Real-time heat flux measurement using directional flame thermometer

• Heat conduction in two layers analyzed for inverse heat conduction problem (IHCP).
• Coupled solutions from two layers estimates heat flux using two sensors in layer 2.
• Solution interpreted as digital filter suitable for online estimation of heat flux.
• Variable properties accommodated via interpolation of filter coefficients.

Real-time measurement of heat flux is an important challenge for several industrial applications, including furnace control. For efficient operation of high-temperature process furnaces, accurate and stable temperature measurements are needed. Directional Flame Thermometer (DFT) offers the ability to use both temperature and heat flux measurements for furnace control. Currently, analysis of dynamic temperature data from DFT to compute heat flux information must be performed off-line using the gathered temperature data and a full-non-linear inverse heat conduction problem (IHCP) analysis. Developing a near real-time algorithm for accurate reduction of the data will allow for continual monitoring of the furnace during operation. This will result in better furnace control and significant savings in energy and cost. This paper provides a solution strategy based on the filter concept for the IHCP associated with DFT. The filter-based solution has the capability of heat flux estimation in near real-time. Two IHCPs are discussed and a coupled solution is proposed to estimate the unknown surface heat flux. The variation of thermal properties with temperature is taken into the account through interpolation of the filter coefficients computed at different temperatures. The solution procedure is validated by comparing the results with a numerical test case developed in ANSYS. Results are also computed using data from a physical experiment with DFT (see Ref. [13]). The heat fluxes obtained are found in good agreement with those obtained from a full non-linear IHCP analysis.