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re: solar panels
3 may 2000
antónio elias wrote:
>do you know a webpage where i can calculate an instalation
>with solar panel for heating a residential place ?
seems straightforward enough...
1. what's your climate? look up the long-term average temperature and
the amount of sun (in say kwh/m^2) that falls on a south wall on an
average day of each winter month where you live (or on a north wall,
if you live in the southern hemisphere.) say you find 5 c for november,
with 4 kwh/m^2, 0 c for december, with 3 kwh/m^2, and -5 c for january,
with 5 kwh/m^2.
2. what's the worst-case month for solar house heating, ie the one with
the least sun per heating degree? if you keep your house at 20 c, then
november has 4kwh/(20c-5c) = 0.27 kwh/c, december has 3/(20-0) = 0.15,
and january has 5/(20-(-5)) = 0.20, so cloudy and cool december is the
worst month. look up the coldest day in december. say that's -20 c.
3. what's the thermal conductance of your house? add up the conductance
of each exterior surface, ie its area in square meters divided by its
thermal resistance in w/m^2c. for example, a 10mx10mx5m tall house with
10 m^2 of metric r0.5 windows and r4 walls and an r5 (us r28.4) ceiling
has 10m^2/(0.5w/m^2c) = 20 w/c of window conductance plus (200-20)m^2/r4
= 45 w/c for the walls plus 100m^2/r5 = 20 for the ceiling, a total of
85 w/c, ie it needs 85 watts of heat for each degree of indoor-outdoor
temperature difference.
4. how airtight is your house? one watt warms about 3 m^3/h of air 1 c,
so a v m^3 house with c air changes per hour (ach) needs about cv/3 watts
per degree of additional heat for air leaks. a fairly airtight 500 m^3
house with 0.3 ach needs an additional 50 w/c of heat, with an effective
conductance of 135 w/c, ie 24h(20c-0c)135w/c = 64.8 kwh/day.
otoh, how big is your electric bill? using 300 kwh/month of electrical
energy indoors adds 10 kwh/day of heat, reducing the heating requirement
to 54.8 kwh/day. if the windows are all on the south and have 50% solar
transmission, they provide another 0.5x10m^2x3kwh = 15 kwh, so the house
only needs 39 kwh of heat on an average december day with an average
amount of sun.
5. what's the heat distribution system, and the minimum usable heat store
temp? a 100 m^2 well-insulated radiant floor with a slowly-moving airfilm
conductance of 8 w/m^2c above has 800 w/c of floor-to-room-air conductance.
the house needs (20c-(-20c))135w/c = 5400 watts of heat on the coldest day,
when the floor temp needs to be at least 20c+5400w/(800w/c) = 26.75 c.
6. what's the average heat store temperature? let's pick 60 c (140 f.)
much warmer, and the solar collection efficiency falls. much cooler, and
the heat store becomes enormous, and the water isn't useful for showers.
this is also a reasonable compromise for combined pv and thermal power
production and rainwater pasteurization.
this temperature determines the heat store size. the house needs about
5x55 = 275 kwh of heat over 5 cloudy 0 c days in a row, and a kg of water
cooling 1 c releases 1.16 wh of heat, so we need 275k/(60-26.75)/1.16
= 7130 liters of water, about 1884 us gallons. let's use something like a
$419.95 1,500 gallon 84" diameter x 60" tall polyethylene tank (empty
weight: 280 pounds) from tractor supply corp.
7. what's the solar collection efficiency? say the panels collect 80%
of the solar energy over 6 hours, with r0.4 thermal resistance, losing
6h(60c-0c)1m^2/r0.4 = 0.9 kwh per day, with a net gain of 1.5 kwh/m^2.
then you need 39kwh/1.5kwh/m^2 = 26m^2 of panels, eg $5.2k at $200/m^2.
nick
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