Nonhomogeneous Heat Conduction Problem and Its Thermal Deflection Due to Internal Heat Generation in a Thin Hollow Circular Disk

Abstract

This article is concerned with the determination of temperature and thermal deflection in a thin hollow circular disk under an unsteady-state temperature field due to internal heat generation within it. Initially, the disk is kept at an arbitrary temperature F(r, z). For times t > 0 heat is generated within the thin hollow circular disk at a rate of g(r, z, t) Btu/hr ft3, while the boundary surfaces at (r = a), (r = b), (z = 0) and (z = h) are kept at temperatures f 1(z, t) and f 2(z, t), f 3(r, t) and f 4(r, t), respectively. The governing heat conduction equation has been solved by using a finite Hankel transform and the generalized finite Fourier transform. The results are obtained in series form in terms of Bessel's functions. As a special case, different metallic disks have been considered. The results for temperature change and the thermal deflection have been computed numerically and illustrated graphically.