Mathematical models of dependence of surface temperatures of exposed metal plates on environmental parameters

Abstract

The present paper sets out the mathematical models that control the surface temperature of metal plates during atmospheric exposure. Heat transfer can be modelled by a series of heat transfer coefficients for different thermal processes, i.e. conduction, natural convection, forced convection, radiative heat losses to the sky, radiative heat transfer to or from the ground, incoming solar radiation, and evaporation and condensation. The model is applied to predict the surface temperature of near horizontal galvanised steel plates. Undercooling of a galvanised plate relative to the ambient air, i.e.the extent to which the temperature of the plate falls below that of its surroundings, is calculated for both clear and cloudy nights, with and without a slight breeze. It is found that breezes and clouds significantly decrease the extent of undercooling. The temperature differences between the plate and the ambient air after sunrise are also calculated. It is found that the prime factors controlling the post-sunrise temperature difference are whether the plate is wet or dry, whether the sky is cloudy or clear, and the wind speed. Under certain conditions, the increase in plate temperature relative to the surrounding air may be substantially suppressed. The time for wetted salts and aerosols to dry on plates post-sunrise is calculated and, under those conditions where the rise in temperature difference is suppressed, it may take a number of hours for aerosols to dry out. Estimates of temperature difference are compared with experimental data, and parametric equations for estimating surface temperature are presented. The relevance of the results to models of atmospheric corrosion is discussed.