An Efficient Method for Calculating Surface Temperature and Heat Flux Based on Embedded Temperature Sensors

Approximate analytical solutions have been obtained for surface temperature and heat flux for the case of two embedded temperature sensors. The solutions have been verified and the range of validity has been established using several methods including comparisons with an exact analytical solution for a linear problem and numerical calculations for a nonlinear problem. The performance of the model is presented in both the frequency domain and the time domain. A propagation of error analysis is presented and is used to establish the optimum spacing between the sensors. The solutions place no restrictions on the boundary or initial conditions and rely only on current values of temperature and its rate of change. The temperature dependence of transport properties is accounted for in an approximate way. The method requires minimal computation and is suitable for implementation as a real-time sensor.