I am designing a heating element consisting of resistance wires coiled around a tube to heat water flowing in the tube. All three heating elements (loads) will have the same resistance and will be connected in delta. I want to control the heat output by varying the voltage to the loads by using a variable transformer. I did some calculations to ensure that the design will work as expected. I would appreciate it if people who know better could tell me whether the procedure I employed to calculate the heat generated, as provided below, is correct.
a) I have access to a three phase 250 V, 30 A electricity. I understand these are line voltage and line current. So the phase current would be 17.34 A, and the total power available would be 13 kW.
b) I want a total of 4.8 kW heating power, so 1.6 kW on each load
c) I know the wire diameter and length I need. Hence, for the given wire material, I know the resistance of each heating element.
Here is where the calculations start.
d) In an excel sheet, I list out a range of voltages (from 100 to 300, say), and for each I divide the phase power (total power/3) by the voltage to find maximum current available (assuming no losses).
e) Then for each leg/load, I find the calculated current by dividing the voltage across it by its resistance.
f) Whichever step (d or e) gives lower value for the current, I take that as the actual current flowing through the load, and I calculate the heat generated by each leg/load as I^2*R.
g) Finally, when I find the correct combination that generates the heat required (1.6 kW), I assume that the other two loads are generating the same amount of heat for a total of the desired 4.8 kW.
So my question is, is this the right way to calculate the heat generated. Also, is it appropriate to isolate each leg/load and perform calculations on it alone, as I have done here.