On uncertainty and local sensitivity analysis for transient conjugate heat transfer problems

The need for simulating real-world behavior of automobiles has led to more and more sophisticated models being added of various physical phenomena for being coupled together. This increases the number of parameters to be set and, consequently, the required knowledge of their relative importance for the solution and the theory behind them. Sensitivity and uncertainty analysis provides the knowledge of parameter importance. In this paper a thermal radiation solver is considered that performs conduction calculations and receives heat transfer coefficient and fluid temperate at a thermal node. The equations of local, discrete, and transient sensitivities for the conjugate heat transfer model solved by the finite difference method are being derived for some parameters. In the past, formulations for the finite element method have been published. This paper builds on the steady-state formulation published previously by the author. A numerical analysis on the stability of the solution matrix is being conducted. From those normalized sensitivity coefficients are calculated dimensionless uncertainty factors. On a simplified example the relative importance of the heat transfer modes at various locations is then investigated by those uncertainty factors and their changes over time.