IOP PUBLISHING METROLOGIA
Metrologia 47 (2010) 33–46 doi:10.1088/0026-1394/47/1/005
Effective emissivity of a cylindrical
cavity with an inclined bottom: II.
Non-isothermal cavity
Alexander V Prokhorov and Leonard M Hanssen
National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, MD 20899, USA
E-mail: leonard.hanssen@nist.gov
Received 20 July 2009, in final form 23 November 2009
Published 16 December 2009
Online at stacks.iop.org/Met/47/33
Abstract
An algorithm of the Monte Carlo method applied to the computation of the spectral and total
effective emissivity of a specular–diffuse, non-isothermal blackbody cavity formed by a
cylindrical tube and a flat inclined bottom is described. The effect of cavity wall temperature
non-uniformity on the cavity radiation characteristics is studied for various combinations of
the affecting parameters.
1. Introduction
In the first part of this work [1], we described the application
of the Monte Carlo method to modelling of the effective
emissivity of an isothermal, specular–diffuse cylindrical
cavity with an inclined bottom. Now we expand the
analysis on such a cavity having a non-isothermal internal
surface.
The effective emissivity of a cavity depends on
its geometric parameters, wall reflectance and diffusity,
temperature distribution over the cavity wall as well as the
conditions of observation. The isothermal approximation
is very useful but not always adequate. Real cavities are
non-isothermal in varying degrees. In order to recall the
existing methods for the calculation of effective emissivities of
isothermal and non-isothermal cavities, we refer the interested
reader to the reviews [2, 3]. The majority of these methods
were developed for axisymmetric cavities with diffuse walls,
so the most common properties of a cylindrical cavity with an
inclined bottom and a non-isothermal radiating surface remain
unexplored. Taking into account the large number of critical
factors and the limited space available, we cannot present an
analysis of all the existing dependences. It is clearly impossible
to provide numerical results for effective emissivities for all
possible temperature distributions, which to a great extent
depend on the design and materials of a particular blackbody
radiator. The scope of this paper is limited to the simple models
used for temperature distributions.
2. Definition of the effective emissivities for a
non-isothermal cavity
The reader is referred to the first part of this work [1] for
the detailed descriptions and definitions of the various forms
of effective emissivity, of which several are used in this
paper. The total and spectral local, directional effective
emissivities for a non-isothermal cavity are defined, as for the
isothermal case, as a ratio of radiances or spectral radiances,
respectively, of an infinitesimal element of a cavity wall in
a given direction to the corresponding quantity of a perfect
blackbody. The principal distinction from the isothermal
cavity case is the fact that there is no unambiguous choice of the
temperature assigned to a non-isothermal cavity to compare it
with a perfect blackbody. That is why a specific temperature
called the ‘reference temperature’, T
ref
, is usually chosen to
characterize the non-isothermal blackbody. The temperature
of the bottom centre (see, for instance, [2, 4, 5]) is suitable for
selection as T
ref
.
The local, directional spectral effective emissivity for a
non-isothermal cavity in a non-refractive environment can be
written in the form
ε
e
(λ,
ξ, ω, T
ref
) =
L
λ
(λ,
ξ, ω)
L
λ,bb
(λ, T
ref
)
, (1)
where L
λ
and L
λ,bb
are, respectively, the spectral radiance
of a cavity with a reference temperature T
ref
, at a point
ξ , a wavelength λ and in a direction ω, and that of a
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