MODELLING OF HEATING OF THE INGOT
IN REGENERATIVE HEATING WELLS
With application of mathematical modelling it is considered Heating of ingots in regenerative heating wells. Alternate submission Fuel through regenerators leads to asymmetrical heating of ingots. Reduction of time between switching valves with identical rate of growth On each interval process allows to intensify temperatures of the furnace Heating of ingots and to reduce fluctuation of temperatures.
Introduction
the Oven facilities of factories of ferrous metallurgy of Ukraine
Consumes a plenty of fuel. Till now the core
Source of fuel was natural gas. However deficiency of natural gas and
Sharply increased cost for 1000 m 
forces
Consumers sharply to reduce use of natural gas and to find others
Sources of heat.
In this connection the role regenerative has increased Heating wells, which owing to heating of air and gas up to high Temperatures, can work on low-calorie fuel as on domain Gas, and on mixes.
In connection with the arisen problem of economy of fuel The decision problems by various criteria of an optimality is necessary. One of such criteria is optimization on a minimum of the charge of fuel.
Work of regenerative heating wells is connected With cyclic submission of fuel. Such submission of fuel leads to that The ingots costing at an ardent window, are heated non-uniformly.
the Analysis of the received results
°Ñ with the sizes 0,715 ´ 0,65 ´ 2,33 m. At calculation it is accepted, that
The identical sizes have the top and bottom basis of an ingot.
the Near side of an ingot Cooperates with the products of combustion leaving an ardent window; distant The side is in a zone of weak circulation, sides are equally washed by products Combustions, therefore the temperature of environment on these sides changes in regular intervals.
1 curves Resulted in figure
Correspond to two cases of heating with various time switch valves.
The first case ( - ) switch valves occurs through 
= 780 ñ, in the second
Case ( ---) switch valves occurs through = 600 ñ.
Both in one and in other case change of temperature of environment through identical number
ïåðåêèäêè valves equally. It leads to that temperature of environment at = 600 ñ grows in time more quickly, than
At switch = 780 ñ. Than
It is less time between switch, that the temperature more quickly grows.
Apparently from figure 1, fluctuation of temperature
During the initial moment of time it is not essential a surface, it practically does not go down,
And remains to a constant. But since time, approximately, 
= 4500 ñ temperature
Products of combustion from a cell strongly decreases. At smaller time between
ïåðåêèäêàìè valves fluctuation of temperature of a surface smaller, than at greater
Time between switch. It is connected by that duration of interaction
The maximal and minimal value of temperature of environment from a surface of a body
It is less and the temperature of a surface will raise or go down on smaller
Size.
the Quantity switch will increase at smaller time
Between switch valves. At the same growth rate temperature of environment for
Certain time will grow up to greater value, and the ingot will get warm up to more
Heat.
So, during heating = 7800 (figure 3)
At = 600 (---) temperature
On a surface has reached value 
°Ñ, and in
To the middle 
°Ñ. At time switch = 780 with
( - ) temperature on a surface 
°Ñ, and in
To the middle 
°Ñ.
a Fig. 2 . Change of temperature On section of a body for the various moments of time
At the same number ïåðåêèäîê valves an ingot with Smaller time between switch valves will heat smaller time, than Ingot with greater time between switch.
= 600 with
Time of heating has made = 4200 with
Temperature curve ( 
) it is located below, than
At = 780 with 
and general time of heating = 5450 with.
In the first case the temperature of a surface is equaled 
°Ñ, temperature
The middle 
°Ñ, and in the second
Case 
°Ñ, 
°Ñ.
If to compare heating ingots on number switch valves, That at greater time between switch ingots are heated longer and temperature on To section will be above, than at ingots at smaller time between switch Valves.
Distributions of temperature on section of a body with a difference in time. During
Time from = 9600 with up to = 10200 about products of combustion adjoin
With a forward side 1 (figure 2) it is direct at an output from an ardent window. Opposite
The side 3 is shaded by an ingot and temperature of environment there less. Distribution
Temperatures on section of an ingot it is presented to a curve 
figure
2 . In a point 1 temperature is equaled
°Ñ, and in a point 10 it is equaled 
°Ñ. During the moment of time = 10200 about products of combustion have changed
Direction of movement on the return and in current of time from = 10200 with up to = 10800 c the side 3 is heated more intensively, than
Side 1. Distribution of temperatures is presented to a curve ( 
-) figure 3. Temperature on the verge of
1 has gone down and became equal 
°Ñ, and on the verge of 3 has raised and
It is equaled 
°Ñ. In all other points on section temperature
Has raised: in a point 2 was equal 
°Ñ became equal 
°Ñ, in a point 9 it was equaled 
°Ñ also has raised up to temperature 
°Ñ.
Conclusions
Modelling heating of ingots Is executed in Regenerative heating wells in view of non-uniformity temperature Fields in a cell, the fuel caused by cyclic submission, in one, in other Direction.
Dynamics of heating of ingots Is resulted at various Duration between switch valves. Change of temperature of environment at smaller Duration of a cycle with the same intensity, as well as at greater duration Cycle, allows to intensify process of heating not only on a surface Ingot but also to increase speed of rise of temperature of its center.
At identical quantity switch valves greater Time of heating corresponds to greater time between switch valves.