Heat loss from a building. Can someone tell me if I did this correctly

[smjpl]

Hi all. I am wondering how long it takes for heat to leave building.
This is the example I have been working on:

A building is 203m^3 and we want to raise temp from 10C to 21.3C.

Vol=203m^3 => mass = 244kg (density may not be completely correct but doesn't matter)
Cp=1.005 kJ/kg.k

Q required = 244 x 1.005 x (11.3) = 2792.6kJ or 2792600J

Q loss through building from u-value calculations is worked out to be 640W or 640J/s

Therefore the room should be back to 10C after (2,792,600/640=4363.4s)

4363.4/3600 (seconds in hour) = 1.21 hrs

Can this be right. Heat your house fully, turn off the heat and 1.21hrs later your back where you started. This house meets the most up to date regulations for minimum acceptable heat loss through the building fabric.

All comments are appreciated.
Cheers

 

[Topher925]

If this is a simple homework problem then it could be correct however it should be posted in the appropriate forum.

If you are trying to determine the actual heat loss from a building then no, your model is way to simple. For starters when you heat a building you're not just heating the air but heating the building itself and its contents. Also, while the "U-value" remains constant the Qloss does not as it is dependent upon temperature difference which changes with time.

If you want to take the lumped parameter approach (which it sounds like you're doing) you will have a system defined by two first order differential equations. One to describe the heating of the air and its heat loss its surroundings, and one of the house itself and its contents.

 

[smjpl]

Firstly cheers for the reply and nope it isn't homework or anything alike. I spent ages writing out a proper reply a minute ago and it all got wiped so I will keep this one short.

Yes its the lumped approach at the moment but I am building in complexity. Start simple and get basics correct first. My question yesterday was more of unit confusion (joules and kWh) and surprise in numbers (how quickly the heat is lost). I forgot to add in one of the losses so it actually happens every 40min. I know this doesn't take dT/dt or contents into account but it also doesn't take air changes through vents and leaks so I would argue its not too far off either.

Thanks for the reply Topher. If anyone has anything else to add I would be glad to hear it.

 

[Watchman2012]

generally speaking and in BTU's (US)

Two factors make up a total heat load of a given "box"

Transmissive calculation: Q=A*ΔT/R
In/ex filtration calculation: Q=.018*V*ΔT

Where Q is the Quantity of heat lost expressed in BTU's
R= R(esistive) value
A= area
ΔT= delta T (the temperature difference between inside and outside) [sometimes expressed as passage of time-aka heating degree days (HDD)]
V= Volume of heated space

Since we are interested in a YEARLY estimate
the calculations are expanded thus:
Transmissive calculation: Q=A*24*HDD/R
In/ex filtration calculation: Q=.018*V*24*HDD

Average heating degree days (HDD) for Maine in 2006 = 7,046 HDD

in transmissive losses you can get gnarly considering the R-value of the wall, floor, ceiling components
ie exterior sheathing, insulation in cavity, interior sheathing(finish wall materials)
plus an air "film" R-value of 1.2 on each side of each physical component
to come up with the total R of the assembly.

if you are careful and accurate, you should come close to an actual consumption estimate
of 15% of actual consumption +/- would be acceptable.

simply translate the BTU value into your value of choice after, MW, Joules etc...

 

[Watchman2012]

also: a design temp of 70'f
means delta-T would be:

20'F outside, 70'F inside = ΔT of 50'F

a general rule of thumb, and a "healthy" interior environment would be an air change rate of ONE total volume of air per hour in a relatively tight structure.

it can vary widely in old buildings to as much as 15 AC/h (or MORE)

a slightly leaky house could be 2-3 AC/h

if you are widely off and KNOW the consumption
try calculating different Ac/h values, (if your transmission measurements were accurate)
to get closer to the actual consumption. it may surprise you just how leaky a structure can be. Wood dries out with colder air-cracks open up, window and door open/closes are more frequent. wind pressure can accelerate air changes etc...