BC