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High-temperature fixed-point radiators: The effect of the heat exchange<br />
within the cavity and between cavity and furnace tube on the temperature<br />
drop across the back wall of the cavity<br />
P. Bloembergen, Y. Yamada<br />
National Metrology Institute of Japan, AIST, Tsukuba, Japan<br />
P. Jimeno Largo<br />
University of Valladolid, Valladolid, Spain<br />
B.B. Khlevnoy<br />
All Russian Research Institute for Optical and Physical Measurements (VNIIOFI), Moscow, Russia<br />
Abstract. At high temperatures the heat exchange within a<br />
cavity radiator and between cavity and front end of the<br />
associated furnace are considerably enhanced and by this<br />
the temperature drop across the back wall of the cavity<br />
within the cavity-furnace combination is markedly<br />
influenced. This will be demonstrated, theoretically and<br />
experimentally, for the eutectic fixed point Re-C, radiating<br />
at a temperature of 2474 °C.<br />
Introduction<br />
For the freezing points of silver and gold the following<br />
equation has been used earlier to estimate the temperature<br />
drop ∆T across the back-wall of the cavity [1]:<br />
4 d ⎛ r ⎞<br />
∆T<br />
= cosθ ⋅ε<br />
⋅σ<br />
⋅T<br />
⋅ ⋅⎜<br />
⎟ (1)<br />
K ⎝ L ⎠<br />
where θ is the tilt angle of the conical bottom, ε the<br />
emissivity of graphite, σ the Stefan-Boltzmann constant, T<br />
the temperature in Kelvin, d the thickness of the cavity<br />
bottom, K the thermal conductivity of graphite, r the<br />
aperture radius and L the cavity length. As shown below<br />
this estimate can be considered only as an upper bound to<br />
∆T since in its derivation heat exchange within the cavity<br />
(radiative and conductive) and between cavity and furnace<br />
front-end (radiative) has been neglected.<br />
2<br />
wavelengths of 650 and 950 nm, shown in columns 4 and 5,<br />
and discussed below. As demonstrated in Table 1, column 2,<br />
Eq. (1) indeed constitutes an upper bound to ∆T(3) ; the<br />
result for the ‘cell only’ relative to that for Eq. (1) shows the<br />
influence of the heat exchange within the cavity.<br />
Profile<br />
∆T(3)<br />
mK<br />
T(3)-T(8)<br />
mK<br />
T(3)-T(8)<br />
650 nm<br />
mK<br />
T(3)-T(8)<br />
950nm<br />
mK<br />
High 79 130 140 ±80 130 ±30<br />
Low 88 201<br />
Cell 136 684<br />
Eq. (1) 219 1340<br />
Table 1: Temperature drop ∆T(3) calculated for a cavity aperture<br />
of 3 mm and differences T(3)-T(8) between cavity-bottom<br />
temperatures calculated and measured for apertures of 3 mm and<br />
8 mm. Details are given in the text.<br />
Simulations based upon the finite-element method<br />
Simulations are presented for the cylindro-conical cavity<br />
in the Re-C eutectic cell 3S2, mounted in furnace VR10<br />
–A19 [2] with following cavity dimensions: L= 45 mm,<br />
diameter = 8 mm, θ = 30 °, d = 3 mm, without and with an<br />
aperture, 3 mm in diameter. For graphite we assumed : ε =<br />
0.86, K(at 2500 °C) = 36.4 Wm -1 K -1 .<br />
Columns 2 and 3 of Table 1 show the temperature drop<br />
∆T(3) for a cavity aperture of 3 mm and the difference<br />
T(3)-T(8) between cavity-bottom temperatures for apertures<br />
of 3 mm and 8 mm, calculated for the furnace-temperature<br />
profiles T(x), denoted as low and high, shown in Figure 1. In<br />
the table these results are compared with calculations (a)<br />
for the cell only, formally implying T(x) = 0 K, (b) by means<br />
of Eq. (1), and (c) with experimental results, obtained at<br />
Figure 1: Furnace-temperature profiles T(x), low and high, used<br />
for calculating the temperature drop ∆T(3) and the differences<br />
T(3)-T(8); x defines the distance to the cavity aperture.<br />
All of the calculated results presented here are based upon<br />
simulations of the temperature drop ∆T at the end of the<br />
melting plateau in which-ideally-the liquid-solid interface<br />
coincides with the outer wall of the cavity tube. The<br />
simulations have been performed using ANSYS, a<br />
finite-element software package; details are given in [3].<br />
Proceedings NEWRAD, 17-19 October 2005, Davos, Switzerland 287