How Do You Calculate Heating Time for Fluid in a Closed Loop System?

[greydient]

If I have a fluid, initial temperature and flow rate known (and constant), that is flowing through a heating element (heat given in Watts), what equation do I use to determine how long it takes the fluid to reach a certain temperature? This is a transient problem, for a closed loop system.

 

[FredGarvin]

When you say "how long" do you mean time or length of heater element?

 

[momentum_waves]

A few suggestions to consider:

Begin on the tank contents side of the problem.
Consider whether tank contents are mixed, or not.
Consider how the fluid exits/enters the tank.
Is the tank insulated?
Consider tank an an externally-heated entity.
Consider the tank pump-around rate.

mw...

 

[greydient]

I mean how long as in time.

 

[russ_watters]

e=m*c*dT <-fluid energy gain
e=p*t <-heat element energy loss

 

[momentum_waves]

The reason I mentioned the tank side of the problem is because you mentioned a closed loop system.

If you have no other mechanism other than a circular pipe loop, with an in-line heater, then simulate the system in a spreadsheet using Russ's equations & work up on the pump-around rate until the system reaches your final temperature. That will give you the final time.

Somehow, though, this would be a somewhat non-physical system, as the general case is a vessel with external heating mechanism eg. pump-around heat-exchanger.

 

[FredGarvin]

Russ's equation could have [tex]\dot{m}[/tex] (mass flow rate) which would give you the energy per unit time. I have done that calculation for coiled heat exchanger elements using a spreadsheet very similar to what momentum_waves mentioned.

 

[greydient]

I guess I'm still a little rusty (and therefore confused). I have my m-dot, but this is how the fluid flow changes with time, not the energy. And I don't have p for my system - just e in Watts.

Can anyone clarify a bit further?

 

[momentum_waves]

Perhaps you could upload a sketch of your problem, indicating what information you do know, as well as your proposed solution?

This would make it simpler for us to visualize & assist you further.

 

[greydient]

I have a fluid flowing through a pump at 2.0gpm, which I know is giving off 100W of heat, then flows through a reservoir to complete the circuit. For our purposes, we are assuming the pump is perfectly insulated. If we know the temperature of the fluid entering the pump starts at -50C, how long until the temperature reaches -35C? Will the fluid ever reach that temperature?

 

[momentum_waves]

I refer you back to my original questions regarding the tank (reservoir) details. These seem to be important in your 'system' problem.

 

[FredGarvin]

Thinking about it, if it is a closed system, then you have a fixed mass of fluid to heat up. you don't need the mass flow rate, just the overall mass of the fluid in the system. Russ' equations would be the correct ones. Just remember, not all of that calculated energy is going to go to the fluid.

Granted, you're not considering the heat due to compression in the pump. If you are pumping at a sufficient pressure, you may be able to get the heat input just from the work of the pump.

 

[momentum_waves]

Heat losses from system piping, reservoir etc will be useful.

 

[russ_watters]

I guess I'm still a little rusty (and therefore confused). I have my m-dot, but this is how the fluid flow changes with time, not the energy.

M is mass. You calculate the energy by using the equation I gave.

And I don't have p for my system - just e in Watts.

Watts is power, not energy. Energy is watt-hours.

For example, if you have a 1kW heating element and 100kg of water circulating through your system, the heating element dissipates 1kWh of energy per hour.

c for water is 4.186 J/g*C and a Joule is a watt-second, so...

1000*3600/4.186/100,000= 8.6 degrees C/hr.

FYI, the question itself contains an error (which is probably why you were confused!), which is what led the others astray. Since it is a closed system, flow rate is irrelevant, only total mass matters.

Also, as others noted, there are other complexities here. I ignored them because we have no information about them, but if your pump is big enough it will add a noticeable amount of heat to the system and unless the system is perfectly insulated, it will lose heat as you add heat.

Btw, I occasionally use the above procedure to manually size the heating element on a water heater/heating system. Water heater volume is based on usage and heating element is based on a "recovery rate", usually taking a full tank of cold water up to operating temperature in about an hour.

 

[momentum_waves]

Nice one Russ.

I've used the spreadsheet approach to determine external pump-around heat-exchanger demand for heating vessels containing bitumen, of all things. As you say, the total system mass is the essential ingredient in determining final heating time.

mw...

 

[greydient]

Thanks to all for the information. I see now the errors in my thinking - I was asking the wrong question, I think.

Our BCs have changed and we no longer need to worry about the temperature, so this is a moot point.

Thanks again.