Schematic diagram for contact melting.
Schematic of the three stages of melting when a block is placed on a surface above the melting temperature.
Temperature profile at the end of stage 1, i.e., . Shown is the exact solution (solid line) compared with the cubic (dashed line), quadratic (dash-dotted line), and exponential (dotted line) heat balance integral method solutions, with marked by “” for each case.
(a) predicted by current method ( dotted line, solid line) and quasisteady solutions, (dashed line) and (dash-dotted line) for , (b) melt height predictions; ( dotted line, solid line), (dashed line), and (dash-dotted line).
(a) when and quasisteady solutions, (dashed line), (dash-dotted line) , (b) when , , and .
Temperature in melt and solid at (dash-dotted line) and (solid line).
Maximum horizontal velocity in the melt region for (a) and (b) .
Variation of with ; (a) and (b) .
Comparison of solutions for (a) and (b) . The solid lines represent the exact solution and the dashed lines are the linear approximation.
Comparison of height with experiment (asterisks) for the current theory with (a) (solid line), (b) (dashed line), (c) Eq. (40) (dash-dotted line), and (d) quasisteady solution of Eq. (16) (dotted line).
Parameter values for ice/water and liquid/solid -octadecane.
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