Measurement of Transient Heat Flux and Surface Temperature Using Embedded Temperature Sensors

摘要

A method for resolving inverse heat conduction problems using approximating polynomials is described. The coefficients are obtained by constraining the even-numbered spatial derivatives of the polynomial at two points within the domain using the heat equation. The result is a linear time-invariant system that can be implemented as a digital filter and is suitable for application in a real-time sensor. The method places no restrictions on boundary or initial conditions, and temperature dependence of transport properties is accounted for in an approximate way. The performance of the model has been validated using analytical and numerical solutions, and results are presented in the frequency and time domains for several orders of polynomials. A propagation of error analysis is presented and is used to establish the optimum location of the sensors.