Calculating Heat Transmission: Tips and Formulas for Scientists

[harm101]

Hello,

I have a few questions for calculating heat tranmission between materials ( i need some formulas and tips).
First of all i need to find out how much energy a water pipe transmit to the concrete where it is in. I couldn't find a formula for this one.
Then the concrete should store some heat which i can calculate with Φ = m * c * Δ T, right?
The concrete will lose some energy to the air. How can i calculate how much heat the concrete will "lose" to the air?

I hope someone could help me with these questions!

 

[CWatters]

I'm going to avoid the question slightly...

Lets say you have a long pipe or coil in the concrete with hot water flowing in one end. The water will loose heat to the concrete and flow out of the other end slightly cooler. The power transmitted from the water to the concrete can be determined by measuring the flow rate and the temperature difference between the flow and return pipes. Let..

Fr = Flow Rate in Litres/second (note it's per second not per min)
Cp = Specific heat capacity of water = 4186 J/(kg·K)
ΔT = Tflow - Treturn

Remembering that 1L water weighs 1kg.
Then the power transferred is P (in watts)..

P = Fr * Cp * ΔT

Example:
Flow rate 2.5 L/Min (= 0.042 L/S)
ΔT = 20C = 20K

P = 0.042 * 4186 * 20 = 3.5 KW

Lets say the concrete heats up until it reaches a steady temperature. At that point all of the power transferred from the water to the concrete must be lost from the concrete to the air so you have 3.5kW heating the air.

It's somewhat harder to work out the actual temperature of the concrete. You don't mention what the pipe is made of or how thick the walls of the pipe are so it's not possible to calculate the thermal resistance between the water and concrete. I expect the thermal resistance of concrete and the thermal properties of the concrete to air interface are out on the web somewhere.

 

[CWatters]

Tell us more about the exact situation. If this is to do with Under Floor Heating there is probably empirical data available.

 

[harm101]

Thanks for the formule and help! I really appricate that!.

Yes it's for a under floor heating system of a barn. Because the floor is really slow (25 cm thick) i need to do some heat calculations.
I will search the resistance of the pipe. This means there will be less energy transmissions?
I couldn't really find how much heat the concrete wil dispose to the air.
Is there also a delay that the heat will travel inside the concrete (From the pipe to the surface) ?

 

[CWatters]

What exactly are you trying to calculate? It's not trivial to do all the calculations needed to fully characterise the system as there are a lot of unknowns. I have UFH in a 65mm thick concrete screed. Takes perhaps an hour to raise the room temperature from 16C to 20C. The running cost will depend more on the heat loss through the walls and roof than details of the UFH.

Has this already been constructed? If not I would try and reduce the thickness of concrete surrounding the pipe by putting insulation down first. If it's already been built it's easier to measure the response time than it is to try and calculate it.

The maximum heat output to the room for a underfloor heating system is around 100 W/m² once it's up to temperature.

You could estimate the maximum time to raise the temperature of the slab. What's the power output of your boiler/furnace? The floor area?

 

[harm101]

I'm going to explain the situation a little bit better
It's a really big barn with 1000m2 floor with a 30cm thick concrete floor. There are several reasons why this floor is this thick.
The deal is to control the temperature of the barn. It must be as efficient and stable as possible. I want to use real time calculations in a algorithm to control the heatpumps. Because there are so many factor's i couldn't just simply measure the reaction time. With raw calculations in takes about 5 - 10 days to heat the floor up with 5 degrees.

I've found the Thermal Conductivity of the pipes: 0.4 Watt/m*К .

Also i found a formula to calculate the concrete heat offset:
"
BS EN 1264-2 defines the formula for calculating floor heat outputs:
Q = 8.92 (AFST – TR) 1.1
Where;
Q is the heat emission in W/m2
TR is the nominal indoor room temperature
AFST is the average floor surface temperature
From this formula the underfloor heating characteristic curve can be produced.
"
Could u confirm this formula is correct?

I think the algorithm has to search to a balance between heat escaping the building and heat output of the floor. When will there be the balance between the water and the concrete? Is this when the water temperature is almost equal to the concrete temperature?

 

[CWatters]

I've not seen that formula but it seems reasonable if AFST is the surface temperature (eg not the bulk temperature) of the concrete.

Once the system is operating in steady state the average power going into the slab/room equals the losses through the walls/roof/windows and to ventilation. Many systems are quite crude and simply turn the boiler full ON/OFF and leave it to the room stat to work out the mark space ratio required to achieve steady state. All very unscientific.

