Nonlinear transient heat transfer analysis of multilayered thermal protection systems by incremental differential quadrature element method

As a first attempt, the incremental differential quadrature element method (IDQEM) is used for the one-dimensional nonlinear transient heat transfer analysis of multilayered thermal protection systems (TPSs) under time-dependent aerodynamic heating. All thermophysical properties are considered to be temperature-dependent (TD). Based on the IDQEM, the multilayered TPS is divided into several spatial sub-domains along the layer interfaces, and the entire heating process is also divided into several temporal sub-domains. For each temporal sub-domain, the governing equations are discretized by the differential quadrature method and then solved by the Newton-Raphson method. The initial condition of each temporal sub-domain is defined by the temperature results at the end of the previous sub-domain. The temperature profile of the TPS during the entire heating process can be obtained by repeating the calculation procedure from the first temporal sub-domain to the last one. Convergence and accuracy of the method are confirmed. Numerical examples are carried out to show the effects of TD thermophysical properties, thermal boundary, and layer thickness on the temperature profile of a three-layer TPS. The results show that the temperature dependency of thermophysical properties is worthy of consideration in predicting the temperature profile of the TPSs.