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