Heat transfer at the sensor of a fiberoptic probe for measuring high frequency temperature oscillations in gas flows

摘要

The oscillatory heat transfer processes at a thin platinum film sensor (thickness on the order of 10~(-3) mm or less) covering the tip of a cylindrica fiberoptic probe (diameter on the order of 1 mm) for measuring temperature oscillations in gas flows were investigated analytically. A differential equation for heat balance taking into account convection, conduction and radiation at the sensor film consisting of a cylindrical part (shell) and a plane part (flat end0 was set up, linearized and solved. From the solution, the ratio of gas temperature amplitude to sensor temperature amplitude, an overall "Transfer-function", was derived. At high frequencies whereby the conduction effects play a dominant role, the overall Transfer-function formally reduces to the Transferfunctions that were previously obtained by taking into consideration either the cylindrical part or the plane part of the sensor aone. However,t he numerical values of the three Transfer-functions may differ a little from one another under the same measurement conditions, because of differences among the convection coefficients. An expression for the overall or effective convection coefficient was derived from the analysis. It was also shown that at high frequencies the axial and radial temperature waves in the probe are practically confined to thin layers adjacent to the sensor and have comparable wave length and wave attenuation. This provides a physical explanation for the formal identity of the three Transfer-functionsat high frequencies.