Quasi-static Thermal Deflection of a Thin Clamped Hollow Circular Disk Due to Heat Generation

Abstract

This paper deals with the determination of the thermal deflection in a thin clamped hollow circular disk defined as a ≤ r ≤ b; 0 ≤ z ≤ h under an unsteady temperature field due to internal heat generation within it. A thin hollow circular disk is considered having an arbitrary initial temperature and subjected to heat flux at the outer circular boundary (r = b) where an inner circular boundary (r = a) is at zero heat flux. Also, the upper surface (z = h) and the lower surface (z = 0) of the disk are at zero temperature. The governing heat conduction equation has been solved by using an integral transform technique. The inner and outer edges of the disk are clamped ${\frac{\partial \omega }{\partial r}=0}$ at r = a, r = b. The results are obtained in a series form in terms of Bessel’s functions and are illustrated graphically.