Don,

You could find an answer to your question in a new book by L. C. Thomas titled "Heat Transfer-Professional Version" 2nd addition (1999).  The answer to your question could be found in Chapter 2 using upper-bound or lower-bound circuits.

Regards,

Thank You for your reply. I see that this book is available at both Amazon.Com and Barnes & Noble on the Internet. I have just receicved my copy of "Heat Transfer Calculations by Finite Differences" by G.M. Dusinberrre and using this book with the "Heat Transfer Handbook" by Roshenow et al,  I think I can set up a spread sheet to do the calculations I need to do. The trick is in using a common time element as the materials change and varying the material thickness element for the different materials as a ration of the different material diffusivies. The book you recommended sounds like a good one to have in your library though.
Also, in circular coordinates with only radial variation, to use an arc angle of 1 radian. This makes the problem set up very easy.
Thanks Again

Don
dleffingwell@snet.net