Melting in spherical enclosures

Date of Award




Degree Name

Doctor of Philosophy (Ph.D.)


Mechanical Engineering

First Committee Member

Subrata Sengupta, Committee Chair


In this study, the melting process in spherical enclosures has been examined. A sphere with a phase change material initially in the solid phase which may be initially subcooled or at its melting temperature, is instantaneously exposed to an uniform temperature, greater than the melting temperature, at the wall. The solid phase is assumed to have a higher density as compared to the liquid and drops down as it melts. Heat transfer to the solid core is primarily by conduction where the liquid layer is thin, whereas natural convection plays as important role in other regions. In those cases when the solid phase is subcooled at the start of the process, some of the heat transferred to the core is used to raise its temperature and only part of the energy is used in melting the solid.A mathematical model has been developed taking the different aspects of the process into account. Suitable simplifications have been made where necessary, in order to reduce computational effort and time. The non-dimensionalized melt time and heat transfer coefficient have been obtained as a function of the property values, operating temperatures and physical size for Md $\ll$ 1, Ste $\ll$ 1, 10$\sp4$ $\leq$ Gr $\leq$ 10$\sp6$, 10 $\leq$ Pr $\leq$ 100, 0.5 $\leq$ Mt $\leq$ 5.0, 0 $\leq$ Sb $\leq$ 0.75, 0.01 $\leq$ 1/Pr$\alpha\sp\circ$ $\leq$ 1.0 and 0.01 $\leq$ Ste/c$\sbsp{\rm p}{\circ}$ $\leq$ 0.2.


Engineering, Mechanical

Link to Full Text