Modified Relationship for Nusselt Numbers on the Side Surface of a Flat Metal Layer of Melt Heated from Below

An analysis was made of the developed modified Nusselt number ratio Nu for estimating thermal loads on the surfaces of a flat horizontal layer of metal melt (liquid-metal coolants, metal melt layers formed inside nuclear power plant (NPP) containers during a severe accident, etc.), heated along its lower surface and having an uneven radial temperature distribution. The need for such an analysis is explained by the fact that the use of known relations for the Nusselt numbers Nu for a liquid/melt layer with an uneven longitudinal temperature distribution leads to significant errors in determining the heat transfer conditions at the boundary surfaces of the layer, which is critical, for example, when implementing the concept of retaining molten materials inside the nuclear power plant in case of a severe accident (SA). In the proposed relation for the Nu number on the lateral surface of the melt layer, both traditional (Rayleigh number) and additional parameters are used, taking into account the temperature conditions on its boundary surfaces (including the lateral one) as well as the dimensions of the layer. To find the unknown coefficients in the modified ratio, the results of several series of numerical experiments were used by the domestic ANES CFD code. Using the ratio obtained for the Nu number, a parametric analysis of the heat-transfer conditions on the side surface of the metal layer of the melt formed during an SA was carried out. According to the results of the analysis, the proposed ratio gives good accuracy in calculations (on average, the error did not exceed 7%) and the predictive efficiency of the developed modified ratio for Nu numbers in the range of Rayleigh numbers from 10⁶ to 10¹². Such a relation for the Nu numbers on the side surface of the melt layer can be used in assessing the thermal loads on the nuclear power plant container during an SA and in other problems where there is a radial nonuniformity of the temperature distribution in a flat liquid/melt layer heated from below.