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oai:recercat.cat:2072/4528542024-06-06T09:49:38Zcom_2072_98col_2072_378195

00925njm 22002777a 4500 dc Font Martínez, Francesc author Myers, T. G. author Mittchell, Sara L. author Centre de Recerca Matemàtica author 2012 In this paper a one-phase supercooled Stefan problem, with a nonlinear relation between the phase change temperature and front velocity, is analysed. The model with the standard linear approximation, valid for small supercooling, is first examined asymptotically. The nonlinear case is more difficult to analyse and only two simple asymptotic results are found. Then, we apply an accurate heat balance integral method to make further progress. Finally, we compare the results found against numerical solutions. The results show that for large supercooling the linear model may be highly inaccurate and even qualitatively incorrect. Similarly as the Stefan number β → 1&sup&+&/sup& the classic Neumann solution which exists down to β =1 is far from the linear and nonlinear supercooled solutions and can significantly overpredict the solidification rate. Transformacions de fase (Física estadística) Similitud (Física) Matèria, Teoria cinètica de la One-dimensional solidification of supercooled melts