A three-part mixed boundary value problem for a heated plate

摘要

The work presents an analytical solution for an axisymmetric heat conduction problem of a plate lying on a foundation covered by an annular thermal isolator. The plate is heated by a uniform temperature field on the opposite side over a circular region. The three-part mixed boundary value problem is reduced to a system of triple integral equations by the Hankel integral transforms method. Instead of the Fredholm integral equations approach method, with the help of an integral relation we develop the unknown functions into a series of Bessel functions product. Using the Gegenbauer addition formula for the Bessel function of zero order, we reduce the formulated problem to an infinite system of algebraic equations. Numerical results are also given for the temperature and the flux for different regions of the plate using the Gauss hypergeomertic function proprieties.