Solution strategy for the inverse determination of the specially varying heat transfer coefficient

Abstract

The solution strategy for the inverse determination of the heat transfer coefficient (HTC) distribution over the water cooled plate has been developed. The HTC distribution in space and time has been approximated using the finite element method with the nonlinear shape functions. The HTC values at nodes of elements have been determined minimizing the objective function. Four objective functions have been tested. The uncertainty of the inverse solutions has been estimated using the developed test function. The test function defines the HTC varying over the cooled plate similarly to the water spray cooling. Based on numerical tests it has been shown that the objective function which has been defined as a norm of the measured and computed temperatures difference should be extended with the norm of the temperature gradients difference. The objective function extension of about 10% of the norm of the temperature gradients difference has reduced low frequency fluctuations of the HTC resulting from the HTC maximum moving over the cooed surface. The inverse solutions to the measured temperatures have been achieved as well. Temperature of the inconel plate heated up to 920°C and then cooled with the full cone water spray nozzle has been measured by 25 thermocouples located 2mm below the cooled surface. The variations of the HTC in time at 9 points located at different distances from the nozzle axis have been presented. It has been shown that the HTC varies significantly as the distance from the water stream axis grows.