A Computational Approach in Obtaining Heat Transfer Dimensionless Correlations

"In this paper a computational approach was employed to estimate the melting of solid spheres immersed in different liquid metals and under different convective conditions. The spheres are made from the same material as the liquid metal. The SIMPLER algorithm was implemented using a three-dimensional system in Cartesian co-ordinates. Experimental validation of the dimensionless correlation was carried out in two fluids with vastly different Prandtl numbers. The dimensionless heat transfer coefficient (Nusselt number) is obtained as a function. of the Reynolds and Prandtl number.IntroductionThere is a paucity of dimensionless convective heat transfer correlations applicable to fluids like liquid metals. The existing correlations cover single Prandtl number metals [l] or at most two different Prandtl number metals [2]. A knowledge of heat transfer rates from particles at high flux levels has become increasingly important to the design of energy transfer systems. Melting of solid particles has been studied extensively as it relates to many engineering and environmental applications, such as materials processing, space applications, water resource and energy conversion. When objects are immersed in a fluid with a temperature higher than their melting point, they melt and produce molten material that then mixes with the surrounding fluid. These objects experience not only size variation but also changes in their shape. This observation is more pronounced when the melting occurs in a forced convective flow.Yuge performed pioneering experimental work on the heat transfer from a sphere to air under mixed convection [3]. He suggested procedures for predicting the Nusselt number. Hieber et al [4] studied the spherical system analytically, but their study was limited to flow with small Reynolds numbers. Many researchers studied the melting dynamics of ice spheres in water at different convective regimes. Aziz et al [5] and Hao et al [6] performed measurements of the heat transfer coefficient in the water system by measuring the melting time of ice spheres in forced convection. Hao et al [7] performed visualization studies of ice spheres melting in water under mixed convection regime. All of this groundbreaking work, however, did not involve the use of liquid metals"