Pressurization of a Solidifying sphere of hot Molten Material quenching in to The Water by The Shell Theory

An approximate analysis is presented of the pressurization in a Solidifying sphere of molten material (Initially at a uniform melting temperature) immersed in an infinite cooling medium . The steady state approximate method is applied to the heat conduction problem with change of phase (The Stefan problem) . This Solution provides the temperature distribution in the shell and rate of solidification , which can be the solid shell . Solidification is dependent both on Biot Number and temperature difference between melting temperature of the molten material and the bulk temperature of the cooling medium . pressurization inside the solid shell increases abruptly in the very early stages of solidification , and then quickly levels off , approaching a maximum value. Stress distributions are evaluated and plotted in dimensionless from. Additional results are presented for the specific case of Aluminum alloy

Keywords:

Shell theory , Solidification , pressurization , Stefan Problem . Steady-state