A numerical solution for the symmetric melting of spheres

Abstract

SUMMARYA numerical method is presented for the solution of the radially symmetric heat conduction problem in a melting sphere. The method employs the embedding technique; this permits the solution to be written in the form of an ordinary integro-differential equation which is readily solved numerically by means of a forward integration scheme. The accuracy of the method is briefly discussed and numerical results for both constant and variable heat inputs are presented.

Experimental and computational study of constrained melting of phase change materials (PCM) inside a spherical capsule

“…Grimado and Boley [1] among others -Moore and Bayazitoglu [2] were first to report on the ''unconstrained" melting (meaning that the solid portion drops within the melt due to its higher density) of PCM both experimentally and numerically. Assuming that the bottom of the solid region melts so as to remain almost spherical, the polar velocity component within the squeezed gap was approximated as being similar to a pressure-driven flow between parallel plates.…”

Fluid dynamics of frozen precipitation at the air–water interface

“…Despite the fact that this method does not account for the kinetic energy contribution (Shin & Juric 2002), it is extensively employed for melting and solidification applications as it does not require empirical coefficients (Juric & Tryggvason 1998). In addition to the static/low-speed phase change of spherical drops (Grimado & Boley 1970; Mcleod, Riley & Sparks 1996; McCue, Wu & Hill 2008), the model is employed for investigation of the impact and freezing of molten metal (Pasandideh-Fard et al. 1996, 2002) and water (Thiévenaz, Séon & Josserand 2019) drops on solid surfaces, and melting of a solid sphere (Hao & Tao 2002) or cylinder (Ameen, Coney & Sheppard 1991) in cross-fluid-flow.…”