I think if your objective is temperature stability you probably need to look at weather compensation. These systems measure the outside air temperature and use that as a proxy for the heat loss. Then they adjust the flow temperature accordingly. The result should be that instead of (for example) running at full power for 25% of the time the boiler runs all the time at a constant 25%. I know that can be done with gas boilers but I don't know if it can be done with a heat pump.

5-10 days to heat the slab 5C sounds like a long time...

It's a really big barn with 1000m2 floor with a 30cm thick concrete floor

Using..
Φ = m * c * Δ T

Volume of concrete is 300m^3
Density of concrete is say 2400kg/m^3
So mass is 720,000kg
Specific heat capacity is about 850 J/kg/K but varies.

So energy required to raise it 5C is
= 720,000 * 850 * 5
= 3060 MJ

Five days is 5 * 24 * 60 * 60 = 432,000 seconds
so boiler/heat pump output must be about

3060 * 10^6 / 432,000 = 7KW

That's not a lot for a 1000sqm barn unless it's quite well insulated.

 

[harm101]

Thanks again for the answer.

That was exactly the plan, with the outside temperature we can calculate the heat losses. But because it's so slow I'm not only looking at the current temperatures, i need to have a look in the future (weather forecast).
So we have 2 crucial parts:
1. Warming up
2. Holding it steady

When warming up, the temperature of the concrete raises. Is the power output from the pipes lower when the temperature of the concrete raise? And how do i calculate the "heat resistance" of the pipes correctly?

When i have more data from the test results i will recalculate and post it.

 

[CWatters]

Materials have a "specific thermal resistance" which is in effect the thermal resistance of a 1m cube. You need to adjust that for the actual thickness and area of the pipe. Lots of info in here..

http://en.wikipedia.org/wiki/Thermal_resistance

I hesitate to suggest you go down the calculation route as it's very hard to accurately model such a complex system. Pretty sure it would be easier to measure the response time. I've done the calculations for a simple heat sink used to cool a semiconductor device but the results wern't a very close match to reality.

 

[CWatters]

When warming up, the temperature of the concrete raises. Is the power output from the pipes lower when the temperature of the concrete raise?

Yes and so does the power output from concrete to room air as the room air temperature rises. This is just one complexity of the dynamic case. It's hard enough just to model the steady state case.

 

[sophiecentaur]

I once tried to calculate the appropriate sizes for (conventional) radiators when planning a central heating system for my home. I found that 'first principles' was a difficult place to start and a simple table, that I found in a magazine produced a very different answer - I had underestimated wildly, with my method. The plumber who did the installation also agreed with the 'official' values.
The last thing you need here is for your heating to be inadequate.
There are many factors with your proposed system which are hard to assess - for instance the heat lost downwards, the rate of air change in your barn.
If you haven't already done so, I would suggest that you look at the many hits that Google will return for the search terms "undefloor heating calculations". On the various sites I found (too numerous to quote here), there were practical matters discussed and also a calculator, which would give you better ball park figures (I suspect) than you'd get when starting from basic Physics. The comments in many of the above posts are very valid but I think they tend to ask as many questions as they answer. Similar problems to yours have already been solved and that experience is well worth making use of. (Stealing commercial ideas for yourself is a really good move here!)

 

[sophiecentaur]

That's not a lot for a 1000sqm barn unless it's quite well insulated.

As CWatters ends his detailed and thoughtful post, when you look at the answer, you really have to relate your final calculated result to how many electric fires you would reckon to need to do the same job. You could do the experiment, even, with a bunch of borrowed heaters.

 

[CWatters]

Another thing to think about is solar gain. Our house gets some sun in the afternoon which effectively turns off the UFH on the west side of the house for most of the afternoon. Then when the sun goes down the UFH doesn't always keep up and the temperature drops a few degrees before the UFH catches up.

 

[sophiecentaur]

the temperature drops a few degrees before the UFH catches up.

That's the kind of thing that an 'intelligent' control system should be able to cope with easily - but how many of our houses have anything better than crude timer and thermostat? I have been looking for a good (useful) Arduino Project to prod me into getting one. It could be a double whammy - good heating control and a good learning exercise, without paying through the nose for some poncy bespoke system.

 

[harm101]

Why wouldn't the result be good? What do you think what would be the best way? I can measure the heat lose through the ground right? When i measure the reaction time i couldn't completely trust on it because the temperatures are changing the whole time (day and night).
I'm not trying to calculate how many electrical power we need, I'm trying to create a smart system for controlling the temperature.
Also i was planning to measure the sun influence and take this in the calculation.

Also thanks for the tip. This forum contains allot of information with some simular problems what i have.