Output of Series Heating Cable (Type-1)

How can be the output calculations for the series heating cable are done: 

Firstly we have some input:

V = Supply Voltage (V)

HL = Heat Loss (W/m)

TL = Total heating Cable Length (m)

𝛼 = Temperature Coefficient (1/◦C)

∆T = Temperature difference b/w maintain temperature and 20◦C

Now we find Ideal resistance (𝑅𝑖):- 

𝑅𝑖 = 𝑉2 / (𝐻𝐿 × 𝑇𝐿2) / (1 + 𝛼∆𝑇)

 Find out Unit 

𝑅𝑖 = 𝑉2/ ((𝑊/𝑚) × 𝑚2) / (1 + (1/◦ C) ×◦ C)

  

Unit of 𝑅𝑖 = (𝑂ℎ𝑚/𝑚) 

Now we will be select cable of less resistance from ideal resistance.

Now we will be calculating resistance on the maintain temperature (𝑅𝑚):-

𝑅𝑚 = 𝑅𝑐 × (1 + α∆𝑇) 

𝑅𝑐 =  𝑆𝑒𝑙𝑒𝑐𝑡𝑒𝑑 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 𝐶𝑎𝑏𝑙𝑒 (𝑂ℎ𝑚/𝑚) 

α =  Temperature Coefficient (1/◦ C)  

∆𝑇 =  Temperature difference b/w maintain temperature and 20 ◦ C  

Unit of 𝑅𝑚 = 𝑂ℎ𝑚/𝑚

 Note:-  α value change as per heating cable resistance.

Now we will be calculating Output of heating cable:- 

𝑂𝑢𝑡𝑝𝑢𝑡 = 𝑉2 / 𝑅𝑚 / 𝑇𝐿2

 Find out Unit

𝑂𝑢𝑡𝑝𝑢𝑡 = 𝑉2 / (𝑂ℎ𝑚/𝑚) / 𝑚2

 

Unit of 𝑂𝑢𝑡𝑝𝑢𝑡 = 𝑊/𝑚