Abstract

• The heat transfer coefficient distribution at the vertical surface of a plate cooled in air was determined. • The plate emissivity was simultaneously determined with the convection heat transfer coefficient. • The inverse solution accuracy resulting from the temperature measurement method as well as from the finite element solution to the plate temperature was determined. • It was shown that the boundary condition model which uses the average Nu number did not allow for simultaneous determination of the plate emissivity and the convection heat transfer coefficient. • As a practical part a new formula for the Nusselt number for the vertical plate cooling in air from an initial temperature up to 900°C was developed. Experiments on the vertical plate cooling in air have been performed. The plate made from EN 1.4845 steel was cooled from temperatures of 700°C and 900°C. The plate temperature was recorded at 36 locations. In addition, the cooling chamber temperature and the air temperature were recorded. The selected heat transfer coefficient (HTC) models taken from literature were added to the finite element solver. It has allowed to reveal the models’ accuracy to the measured temperatures. The average temperature error (ATE) varied from 8.2 K to 33.4 K. The best accuracy gave the Churchill and Chu model. The highest ATE gave the Eckert and Jackson formula. It has been shown that the tested models were not sufficient for modeling a vertical plate cooling from high temperatures. Next, an inverse method has been employed to retrieve the convection heat losses simultaneously with the plate emissivity. Two HTC models have been employed in the inverse solution to the convection heat losses at the vertical plate cooled in air. The heat flux at the plate surface was determined as a sum of heat fluxes resulting from natural convection and radiation. The uncertainty tests confirmed a high accuracy of 1.5% of a local HTC model. The decomposition of the total heat flux into the convection and radiation part was possible only in the case of a local HTC model. It has been shown, that during transient cooling of a vertical plate in air the convection heat losses for plate temperature above 200°C differ significantly from that reported in the literature. For practical applications, a new model for calculating the convection heat losses has been proposed. The model involves the temperature excess only as an independent variable. The model can be applied for vertical plates cooling from temperatures reaching up to 900°C.

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