چكيده
Abstract
In this investigation two dimensional analytical solution of heat
conduction equation applied in a hollow sphere, which is subjected
to a periodic boundary condition. The material is assumed to be
homogenous and isotropic with time-independent thermal properties.
The periodic boundary condition has been simulated with harmonic
oscillation yet, but there are some differences with the real situation.
So, we use Fourier expansion to simulate periodic boundary
condition as a summation of harmonic oscillations. To solve the
problem, first of all, the boundary condition is assumed to be a
constant and by applying the method of separation of variables, the
temperature distribution in a hollow sphere is obtained. Then by
Duhamel's principle, the temperature field under periodic boundary
condition is determined. The validity of the solution is demonstrated
by comparing the results for the hollow sphere with the results for a
solid sphere under harmonic oscillation boundary condition. With
the known temperature field in the hollow sphere, we can calculate
the thermal stress field.
