Melting of unfixed material inside an elliptical capsule

An approximate mathematical model of contact melting of an unfixed material in an elliptical capsule is developed. The main characteristic scales and non-dimensional parameters which describe the principal features of the melting process are found. Choosing the special heat flux distribution on the wall of the capsule allows us to derive a closed-form evolution equation for the motion of the solid, which also determines the melting rate. It is shown that the melting rate depends on the shape of the capsule. The elliptical capsules show higher rate of melting than the circular ones. The vertically elongated capsules provide more effective melting than the horizontally elongated ones, even though they have the same aspect-ratios and vertical cross-sectional areas. The time required for complete melting can be achieved by the right choice of the shape of the capsule, which is specified by the value of the aspect ratio. This is especially important for the design of practical latent-heat-thermal-energy systems.