An exact analysis for heat conduction in laminated infinite cylindrical arches subjected to Dirichlet boundary conditions

Abstract

The temperature field within a layered arch subjected to Dirichlet Boundary Conditions is investigated based on the exact heat conduction theory. An analytical method is shown to obtain the temperature field in the arch. Because of the complex of the temperature boundary conditions, the temperature field is divided into two parts with the linear superposition principle. The first part is a temperature filed from the temperature boundary conditions on the lateral surfaces. The second part is from the temperature conditions on the outside surfaces expect the influence from the two edges. The temperature solution of the first part is constructed directly according to the temperature boundary conditions on the lateral surfaces. The temperature solution of the second part is studied with transfer matrix method. The convergence of the solutions is checked with respect to the number of the terms of series. Comparing the results with those obtained from the finite element method, the correctness of the present method is verified. Finally, the influences of surface temperature and the thickness-radius ratio h∕r0 on the distribution of temperature in the arch are discussed in detail.