The influence of convection on heat transfer in liquid tin
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I.
INTRODUCTION
I N studies of the solidification of metals dynamic temperature distributions during solidification have been determined using heat transfer analysis and computer calculations. As part of this analysis assumptions have been made concerning heat transfer in the liquid metal with fluid flow present in the melt. For example, in mathematical models of the continuous casting of steel, heat transfer was determined using an effective thermal conductivity which was the thermal conductivity of the liquid without flow, multiplied by an arbitrary number between 7 to 10.t 23 The objective of the present investigation was to determine experimentally how the heat transfer coefficient in the melt is related to fluid flow. Fluid flow in the melt can result from natural convection due to temperature and solute gradients in the melt or forced convection. In this investigation the dependence of heat transfer on fluid flow was determined by measuring the heat transfer as a function of the imposed temperature difference across a cell containing liquid tin. The fluid flow in the melt is related to the temperature difference across the cell.
wall by teflon spacers at the edges, leaving a space of 1.6 mm. The liquid metal can be rapidly quenched by filling the space between the inner and outer walls with water. The liquid cavity in cell B is 100 • 100 • 3.2 mink Cell A had a stainless steel block at the cold end of the celt with two thermocouples soldered 12 mm above and below the center point on the outer surface, as shown in Figure 1. In addition, two thermocouples were positioned on either side of the melt. soldered to the center points of the inside faces of the hot and cold end blocks, as ~hov,,n. To determine a value for the effective thermal conductivity of the melt, it was a~bumed that the heat flow was one-dimensional, giving
q, = ~),,,
[1]
where c}, and ~,,, are the rates of heat flow through the cold end block and the melt, respectively. Substituting for C'l, and CELL A ---~
L,qu,d Tm
~ /,
Gloss
~]
F
II.
T
PROCEDURE
Fluid flow in liquid tin due to natural convection was examined by Stewart and Weinberg 4 using a thin vertical square cavity cell. A relationship between the extent of flow and the temperature difference across the cell was established, using radioactive tracers to delineate the flow. The results were compared to the numerical solutions of the Energy and Navier-Stokes equations for the system/6 A flow cell similar to that used by Stewart was used in the present investigation. Two cells were used having the configuration shown in Figure l. In measuring heat flow across the cell it is necessary to minimize the heat flow through the cell walls. For this reason the walls of cell A were made of glass 3.2 mm thick, with a liquid cavity 38 • 38 • 3.2 mm 3. The second cell, B. was designed to allow the liquid metal to be rapidly quenched, and still be suitable for heat flow measurements. The inner wall next to the liquid metal is aluminum sheet 0.8 mm thick. The outer wall is stainless steel
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