Fuzzy pid based Temperature Control of Electric Furnace for Glass Tempering Process

Heat flow rate: 
The heat flow rate Q can be calculated as [35] 
( 
)
-----------------------------------------------------------------------3.21 
Where 
 
H is the amount heat flow (input power)in material Mcal/hour,
 
Q is the flow rate of heat through array of nozzles to glass surface by 
compressed air (radiation and convention)
 
 is density of air
 
 
 is the specific heat of air, Mcal / deg .ton, 
 
is heating temperature 
 
is lower temp/room temperature
The required amount of heat flow (input power) H can be calculated as 
1. By conduction [36] 
Rate of heat conduction ∞ 
( )( )
---------------------------------------------------------------------------------------3.22 
Where,
 
(
)is is the thermal conductivity of the glass 
 
( ) Thickness of the glass and furnace chamber that has physical
contact to the heater
Thus
2. By convention and radiation 

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Fuzzy PID Based Temperature Control of Electric Furnace for Glass Tempering Process
M.Sc. Thesis, Addis Ababa University, December 2016 
30 
By radiation heat transfer to or from a surface surrounded by a gas such as air occurs parallel 
to conduction (or convection, if there is bulk gas motion) between the surface and the gas [36]. 
Thus the total heat transfer is determined by adding the contributions of both heat transfer 
mechanisms. For simplicity and convenience, this is often done by defining a combined heat 
transfer coefficient
that includes the effects of both convection and radiation 
( 
)--------------------------------------------------------3.23 
Where,
 
( 
)
 
is surface temperature and ( 
) is temperature of the gas. 
 
is surface area of the glass to be heated. 
Thus
60,616.6 watt 
Therefore total amount of heat transfer is
-----------------------------------------------------------3.24 
Assumptions 

volume of the furnace chamber is chosen to be V=4m^3 

velocity of the glass is chosen to be

Length of furnace =2m 
=0.18 cal/gram
o
C 
=2.5gram/cm^3 
Electric Power =120kw=120kJ/s 
Thus substituting in Eq.(3.21)
Q= 0.16m^3/s 
Substituting the values of Q , V,
in Eq.(3.5) yields: 

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Fuzzy PID Based Temperature Control of Electric Furnace for Glass Tempering Process
M.Sc. Thesis, Addis Ababa University, December 2016 
31 
K=13.07 and 
T=25s
And the delay time
=20s 
Thus the dynamic model of glass tempering resistance furnace is 
( )
( )
( )
----------
------------------------------------------3.25