MATHEMATICAL MODEL OF HEATING A PRISM WITH BOUNDARY 
CONDITIONS OF THE 3RD KIND

Yu. M. Pleskachevskii,a V. I. Timoshpol'skii,b
S. V. Shil'ko,a S. L. Gavrilenko,a
and S. M. Kabishovc

UDC 669.041

This paper describes the procedure of computational determination 
of the temperature field of a prismatic workpiece heated in a continuous 
furnace with account for the temperature dependence of the thermal 
diffusivity. For a numerical solution of the two-dimensional heat 
conduction equation with boundary conditions of the 3rd kind, an implicit 
scheme has been used. The calculated time dependences of the temperature 
for three characteristic points of the cross-section of the prismatic 
steel workpiece have been compared to the experimental data. The heat 
transfer coefficients at which the experimental data and the calculated 
values have a minimum discrepancy have been determined.

aV. A. Belyi Institute of Mechanics of Metal-Polymer 
Systems, NAS of Belarus, 32a Kirov Str., Gomel, 246050, Belarus; 
email: shilko_mpria@mail.ru; bPresidium of the National Academy of Sciences of Belarus,
Minsk; cBelarusian National Technical University, Minsk. 
Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 80, No. 6, pp. 3-8, 
November-December, 2007. Original article submitted April 10, 
2007.