An iterative, analytical method for solving conjugate heat transfer problems

Abstract

Conjugate heat transfer involving convection and conduction in a fluid flow and a solid body in contact with each other occurs commonly in engineering applications. While analytical solutions for individual convection and conduction problems are relatively easier, it is a lot more challenging to solve the combined conjugate heat transfer problem. In this paper, an iterative method is developed for analytically solving conjugate heat transfer problems. Based on an initial assumption of the temperature field at the solid–fluid interface, the temperature distributions in the fluid and solid body are determined by separately solving the governing energy conservation equations in the two domains. These solutions are used to improve the initial assumption of the interface temperature until convergence. It is found that only a few iterations of this process are needed for convergence. Temperature fields computed from this analytical approach are found to be in good agreement with finite element simulation results. The iterative analytical approach is used to solve two technologically relevant problems related to internal and external flows. Given the general nature of the iterative approach, results from this paper may be helpful in solving a variety of conjugate heat transfer problems.