An approximate analytical method for nonlinear transient heat transfer through a metallic thermal protection system

Metallic thermal protection system (MTPS) is being investigated more popular in present. In preliminary design, the MTPS can be simplified as a multilayer plate, and a one-dimensional transient heat transfer analysis is commonly used to size the thickness of MTPS. A novel approximate analytical method based on separation of variables and orthogonal expansion technique is presented for temperature prediction through MTPS subjected to convection and radiation boundary conditions, which considers the effects of temperature-dependent thermal material properties. The proposed method applies a set of linear functions with space-variable to describe the distribution of thermal diffusivity through the thickness direction, and it adopts a numerical solution dividing the whole process of heat transfer into a chosen number of time steps to solve the problem of boundary conditions variation with time. An advanced linearized approximation for radiation boundary condition is developed for modified use with the analytical model. Implementation of the proposed method is demonstrated by applying it to determine the problem of nonlinear transient heat transfer through a MTPS made of Titanium 6-4 and Saffil, and a good agreement is presented by comparing with the finite element method (FEM) results.