Inverse method implementation to heat transfer coefficient determination over the plate cooled by water spray

The three-dimensional (3D) inverse solution to water spray cooling from 925 degrees C to room temperature of the AISI 309 steel plate has been presented. The finite element method with linear and nonlinear shape function has been employed in forward simulations of the plate temperature and in the inverse solutions. The forward finite element solvers have been first compared with the analytical solution to the plate cooling. The reduced finite element models have been compared with the reference model for plate cooling under variable in time and space heat transfer coefficient (HTC) and for the temperature-dependent thermophysical properties of steel. It has been shown that the reduced finite element model with only 216 degrees of freedom which utilizes nonlinear shape functions has given the inverse solution to the heat transfer at the cooled surface with the accuracy of 1.6%. The influence of the thermocouple location uncertainty and the temperature dependence of thermophysical properties have been tested in inverse solutions. The implementation of the reduced finite element heat conduction models and the function specification method in space and time have allowed to achieve the 3D inverse solution to the overall heat transfer at the cooled surface with the accuracy of 2%. The developed 3D inverse solution has been employed to the determination of the HTC distribution over the AISI 309 steel plate cooled by the water spray nozzle. The thermal characteristic of the full cone swirl spray nozzle has been developed.