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

Duhamel's integral and unit step response derived for a hollow cylinder were used to derive an analytical solution for the transient temperature distribution across a tubular component internally subjected to exponential thermal loading with external convection to the surrounding environment. Excellent agreement was seen between the derived solution and a piecewise linear, finite element simulation. Because of the flexibility of the exponential boundary conditions used, the derived, closed-form solution has many practical research and industrial applications including the design process, as well as providing a first guess for an iterative, finite element analysis when materials nonlinearities are involved.