heat transfer cals

Related to the questions on diversions. I am completely stumped on this one. How to calculate the following. with no battery. assume full sun, two x 45 watt solar panels in series, (90 watt at 3.2 amps) direct connection to a 500 watt-120 AC volt element heater in a five gallon tank at temperature of water 32 (at freezing) what will the rate of increase be in degree rise per hour? The water tank is a standard 5 gallon RV style insulation is batten wool glass. Outside AIR temperature is also at 32 degrees

thanks for any help on this one.

Comments

  • BB.BB. Super Moderators, Administrators Posts: 31,171 admin
    Re: heat transfer cals

    As a first approximation:

    V=IR
    P=I*V=I2R=V2/R

    (120 VAC)2 / 500 Watt Element = 28.8 Ohm Resistance

    Assuming your 45 watt solar panels are ~Vmp=17.5 volts with Imp~ and you have two panels:
    • 90 Watts / 3.2 amps = 28.125 volts (two panels in series)
    • 45 watt / 3.2 amps = 14 volts Vmp
    • 14 volts / 28.8 ohms = 0.49 amps
    • 28.125v/28.8ohms = 0.99 amps

    So--With to panels in full noon time sun, the maximum current you can push through the heating element is ~0.99 amps
    • 0.99 amps * 28.125 volts = 27.8 watts maximum

    • 1 watt is approximately 3.41214 BTU/h
    • 1 BTU = 1 lb of water per 1 degree F
    • 1 gallon of water weights 8.33 lbs

    • 27.8 watts * 3.41214 F 1 lb of water per 1 degree F per hour per watt * 1/(5 gallons of water * 8.33 lbs per gallon) = 2.3 degree F per hour (5 gallons of water at 100% efficiency)

    If you assume that you have ~2 hours of near noon time sun (winter?), at best you can warm the water tank by ~5 degrees per day.

    Your 500 watt element running on 120 VAC:
    • 500 watts * 3.41214 F 1 lb of water per 1 degree F per hour per watt * 1/(5 gallons of water * 8.33 lbs per gallon) = 41 degree F per hour (5 gallons of water at 100% efficiency)

    Or about ~2 hours for ~82 F rise (or +32F starting temp, 114 degree F final temperature).

    I think I got all the conversion factors correct. The numbers seem roughly correct.

    -Bill
    Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
  • twinomadtwinomad Registered Users Posts: 6
    Re: heat transfer cals

    Thanks, The attempt was to use several small sized water or oil space heaters. It seems that this is "not going to end well" at least as presently planned it. Let us try something else. Is it better then to use a invertor than to try to use DC directly. Let me give an example: , With a 120VAC - 1000 watt oil heater for our cabin to use an invertor or buy more Panels and build up the DC amps/volt input. The original thought was that wiring DC directly to the heater element would heat as sun was available though out the day regardless of outside temperatures, where as fluid types would freeze and need pumps.
  • icarusicarus Solar Expert Posts: 5,400 ✭✭✭✭
    Re: heat transfer cals

    What is it you are trying to do? Is your goal simply a diversion load, or are you trying to heat water (or space ) from PV? If the later is the case, consider a simple solar water heater system, which is very much more efficient and indeed more cost effective as well.

    Tony
  • BB.BB. Super Moderators, Administrators Posts: 31,171 admin
    Re: heat transfer cals

    Getting heat from solar electric panels is very expensive... Most systems would work best if done with a battery bank (rather than connecting solar panels to some form of electric heater).

    There are some people that have taken modern heat pump based Mini-Split AC systems and used those to heat their homes--Heat pump systems can be 2x more efficient vs resistance electric heaters (still more efficient than resistance heaters even with some snow on the ground).

    Sanyo mini split AC (inverter/variable speed)


    Unfortunately, Sanyo was purchased by Panasonic, and their very nice 120 VAC heat pump system seems to be no-more.

    If propane/heating oil/etc. is not available in your area--We can talk about the details of setting up electric solar power system. But it may still be scary expensive as most regions that get snow on the ground in the winter simply do not have that much sun available in winter (short winter days)--And it becomes very difficult to gather a lot of solar power in such situations. Very large solar arrays can help, but you would still need alternative power (genset+fuel) during many weeks of poor weather/sun during winter.

