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.