Surface heat transfer coefficient measurement by immersed temperature sensor and inverse modelling

Abstract

A transient surface heating or cooling process of a solid is considered. A procedure for the determination of surface temperature and surface heat flux density during such a process is presented using a submersed temperature sensor in the solid. From this measured temperature the surface temperature and surface heat flux density are calculated by inverse process modelling. This method is prone to errors since measurement errors are amplified in the inverse process modelling and can thus easily become unacceptably large. The LSQR regularisation algorithm is optimised for fast performance as well as less memory requirement and applied to the inverse problem solution. The proposed method allows to simulate an experimental setup and to determine the accuracy of the results gained from the simulated experiment. This is essential for the determination of the accuracy of a planned or existing test facility. The influence of process parameters like sensor depth, sensor noise level, sampling rate, heat flux density amplitude and cooling/heating process duration is investigated. In most cases it is very important to carefully adjust the process parameters in order to obtain reliable and accurate results. Additionally the proper selection of the regularisation parameter required for the inverse problem solution is analysed.

Continuous Casting Secondary Cooling: Laboratory Heat Transfer Measurements and Accuracy Considerations by Comparison with the Real Situation

“…Especially for the high-performance cooling required Figure 10. Left: electrically insulated thermocouple in the metallic probe with a drilled hole, cooled surface is on top; right: ceramic (insulating) probe material with a moulded thermocouple; red dots denote the effective measuring position of the thermocouple, [18] black lines represent the distance from the surface in tenths of millimeters. Figure 9.…”

“…This can be achieved by adopting the sensor depth and the sampling rate to the cooling conditions and the sensor noise. [18] The following figures show results from the simulations of a cooling process corresponding to an average heat flux density of %500 kW m À2 . In Figure 9a, it is shown that how the measurement error can be reduced by placing the sensor closer to the surface and reducing the sensor noise level.…”

“…For time discrete systems, the folding operation is a convolution of two vectors that can be calculated efficiently using the fast Fourier transformation. [ 18 ] Now the initial condition is generally not correct as it would imply a homogeneous cooling for . The passage of the strand beyond one nozzle row after the other can be seen as a quasiperiodical process, where the influence of the initial condition disappears quickly.…”

“…Therefore, it is necessary to make the problem as little as possible “ill posed.” This can be achieved by adopting the sensor depth and the sampling rate to the cooling conditions and the sensor noise. [ 18 ]…”

“…Heat flux measurement error using an immersed temperature sensor: a) with different noise signal levels as a function of the sensor depth, b) as a function of the sampling frequency, [ 18 ] n denotes the number of samples used for the heat flux determination.…”