    Now-Guessing if you are from Prescott Arizona region--You may be in one of the few regions were solar power for heating in dead of winter may actually be practical. Using PV Watts for Prescott AZ with a fixed solar array titled to latitude:
    Month    Solar Radiation (kWh/m 2/day)
    1      5.28     
    2      5.71     
    3      6.15     
    4      6.78     
    5      7.06     
    6      7.07     
    7      6.33     
    8      6.51     
    9      6.59     
    10      6.52     
    11      5.58     
    12      4.99     
    Year      6.22      
    

    Say you want to use a 1.5 kW electric heater for ~10 hours per day. Assuming capturing solar during the day and running heat at night with typical system efficiency:
    • 1,500 Watts * 10 hours * 1/0.52 overall system efficiency * 1/4.99 hours December sun = 5,781 Watt array minimum

    And a battery bank to supply 2 days of power with 50% reserve (for longer battery life):
    • 1,500 Watts * 10 hours * 1/0.85 inverter efficiency * 1/48 volt battery bank * 2 days * 1/0.50 max discharge = 1,471 AH @ 48 volt battery bank

    That is not a small system--But it gives you a good idea of what could be done "by the numbers". In theory, if you use a heat pump system, the size of the system could be reduced by upwards of 50%--Which would give you A/C in the summer too.

    -Bill
    Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
  • twinomadtwinomad Registered Users Posts: 6
    Re: heat transfer cals

    SOlar is not ready for prime time, Yes I am at similar latitude to Prescott, But At 8000ft. At first I thought a this might be simple process. But the numbers at 5781 watt array just to heat one cabin heater clearly shows this is not the case. Any system that uses water is not in the picture because at this altitude in winter when not heated the cabin soon goes down to outside temperature, in windy times that is equal to 50 below zero. But most of the time there is bright sunshine because of snow cover and again because it 8000ft. Propane does not work well and its back to oil stoves and good old back up called a wood stove.

    s
    BB. wrote: »
    Getting heat from solar electric panels is very expensive... Most systems would work best if done with a battery bank (rather than connecting solar panels to some form of electric heater).

    There are some people that have taken modern heat pump based Mini-Split AC systems and used those to heat their homes--Heat pump systems can be 2x more efficient vs resistance electric heaters (still more efficient than resistance heaters even with some snow on the ground).

    Sanyo mini split AC (inverter/variable speed)


    Unfortunately, Sanyo was purchased by Panasonic, and their very nice 120 VAC heat pump system seems to be no-more.

    If propane/heating oil/etc. is not available in your area--We can talk about the details of setting up electric solar power system. But it may still be scary expensive as most regions that get snow on the ground in the winter simply do not have that much sun available in winter (short winter days)--And it becomes very difficult to gather a lot of solar power in such situations. Very large solar arrays can help, but you would still need alternative power (genset+fuel) during many weeks of poor weather/sun during winter.

    Now-Guessing if you are from Prescott Arizona region--You may be in one of the few regions were solar power for heating in dead of winter may actually be practical. Using PV Watts for Prescott AZ with a fixed solar array titled to latitude:
    Month    Solar Radiation (kWh/m 2/day)
    1      5.28     
    2      5.71     
    3      6.15     
    4      6.78     
    5      7.06     
    6      7.07     
    7      6.33     
    8      6.51     
    9      6.59     
    10      6.52     
    11      5.58     
    12      4.99     
    Year      6.22      
    

    Say you want to use a 1.5 kW electric heater for ~10 hours per day. Assuming capturing solar during the day and running heat at night with typical system efficiency:
    • 1,500 Watts * 10 hours * 1/0.52 overall system efficiency * 1/4.99 hours December sun = 5,781 Watt array minimum

    And a battery bank to supply 2 days of power with 50% reserve (for longer battery life):
    • 1,500 Watts * 10 hours * 1/0.85 inverter efficiency * 1/48 volt battery bank * 2 days * 1/0.50 max discharge = 1,471 AH @ 48 volt battery bank

    That is not a small system--But it gives you a good idea of what could be done "by the numbers". In theory, if you use a heat pump system, the size of the system could be reduced by upwards of 50%--Which would give you A/C in the summer too.

    -Bill
  • BB.BB. Super Moderators, Administrators Posts: 31,171 admin
    Re: heat transfer cals

    People have made solar thermal heaters work in some pretty cold places... This is a favorite of mine to point at--Everything was pretty much "home made":

    http://www.builditsolar.com/Projects/SpaceHeating/SolarShed/solarshed.htm

    And--I just pulled numbers out of the air (10 hours on a 1.5 kW electric heater)... I have no idea of how much heat your place really needs. If you need 1/2 that amount in the way of heat--Then you can cut "my numbers" by half too.

    Don't look at solar as being the only source of heat--If you can get 10+ months of heat and use supplemental propane/oil/wood heat in the depths of month or two of winter--You probably still can come out ahead (and not spend a bunch of money on an overly large solar system for the other 8-10 months of the year).

    I was hoping to not scare you off--But look at conservation (lots of insulation, double or triple pane windows, more insulation, possibly air sourced heat pump--probably better for most people vs ground source heat pump unless you have a lot of property, etc..

