Abstract
Melting of ice in a cubical enclosure partially heated from above was studied. Half of the upper surface was maintained at room temperature and the other half at 70°C. The ice cube was maintained at its melting point at the bottom. The other side surfaces were insulated. The process was first modeled by ignoring the effect of natural convection in the liquid phase. The resulting equations of conservation of energy were solved in each phase. The motion of melting front was governed by an energy balance at the interface. This conduction model was verified by applying it to a I-D phase change problem for which an analytical solution is available. Preliminary experiments conducted resulted in a progress of the phase front faster than that predicted by the conduction model and the interface was smoother due to strong effects of natural convection in the liquid phase, except for the initial start of melting The model was then extended to include convective heat transfer in such a way that the liquid phase was assumed to be a mixed body subjected to natural convection from the top surface and the liquid-solid interface. The flux at the interface was obtained by finding a heat transfer coefficient for natural convection with a cold plate facing upward. The predictions of this convection model agreed well with the experimental results.
Highlights
Melting of ice in a cubical enclosure partially heated from above was studied
A number of studies dealing with analytical or numerical aspects of particular melting or freezing heat transfer problems have appeared in the literature [1,2,3,4,5,6,7,8,9] It has been observed that most studies are for the case of cooling or heating from vertical walls and many models lack quantitative comparison with experiments
Models for phase change problems are in general based on conduction type of heat transfer, both in solid and liquid the actual physical processes show that convection type of heat transfer may be present in the liquid and often plays an important role [10,11,12,13]
Summary
Preliminary experiments showed that ice was melting faster than predicted by the conduction model. Upon the establishment of the strong natural convection effects in the liquid phase in the preliminary experiments, it was decided to use a simplified approach neglecting the small inclination of the melt front to model the averaged convection effects. Where T, is the liquid bulk temperature, T* = o 5(T,,+6,+T,'), m is mass, C is specific heat capacity, h is heat transfer coefficient, A is cross-sectional area of the ice cube and subscripts hot, room and melt refer to top heated surface, top unheated surface and melt front (liquidsolid interface), respectively. At grid points near the melt front, string-intersected approximations to derivatives were used [16-19]. Central differencing was performed to approximate the spatial derivatives at all interior grid points. The discretization details for the case of conduction type of heat transfer, both in solid and liquid, are as follows
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