SUPERHEATER TUBE FLAT WALL STATIONARY TEMPERATURE FIELD

The BKZ-220-100-9 steam generator platen superheater tube flat wall stationary temperature fields analysis have been made. The six steel grades, using in boiler fabrication, namely, St. 10, St. 20, 12H1MF, 15HM, 1H18N9T and 12H18N12T, have been used. The temperature curves calculation has been made by using outer and inner surface heattransfer coefficients nine different combinations. 1 Problem physical model The present paper takes the BKZ-220-100-9 steam generator platen superheater tube element as an investigation object. The investigation object wall is flushed with the following operation mediums such as flue gases with the temperature of 1374.15 K on the outer surface and steam with the temperature of 619.15 K on the inner surface [1, 2]. It follows that the steam heating process occurs in tubes using the heat released by flue gases by means of a heat-transfer through the cylindrical wall. The heat is transferred through the wall by means of the heat conductivity process and from the inner surface to the steam by convection. The steels heat conductivity coefficients are known [3, 4] and have constant values (Table 1). The object calculation geometrical characteristics and heat-transfer coefficients are known also [1, 2] and are the constant values (Table 1). The investigation object stationary temperature distributions analysis for a six steel grades at the various outer and the inner surfaces heat-transfer coefficients combinations are the present paper problem. The one-dimensional stationary heat conductivity equation with the third type boundary conditions is used for a task set solving. 2 Problem mathematical model The flat wall stationary temperature field is determined by a mathematical model follows as: 2 ( ) 0, , 1 2 2 d T x L x L


Problem physical model
The present paper takes the BKZ-220-100-9 steam generator platen superheater tube element as an investigation object.The investigation object wall is flushed with the following operation mediums such as flue gases with the temperature of 1374.15K on the outer surface and steam with the temperature of 619.15K on the inner surface [1,2].It follows that the steam heating process occurs in tubes using the heat released by flue gases by means of a heat-transfer through the cylindrical wall.The heat is transferred through the wall by means of the heat conductivity process and from the inner surface to the steam by convection.The steels heat conductivity coefficients are known [3,4] and have constant values (Table 1).The object calculation geometrical characteristics and heat-transfer coefficients are known also [1,2] and are the constant values (Table 1).The investigation object stationary temperature distributions analysis for a six steel grades at the various outer and the inner surfaces heat-transfer coefficients combinations are the present paper problem.The one-dimensional stationary heat conductivity equation with the third type boundary conditions is used for a task set solving.

Problem mathematical model
The flat wall stationary temperature field is determined by a mathematical model follows as: 2 ( ) 0, , 1 2 2 λ is the steel heat conductivity coefficient, measured by Wt per m per K. αm1, αm2 are heattransfer coefficients on the inner and outer surface, respectively, measured by Wt per square meter per K. Тm1, Тm2 are medium temperatures on the outer and the inner surface, respectively, measured in K.The (1) equation analytical solution is obtained in compliance with [5,6] and looks like so: (2) G is the wall thickness, measured in m.This expression is as follows in a dimensionless form: (3) The obtained solution check are made by its substitution from an initial equation and corresponding boundary conditions (1).This equation dimensions check are made also.The made check results have confirmed the computed solution accuracy.

Results and discussion
The nine heat-transfer coefficients variations on the outer and the inner surfaces are used in the paper.αzh1 and αzh2 are reduced by 100, 10 4 and 2 times, respectively, from the first alternative to the forth alternative comparing with the seventh alternative.Αzh2 is reduced by 10 times in the fifth alternative, but is increased by 10, 20 and 30 times, respectively, from the seventh to the ninth alternatives comparing with the calculation value [1,2].The made calculations results are showed below.а is the temperature difference on the inner surface (∆Тwm1 = Т(x = 0) -Тwm1), K; б is temperature drop in the cylindrical wall (δТ = Т(x = L) -T(x = 0)), K; в is temperature difference on the outer surface (∆Тwm2 = Тwm2 -Т(x = L)), K.
Analyzing the flat and cylindrical walls temperature curves showed in figure 1, as you can see the obtained results correspond to the physical meaning.The high temperatures are on the outer surface, but on the inner surface temperatures are below.The temperature curves from the first to the ninth alternatives are the same qualitatively, but there is their quantitative distinction.
The 1, 2, 3, 4 and 7 temperature curves vertical intercept is particularly useful.This flat wall intercept temperature is the same for all five temperature curves, in spite of the thermal physical properties distinction.At the same time this law may be observed for all six steel grades.This vertical intercept coordinates may be determined by using any two temperature curves, forming this vertical intercept, for various Biot numbers, found from expression (2).These mathematical expressions are shown below: ∆Тm27/ ∆Тm21 = 0.960; ∆Тm17/∆Тm11 = 0.960; ∆Тm28/ ∆Тm21 = 0.46; ∆Тm18/∆Тm11 = 1.38.The example demonstrates the temperature curves with the outer surface supplied heats and inner surface transferred heats equal ratios and platen superheater outer and inner surfaces temperature differences and heat-transfer coefficients equal ratios have vertical intercept.

Conclusions
There are temperature distributions vertical intercepts for steels discussed in the paper.It is possible if there are the outer surface supplied heats and inner surface transferred heats ratios equality and the superheater outer and inner surfaces temperature differences and heat-transfer coefficients ratios equality.
T x L are temperatures on the left and the right boundaries, measured in K.

Table 2 .
Temperature differences and temperature drops, K.