- The size and length of heating element for given temperature is calculated by knowing electrical input and input voltage.
- The heating element may be circular or rectangular in shape.
- The rectangle shape is generally used in toasters, ovens, vulcanizers etc.
- As the heat will be dissipated from the heating element at higher temperature, it is assume that all the heat is dissipated by radiation.
Circular Shape
Let V be the supply voltage and R be the resistance of heating element. The Electrical input
voltage P = V2 / R………..( 1 )
Where R is the
resistance of heating element and V is the supply voltage
Resistance R =
ρL / a
= ρL / ( πd2 /
4 ) ( circular heating element )
= 4ρL / ( πd2
)……………….( 2 )
From equation ( 1
) and ( 2 )
Electrical input
power P = V2 / [ 4ρL / ( πd2 ) ]
= ( πd2
V2 ) / 4ρL ………( 3 )
OR
L / d2 = π
V2 / 4ρP …..…………( 4 )
Where
P = Electrical
input power / phase
V = Operating
voltage / phase
R = Resistance
of the heating element in ohm
ρ = Resistivity
of the heating element in ohm – meter
L = Length of
heating element in meter
d = Diameter of
circular heating element in meter
Heat dissipated per unit area according to Stephen’s law
H = 5.72 ke[ ( T1
/100 )4 – ( T2 /100 )4 ] ………… ( 5 )
Where
T1 =
Absolute temperature of heating element in Kelvin
T2 =
Absolute temperature of charge in Kelvin
e = Emissivity
and
k = Radiant
efficiency
The surface area
of circular heating element S = πdL
Total heat
dissipated = πdL × H…………….( 6 )
At steady state
temperature
Power input =
heat dissipated
P = πdL × H [ From equation ( 1
) and ( 6 ) ]
( πd2 V2
) / 4ρL = πdLH [ From equation ( 3
) ]
d / L2
= 4ρH / V2………………..( 7 )
The length and
diameter of heating element is find out by solving equation ( 4 ) and ( 7 ).
Ribbon
( Rectangular ) type element
Let w be the
width and t be thickness of heating element.
Power input P =
V2 / R
= V2
/ ( ρL / a )
= V2
/ ( ρL / wt ) ( area = wt )
= V2 wt
/ ρL
OR
L / w = V2 t
/ ρP……….( 8 )
The surface area
of rectangular element S = 2Lw
Total heat
dissipated = 2Lw × H
At steady state
temperature
Power input =
heat dissipated
P = 2wLH
Lw = P /2H………….(
9 )
The length and
width of heating element can find out by solving equation ( 8 ) and ( 9 ).
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