Temperature distribution in a multi-layer cylinder with circumferentially-varying convective heat transfer boundary conditions

Theoretical modeling of thermal conduction in a multilayer cylinder has been studied in multiple past papers due to its significance in engineering applications such as nuclear engineering, energy storage and sensing. Most past papers have assumed a constant convective heat transfer coefficient on the outer surface of the cylinder. However, a circumferentially varying heat transfer coefficient may be appropriate in several applications due to the distributed nature of fluid flow around the cylinder. This paper presents a theoretical model for steady-state thermal conduction in a multilayer cylinder with circumferentially-varying convective heat transfer coefficient on the cylinder surface. The theoretical model is presented for both solid and annular cylinders. A series solution is derived for the temperature distribution in each layer by using the convective boundary condition(s) to derive a set of linear algebraic equations for the coefficients of the inner-most layer. Results are shown to be in good agreement with numerical simulations and with closed-form solutions for special cases. The impact of various problem parameters, such as internal heat generation rate and thermal contact resistances on the temperature distribution is analyzed. It is expected that the results presented in this work will improve the theoretical understanding of multilayer heat transfer and be of practical use in multiple engineering applications.