Effect of thermal inertia at resistance heaters

[heinasirkka]

Hello everybody,

I'm confused about how to deduce the real applied heat at an inline resistance heater. The heater I have has 4 heating elements that is in direct contact with the refrigerant. It has rated power of 40kW (each heating element rod has 10kW). I can apply a partial power. However the device applies the desired partial power by applying discontinuous 100% power and taking the average on a time interval. In this case, I can track the electrical power applied. However, there will be extra transferred heat due to the thermal inertia of the heating element rods, when 0% of the power is applied subsequent to a 100% power input. Does anybody have a comment on how this is taken into account in deducing the real applied heat? Can we assume that the applied heat will remain the same as the applied electrical power for a given amount of time?

Kind regards,
Kaya

 

[LittleInch]

You need to define what you mean by "real applied heat" as this isn't a term I've seen before.

Do you mean total energy?
Temperature of the fluid?
Heat flux?

Energy can't be destroyed so the electrical energy consumed will equal the total energy transferred to the fluid over a decent time duration. Energy transfer will be an S curve at the start and an S curve at the end of each 100% current input phase. How steep that curve is will depend on many factors including thermal mass of your heater element, thermal conductivity of your fluid, heat transfer coefficient between heater and fluid. Overall though unless your on periods are very short, this small time to heat up or cool down should be insignificant.

However I can't see why you want to know this to the finite degree?

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[heinasirkka]

Thank you for your reply LittleInch!

The term "real applied heat" is indeed a term found by myself. I just wondered if there will be some kind of discrepancy between the used electrical power and applied heat power at an electrical heater. I suspected that thermal inertia might cause this. I'm trying to understand how the electrical heaters work and what to expect from their operational behaviour. I want to be able to measure the applied heat power inside the heater by measuring its electrical power use via a power meter. I presume that for a given time the electrical and heat power will be same (or negligible difference).

Regards,
Kaya

 

[LittleInch]

There shouldn't be any discrepancy, but a small amount heat might leak out somewhere else.

The only thing you might find is that on a start the current might be initially high and then reduce as the element wire inside the heater heats up and hence resistance increases. Depending on the size and length of wire this could be a very short transition or take a while.



Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[heinasirkka]

Thank you for your answers!

 

[IRstuff]

Conservation of energy. What you allude to, a difference between the real (no inductance or capacitance) electrical power in a resistance vs. its thermal power does not exist. The transient lag is accounted for by the controller, based on the achieved temperature and the temperature setpoint.

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[lukaiENG]

it's worth noting too that resistive heaters are generally pretty low mass and therefore have a low thermal mass which means that they very quickly ramp up to a steady state condition where electrical energy in = heat energy out.
If your heater is on for anything other than very short durations the thermal inertia of the heater is basically irrelevant

 

[MintJulep]

However, there will be extra transferred heat due to the thermal inertia of the heating element rods

No. There is no "extra heat".

Heat in = Heat out + Heat stored.

Simple energy balance.

"Thermal inertia" is the heat stored term.

When Heat in is positive heat stored will increase until it reaches the point where the temperature of the elements results in a steady-state balance for the system.

When Heat in is zero the head stored will decrease until the element temperature equals the fluid temperature.

 

[Compositepro]

heinasirkka, there is no such thing as "thermal inertia". What you are probably referring to is how heat capacity and thermal conductivity interact to slow the speed with which temperature changes propagate through a material. The ratio of thermal conductivity to heat capacity is known as thermal diffusivity. This is really far more than you need to know at this point, however.

You probably do know the difference between energy and power, but you are using the terms interchangeably (and therefore incorrectly) in your questions. This will greatly hinder your efforts to understand basic thermodynamics

 

[heinasirkka]

Thanks everybody for the answers. Sorry for my interchangeable use of power and energy, I lack some fundamentals in thermodynamics.

Compositepro, thermal inertia is indeed a sort of made up terminology, based on the rate of dissipation of the stored heat, and basically represents a system behaviour characteristic rather than a physical phenomenon.