Temperature stresses in thick circular cylindrical shells used in nuclear reactors with exponential heat generation within the shell wall thickness

Abstract

In the preceding paper, formulae and graphs were given which enabled estimates to be made of heat flow, temperature and stresses through the thickness of the circular cylindrical shell, when heat was not generated inside the thickness and when it was generated according to a uniform path. Situations of heat generation in shell thickness are commonly encountered in the shields of nuclear reactors. All the expressions given for stress in the preceding paper may be reduced to the following form: σ{Eαqa²/[(1 - ν)k]}η, where η is a factor associated with the stress which depends upon heat generation profiles, internal and external temperatures T _a and T _b of the shell and its thermal conductivity k, for each radius r.

Another common heat generation which occurs in these shells has an exponential path. For these cases, the circumferential thermal stress σ_ϑ may be given in the following form: σ_ϑ = {Eαq(β⁻¹)²/[(1 - ν)k]}η_ϑ, where β is the exponential absorption factor which is related to the quantitative measure of the generated heat and η_ϑ is the non-dimensional circumferential stress. In the present paper graphs are furnished to estimate the parameter η_ϑ in order to foresee the values of stresses in the circumferential directions at the internal and external radii of the shell for the case of exponential heat generation through the wall thickness. They apply only when: (a) all generated heat flows inside the vessel or (b) all heat flows outside the vessel or (c) T _a = T _b .

Application of the principle of superposition shows how to evaluate the stresses where the generated heat paths are not uniform, triangular or exponential.