MODELING AND CALCULATION OF THE TEMPERATURE FIELDS
IN TWO-LAYER ARTICLES
V. T. Shmuradko,
O. V. Roman,
F. I. Panteleenko,
O. P. Reut,
A. G. Tarasov,
A. V. Drozdov,
and N. V. Kirshina
Translated from Novye Ogneupory, No. 9, pp. 16 – 23, September, 2011.
Original article submitted July 27, 2011.
A mathematical model and algorithm for calculation of the temperature fields for two-layer articles are devel
oped. Using the new algorithm a program is created and numerical calculations of the temperature fields that
develop in a two-layer article (nonswirl nozzle) in the course of preparation of the pony ladle of a continu
ous-casting machine for service and in its operating regime are performed. With the use of the program and
computer software (in light of experimental results) it becomes possible to perform calculations and predict
the sintering mode of ceramic refractory materials as well as optimize the temperature and time heat-treatment
diagrams of one- and two-layer articles.
Keywords: mathematical model, computation algorithm, initial and boundary conditions, heat conduction,
temperature field, two-layer material, nonswirl nozzle, crucible, sintering
Statement of problem. We will use for the calculations
the axisymmetric heat-conduction equation expressed in
terms of cylindrical coordinates:
where t(r, z, t) is temperature; a =
, thermal conductivity;
r, density; c, heat capacity; and l, heat conduction of mate
rial of crucible.
In determining the boundary conditions we will not take
into account the effect of radiation and convective flows
caused by the presence of melt on the free surface of the noz-
zle (crucible). We will assume that heat exchange with z > z
is caused solely by the temperature difference between the
wall and the medium, the temperature of which will be as
sumed to be constant and equal to t
. In fact, it may differ
significantly from reality but with such an assumption we
will have maximum temperature gradients and, conse
quently, maximum design stresses, which corresponds to the
objectives of the calculations.
Initial conditions. The temperature of the crucible is
equal to the ambient temperature:
= const. (2)
The third-order boundary conditions are written in the
£ z £ z
where l is the heat conductivity of the wall; n, outer normal
to the heat-exchange surface; a, convective heat-transfer co
efficient; c, wall index; and t
, ambient temperature.
Refractories and Industrial Ceramics Vol. 52, No. 5, January, 2012
1083-4877/12/05205-0319 © 2012 Springer Science+Business Media, Inc.
O. V. Roman (director), V. T. Shmuradko, et al., Development of
High-Temperature Composite Materials and a Technology for the
Fabrication of Two-Layer Nonswirl Nozzles with Stable Thermal
and Corrosion-Erosion Properties in Pouring of Steel under the
Conditions of RUP BMZ and Management of their Production
(text) [in Russian]. Report on Scientific Research Project (final
report), BG NPK PM GU NII IP with OP, O. V., Minsk (2005),
110 pp.; bibliography p. 109; No. GR 20032592
GNUIPM National Academy of Sciences of Belarus, Minsk, Re
public of Belarus.
Belarus National Technical University, Minsk, Republic of Belarus.