Subject: Heat Loss & Solar Gain Calculations

From: "Neil Evensen" <[email-masked]>
Date: Thu, 18 Nov 1999 21:55:45 -0000

Hi,

For my physics class I'm writing a research & analysis project on passive
solar design and I would very much appreciate some help with my
calculations.

I'm trying to see how well the sun could heat a 5x5x5 metre living space
with a 5'C outside temperature and solar radiation of 350 W per square metre
(These seem like reasonable figures but I'm open to suggestions).

I'd like to show the difference in efficiency of a cube built from bricks,
and a cube built from bricks with a layer of glass on the outside.

Here's what I've been able to do so far...

To start with I've said that I want an inside temperature of 15'C

Heat Loss = U value x S.Area x dTemp.

If the walls and ceiling were made of solid brick this would be

2.1 x 125 x 10 = 2625 W

I'm not quite sure how to calculate solar gain but I've made an attempt...

I thought that thermal conductivity would be a useful figure to work out so
err?

Thermal conductivity = ( Heat Loss? x thickness ) / ( S.Area x dTemp. )

(I've said that the wall's half a metre thick, I'm guessing that the U-value
is independent of thickness)

= (2625x0.5)/(125x10) = 1.05 W/m/'C

Trouble is that these workings only seem to take into account temperature
and not direct solar radiation, which I would guess is quite important.  Is
there some other way of doing this?

My plan with the layer of glass was to calculate how hot the air between the
glass and the bricks would be.  Hopefully it would be more than 15'C so heat
should flow into the room, right?

Say there's a gap of .02 m between the glass and the bricks.

I figured that I could find the temperature using

dT = energy in/mass x specific heat capacity

The volume of the gap is about 123.5, the density of air 1.293 kg/m^3 so the
mass about 160 kg.  This may be wrong but I read the specific heat capacity
of air is around 993 J/Kg/K.

dT = 350/160 x 993

= .002202920443 'K

So the air increases in temperature at a rate of .0022 'K per second. If the
air in the gap starts at 5'C that's 278.15 'K.  So in 1 hour the temperature
would have risen by 7.93044 'K, giving a temperature of around 13'C.  Does
this increase in temperature stop?  I guess I need to calculate the heat
loss of the glass, but what temperatures do I use?

Sorry I haven't been able to ask any definite questions, but I don't really
know what I'm doing.  Any help would be much appreciated.

Thanks,

Neil

---

From: "Tim Dierauf" <[email-masked]>
Date: 19 Nov 1999 10:41:34 EST

Neil,

I'm sorry, but I don't have time to check your methods. However, your
project is covered in must introductory HVAC engineering text books. The one
that I used is _Heating and Cooling of Buildings, Design for Efficiency_ by
J. Kreider and A. Rabl, McGraw-Hill, 1994.

I also recommend the following which is a graduate level solar engineering
text: _Solar Engineering of Thermal Processes_ by J. Duffie and W. Beckman,
John Wiley & Sons, 1991.

Good luck,
Tim

Neil Evensen wrote in message
<[email-masked]>...