Technical Note Transient analysis of internally heated tubular components with exponential thermal loading and external convection

Abstract

Tubular components subjected to severe thermal conditions are widely used by industry in many applications such as radiant burners and heat exchangers. As would be expected, these applications often involve thermal transients that are severe enough to induce fatigue, and eventually failure. In order to be able to predict these failures and the thermoelastic stresses that are the underlying cause, a detailed understanding of the transient temperature distributions is essential. Although there have been numerous analytical models, they have been limited to severe and often unrealistic step or linear temperature changes [1, 2] . More recent studies [3–5] have shown the potentially complicated time dependence of the surface temperature loading and need for improved estimates using finite-element analysis along with a temperature-matching scheme when temperature dependent materials properties are involved. However, the finite element calculations were iterative and required an analytical starting point for the prescribed surface temperatures, as well as a means for verifying the numerical solution. Because of these needs, an analytical model of the thermal transients developed within tubular components subjected to a more realistic, time dependent boundary condition is ultimately required. Accordingly, this paper derives the equations for a hollow cylinder with a plausible exponential boundary condition of the form H ( t) = V (1− e −ct ) for the internal surface with external convection to the external environment. Additionally, the unit response of a cylinder subjected to an internal step load with external convection is also derived.