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## Annual energy consumption

Hi everyone,

In the Ashrae book, the annual heating consumption formula is:
Q = 24*q*HDD/n*(Tin – Tout)

Q = Annual energy consumption
q = Heating gain (Btuh)
HDD = Heating degree days
n = Efficiency
Tin = Indoor temperature (Balance temperature) in F
Tout = Outdoor temperature in F

For example: If my heating unit capacity is 75000 Btuh, my indoor temperature is 72 F and my seasonal outdoor temperature is 20 F, HDD is 4500 and the efficiency is 0.9
My annual energy consumption is: 173 077 kBtuh

If I decrease my indoor temperature at 70F, my annual energy consumption increase at 180 000 kBtuh.

We are supposed to have lower annual consumption by decreasing indoor temperature, right?
If not, can you correct my reasoning?

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No volunteers to help me?

3. I don't have the ASHRAE book in front of me to verify, but looking at the units, they don't quite pencil out.

q is BTU/hr (rate of change of heat)
HDD is days > the 24 is to convert from hours to day
T is °F

Using your equation, the units for Q would be BTU/°F.

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Hello BASengineer,
Thank you for the reply and the correction of Q units. Good point.
My question is about the annual energy cosumption who increase with the decrease of DT and vice versa.

Have you an idea? If is it the correct formula to estimate the energy consumption?

Best regards !

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I agree with @Malmo. That equation does not make sense. Which ASHRAE book is it from? Can you post screenshot of the page?

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Hello coolcoil,

I try to post a screenshot. It's my first time to post a
picture later.

7. Originally Posted by Malmo
Hello BASengineer,
Thank you for the reply and the correction of Q units. Good point.
My question is about the annual energy cosumption who increase with the decrease of DT and vice versa.

Have you an idea? If is it the correct formula to estimate the energy consumption?

Best regards !
I looked it into a little bit further, as it's been a while since I've had to deal with degree days.

So HDD units are actually °F. See https://www.e-education.psu.edu/egee102/node/2076. That cancels out the units from (Tin - Tout). I apologize for the misinformation of the HDD units being days.

q is correct as Btu/hr. Q will result in Btu/hr as well, which can be converted to kW (1 kW = 3412.1 Btu/hr).

If you can post a screenshot of that section of the ASHRAE book or have the chapter, that'd be helpful.

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Thank you for this informations. I haven't a problem with the units but the sens of the formula.
In the Ashrae Booke "Fundamental" 2013. 31st Chapter.
I will post a screenshot later, I have difficulties to insert a picture with my ipad.

Thank you !

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This is a screenshot of the formula from the fundamental of ashrae book

[IMG][/IMG]

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Ktot = Heat loss coefficient

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Another way to look at it is to start with Newton's Law of Cooling. For a flat surface:
Btu/hr = U x A x (delta T), where U = heat transfer coefficient (btu/ft2-hr-F) and A is the area (ft2)

Annual BTU from Degree Days: BTU = U x A x DD x 24hrs/day

From Newton's Law: U x A = Btuh/(delta T). Substituting into the Annual BTU equation:
BTU = [Btuh/(delta T)] x DD x 24hrs/day

This appears to be the same as:
Q = 24*q*HDD/n*(Tin-Tout) (with the addition of efficiency)

I've seen the transfer equations many times, but this is new twist in looking at it. Sort of an 'inverse modeling' approach since you have the heating unit capacity (btuh).

Attached is my current CEM "Cheat Sheet".

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Hi tridiumtec.