Transient analytical temperature distributions in cylindrical packed beds volumetrically heated by radiogenic decay energy

Abstract

Analytical solutions are presented for the problem of the transient distribution of fluid and solid phase temperatures in a packed, porous, cylindrical particle bed with constant thermophysical properties. The packed particle bed is volumetrically heated by radiogenic decay energy from fission products. Flowing through the particle bed by forced convection is a single-phase fluid, either subcooled liquid or superheated vapor. The dynamic response of the packed bed is for low Reynolds numbers. In this case the transient will develop through the packed bed slowly enough for interphase heat transfer to keep the fluid and solid phase temperatures from having large differences. The two-dimensional, time-dependent Modified Dispersion-Concentric Model (D-C model) is used in the analysis of this problem. The D-C model energy equations are solved using Green's function. The mathematical solution characteristics for the transient fluid and solid phase temperature distributions are presented for three different volumetric heat generation terms: two-dimensional, time-dependent; simplified two-dimensional, time-dependent; and two-dimensional, time-independent. Using the two time-dependent volumetric heat generation terms, a comparison is presented for the transient fluid and solid phase temperatures and the radioactive decay heat power coming from the fission products in the particles.