Analysis of Multilayer Cylindrical Thermal Conduction with a Time-Varying Convective Boundary Condition

Abstract Heat transfer in a multilayer body plays a key role in design and optimization of several engineering systems. While the analysis of simple multilayer problems is quite straightforward, realistic scenarios such as time-dependent boundary conditions result in significant complications in analysis. This work presents thermal analysis of a heat-generating multilayer cylinder with time-varying convective heat transfer at the boundary. Such a scenario may occur in applications such as nuclear reactors, jet impingement cooling, turbine blade heat transfer, as well as casting and related manufacturing processes. Analysis is presented for both annular and solid cylinders. A derivation for the temperature distribution is carried out, using a shifting function to split the time-dependent boundary condition into two parts, followed by appropriate mathematical substitution. For particular special cases, the analytical results derived here are shown to reduce exactly to results from past work. Good agreement of the theoretical results with numerical simulations is also demonstrated. Thermal response to a various realistic time-dependent boundary conditions is analyzed. This work may enable the theoretical design and optimization of realistic multilayer problems, and may serve as a design tool for optimization of engineering systems where multilayer thermal conduction plays a key role.