International Scientific Journal

One-dimensional melting and freezing problem in a finite slab with time-dependent convective boundary condition is solved using the heat-balance integral method. The temperature, T4 1(t), is applied at the left face and decreases linearly with time while the other face of the slab is imposed with a constant convective boundary condition where T4 2 is held at a fixed temperature. In this study, the initial condition of the solid is subcooled (initial temperature is below the melting point). The temperature, T4 1(t) at time t = 0 is so chosen such that convective heating takes place and eventually the slab begins to melt (i. e., T4 1(0) > Tf > T4 2). The transient heat conduction problem, until the phase-change starts, is also solved using the heat-balance integral method. Once phase-change process starts, the solid-liquid interface is found to proceed to the right. As time continues, and T4,1(t) decreases with time, the phase-change front slows, stops, and may even reverse direction. Hence this problem features sequential melting and freezing of the slab with partial penetration of the solid-liquid front before reversal of the phase-change process. The effect of varying the Biot number at the right face of the slab is investigated to determine its impact on the growth/recession of the solid-liquid interface. Temperature profiles in solid and liquid regions for the different cases are reported in detail. One of the results for Biot number, Bi2=1.5 are also compared with those obtained by having a constant value of T4 1(t).

PAPER SUBMITTED: 2008-09-24

PAPER REVISED: 2009-03-10

PAPER ACCEPTED: 2009-03-20

DOI REFERENCE: https://doi.org/10.2298/TSCI0902141R

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© 2021 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence