Three different diameter ice spheres were formed and allowed to melt in air. Each sphere was suspended by a string from a cantilevered beam, which had strain gages attached. A four active element Wheatstone Bridge was used to measure the output of the strain gages. The output signal was calibrated to measure weight of the sphere at any time during the phase change process. Data on weight versus time were thus obtained using a recorder.
The objective of this study is to relate Nusselt number to Rayleigh number, as is done in the literature. Characteristic length is needed to find the Nusselt and Rayleigh numbers, but because of the changing geometry of the melting ice spheres, defining characteristic length to appropriately correlate the data becomes difficult.
A number of researchers have proposed equations for characteristic length for melting ice objects. Three different characteristic lengths were determined based on previous work with melting ice spheres, and used to calculate values of Nusselt and Rayleigh numbers at various instants in time. The geometry of each sphere changed during the melting process as did surface area and volume. Three different Nusselt vs Rayleigh number graphs resulted, which are contrasted and compared.
A fourth characteristic length was proposed for the data of this study, which yielded excellent results. An equation relating Nusselt number to Rayleigh number was derived with a correlation coefficient of 0.975. Rayleigh numbers ranged 1.0 × 104 to 1.2 × 107, while Nusselt number ranged from 4 to 10.2. It was found that the Nusselt number could be predicted with
Nu = 1.45 Ra0.126