Please use this identifier to cite or link to this item: `http://hdl.handle.net/10646/3458`
 Title: Unsteady contact melting of a rectangular cross section material on a flat plate. Authors: Myer, T GMitchell, S LMuchatibaya, Gift metadata.dc.contributor.authoremail: tim.myers@ymail.com metadata.dc.type: Article Keywords: Stefan conditionheat equationsﬂuid pressureheat balance integral method Issue Date: 6-Oct-2008 Publisher: American Institute of Physics Citation: Myers, T. G., Mitchell, S. L., & Muchatibaya, G. (2008). Unsteady contact melting of a rectangular cross-section material on a flat plate. Physics of Fluids, 20(10), 103101. Abstract: The work in this paper concerns a mathematical model of the contact melting process of a rectangular material in contact with a hot plate. The problem is described by a coupled system of heat equations in the solid and melt layer, ﬂuid ﬂow in the melt, a Stefan condition at the melt interface, and a force balance between the weight of the solid and the ﬂuid pressure. Since the melt layer remains thin throughout the process, we use the lubrication approximation to the ﬂuid equations and assume that the heat ﬂow in the ﬂuid is dominated by conduction across the thin ﬁlm. In the solid we employ a heat balance integral method. Results show that the ﬁlm height has initial and ﬁnal rapid increases, whereas for intermediate times the height slowly increases. The quasisteady state of previous models is never attained: This is shown to be an effect of neglecting the change in mass and conduction in the solid. The previously observed initial inﬁnite velocity of the melt is shown to be a result of the perfect thermal contact assumption. For a water-ice system the melting rate is shown to be approximately linear, this allows us to reduce the problem to solving a single ﬁrst order differential equation for the liquid layer thickness. The main analysis is carried out in two dimensions, but we brieﬂy highlight the extension to three dimensions. The method is veriﬁed by comparison with previously published experimental results on the melting of n-octadecane. URI: http://hdl.handle.net/10646/3458 ISSN: 103101 Appears in Collections: Department of Mathematics Staff Publications

Files in This Item:
File Description SizeFormat