6454

6454

حل تحليلي ميدان دما و تنش ناشي از آن در كره توخاليتحت شرط مرزي پريوديك بكمك بسط فورير

كارشناسي ارشد

مكانيك

آبان83

آبان83

استاد راهنما : دكتر عاطفي

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.