## 04/06/2019

### Design of Heating Element

• 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
The surface area of circular heating element S = πdL
Total heat dissipated = πdL × H…………….( 6 )
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