Freezing a saturated liquid inside a sphere

A new semi-analytical procedure is employed for the problem of freezing a saturated liquid inside a spherical container and including the effect of radiation at the container surface. Generally moving boundary problems of this type involve a boundary layer analysis. The approximation scheme employed here avoids this complication and gives rise to successive estimates of the time rc for complete solidification of the sphere. In addition an integral formulation is adopted to independently establish bounds for tc. The upper and lower bounds obtained are the standard order one corrected estimate of tc and the pseudo steady-state estimate of rc, respectively. Numerical values of the successive estimates for tc indicate firstly satisfactory convergence and secondly that they are indeed consistent with the bounds independently established. Numerical values obtained for the position of the moving front are in agreement with previous results arising from both a completely numerical solution and an alternative semi-analytical solution of the problem.