MATHEMATICAL MODELLING AND ITS SIMULATION OF A QUASI-STATIC THERMOELASTIC PROBLEM IN A SEMI-INFINITE HOLLOW CIRCULAR DISK DUE TO INTERNAL HEAT GENERATION

Abstract

The present paper deals with the determination of temperature, displacement and thermal stresses in a semi-infinite hollow circular disk due to internal heat generation within it. Initially the disk is kept at arbitrary temperature F(r, z). For times t ＞ 0 heat is generated within the circular disk at a rate of g(r, z, t) Btu/hr.ft³. The heat flux is applied on the inner circular boundary (r = a) and the outer circular boundary (r = b). Also, the lower surface (z = 0) is kept at temperature Q₃(r, t) and the upper surface (z = ∞) is kept at zero temperature. Hollow circular disk extends in the z-direction from z = 0 to infinity. The governing heat conduction equation has been solved by using finite Hankel transform and the generalized finite Fourier transform. As a special case mathematical model is constructed for different metallic disk have been considered. The results are obtained in series form in terms of Bessel’s functions. These have been computed numerically and illustrated graphically.