    A paper design (or three) and then compare against traditional propane/oil/wood heating---And see how close (or how far off) you are to having a cost effective solution that does not use expensive fossil fuels or waste money on batteries+solar panels+charge controllers+inverters+etc...

    -Bill
    Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
  • twinomadtwinomad Registered Users Posts: 6
    Re: heat transfer cals

    To BB.
    I forgot to mention why we were trying for a direct connection from 12VDC panel to 120VAC heater is that low temperatures and high altitude just kill batteries. Last year we brought two marine deep cy. up here by pack mule. The batteries did not arrive in the best condition we had hoped. So the thought of directly connecting to panel of 180 watt /17.6 volts might be enough to excite the little space heaters that are sold at wally world, Some are 500 watt resistance heaters. the larger ones are about 1400 watts oil filled. (Snow storms can dump 4 to 6 feet at a time.) So they have to be mounted high, As side note, black bears love to lay on them in the winter as the panels are nearly dark and get really hot.
  • icarusicarus Solar Expert Posts: 5,400 ✭✭✭✭
    Re: heat transfer cals

    Sorry, but you need to do a bit more research. There are a number of solar heating options (not including resistance PV electric) including passive solar thermal mass, evacuated tube hot water/space heat, flat plate record systems. To say thaqt solr is " not ready for prime time is" shall we say, a bit...incorrect.

    Evacuated tube systems coupled with thermal loop, glycol systems work very well in cold climes, and can return much higher BTU harvest more efficiently than PV, and indeed at much lower per BTU cost. While this forum is geared more toward PV than space and water heating, there are many with some considerble experience.

    Like I said earlier, do some more research, and I believe you will find a plethora of good info, and you wil find that in your area, (even with cold temps) solar heating makes great sense, at least in part. As an example, in our northern clime, we see temps of -40 and colder, but if the sun is out, we can let the fire go out most of the day, simply from the sun in our south facing windows.

    Tony
  • CariboocootCariboocoot Banned Posts: 17,615 ✭✭
    Re: heat transfer cals

    Speaking as someone who does live at high elevation, gets some pretty deep snow fall, really cold temperatures, and three different colours of bears ...

    Direct heating with solar panels has a couple of drawbacks. The first being "a Watt is a Watt", meaning if you expect to run a 1400 Watt heater you need to have 1400 Watts available to get full performance from it. Heat transfer calcs needn't enter into it at all; you're simply shifting the Voltage and current type. Panels do not put out their rated Wattage, but rather an average that is usually significantly below the rating. The good news is that in cold temps the Voltage goes up a bit and at high elevations the current is somewhat better (increased insolation). The other drawback is that the thermostatic controls on these heaters are meant to switch AC, not DC, and may not stand up for very long if used for non-rated current type, Amps, or Voltage.

    On the whole it isn't very practical to use PV for direct heating purposes because you only get power when the sun shines. You can accomplish the same thing with direct solar heating usually with greater efficiency (panels are <20% efficient).

    So to run a single 1400 Watt heater you'd need about 1800 Watts of PV (which could be wired up to provide approximately the correct 120 Volts) and a thermostatic control that wouldn't fry from trying to do the switching. Pretty expensive way of doing it.
  • BB.BB. Super Moderators, Administrators Posts: 31,171 admin
    Re: heat transfer cals
    twinomad wrote: »
    To BB.
    I forgot to mention why we were trying for a direct connection from 12VDC panel to 120VAC heater is that low temperatures and high altitude just kill batteries. Last year we brought two marine deep cy. up here by pack mule. The batteries did not arrive in the best condition we had hoped. So the thought of directly connecting to panel of 180 watt /17.6 volts might be enough to excite the little space heaters that are sold at wally world, Some are 500 watt resistance heaters. the larger ones are about 1400 watts oil filled. (Snow storms can dump 4 to 6 feet at a time.)...

    Marine batteries are not really good deep cycle batteries... Some people have pretty good luck with them--But I would suggest good quality "Golf Cart" batteries instead. If treated correctly, they should last you 3-5 years.

    You might look at sealed batteries--If you cannot bring up distilled water (or use filtered rainwater/snow), if you used stream/ground water for refilling the batteries, that could kill them pretty quickly.

    AGM, while much more expensive, may be better for this application as they do not need watering (if properly charged).

    Do you have any idea of how much power (Watt*Hours/Amp*Hours) per day you use? And how many watts of solar panels you installed?

    I believe in building a "balanced" system... The loads size the battery bank. The battery bank+loads size the solar array.

    Lead Acid batteries are pretty nice (compared to other battery chemistries)--Although, they are extremely heavy and not very high power density. But, they do not like to be over discharged/under charged--that can cut years off of their life.

    -Bill
    Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
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