Solar Collection and Energy Transport. Fixing of atmospheric Carbon into the biomass photosynthesis is a form of solar collection and energy storage.

The Key to efficient use of solar energy lies in efficient modes of heat transfer. There are three possible modes:

• Conduction
• Convection
• Radiation

Conduction	Transfer of energy via the vibration of atoms in some medium. The best conductors are silver and copper.
Convection	Transfer of energy via the bulk motion of a medium (e.g. air, water)
Thermal Radiation	Cooling of a material to thermal equilibrium via radiation losses. Stored energy re-emitted (Power per unit Area) goes as T4

Thermal Conduction:

• heat energy flows from regions of high temperature to low temperature
• wide variation among different materials depends on the density of free electrons in the material

  Thermal Conductivity of some Materials in relative Units

  • Silver 1.0
  • Copper 0.93
  • Gold 0.70
  • Aluminum 0.48
  • Steel 0.12
  • Concrete 0.004
  • Brick 0.002
  • Wood 0.0002
  • Air 0.00005

So Clearly metals are required for efficient heat transfer.

Heat flow through a wall:

Convection: liquids and gases transfer heat this way motion of the medium between regions of different temperatures.

Fireplaces produce natural convection warm air rises and is replaced by cold air

Most space heating systems operate via convective heat transfer (forced air)

Thermal Radiation:

Material absorbs sunlight and heats up and then re-radiates that as long wavelength infrared radiation (heat radiation).

Was effectively used centuries ago in American Southwest ( Mesa Verde).

Sandstone dwellings and walls would absorb much sunlight during the day and then re-radiate that as heat at night.

In general, recovering incident solar radiation via subsequent thermal radiation of materials is not practical and large amounts of thermal mass are required. This can be a) expensive and b) space intensive.

Thermal Mass:

• efficiency depends upon specific heat of material and its thermal conductivity
  • Specific Heat measure of how much energy a substance can store. This is measured on a scale of 0 to 1. Water has a specific heat of 1.

  • Thermal conductivity measure of efficiency of heat transfer (i.e. getting it back when you want it)

Values for typical materials:

Material	Specific Heat	Thermal Conductivity
Water	1.0	4.2
Iron	0.1	320
Glass	0.2	4.0
Stone	0.2	3.0
Wood (Oak)	0.6	1.4
Brick	0.2	4.6
Concrete	0.15	12
Sand	0.2	2.3

Water is the clear winner followed by concrete. So thermal mass is most effectively used in the form of large tanks of water or several tons of concrete in an insulated container.

Solar Energy: Collector Systems
Variation of Incident Sunshine with location in the US

Flat Plate Collector Systems:

Heat transfer to a circulating liquid (antifreeze) to be used as supplemental space heating source in the Winter

Basic System Design

On average, a house loses 1 BTU per cubic foot per degree day

A degree day = 65 - average 24 hour temperature

Requirements:
• 1500 sq. feet and 8 ft ceilings 12,000 BTU per degree day to maintain interior heat at 65 degrees
• Consider a winter day with average 24 hour temperature = 15 F ( 50 degree days) need 600,000 BTUs to keep house at 65 degrees
• 100,000 Btus comes from internal sources (lighting, cooking, families, TV, etc) need 500,000 more BTUs

• Assume incident radiation is 600 Watts per sq. meter on a slanted collector surface averaged over 8 hours.
• There are 3.41 BTUs per Watt so this is equivalent to 600 x 8hrs x 3.41 = 16,400 BTUs per sq. meter per day (8 hours)
• Assume collector efficiency is 50% (this is not a photovoltaic device; we are merely heating something up and transferring that heat to a working circulating fluid)
• The net yield is then 8200 BTU per day per sq. meter

• We need 500,000 BTUs how many sq. meters are required?

• 500,000/8200 = 60 sq meters 648 sq feet (25x25 feet of collectors)

  Heat Storage:

• Water stores heat at the rate of 62.4 BTUs per cubic foot per degree F
• Stones 20 BTUs per cubic foot per degree F (lower efficiency due to voids in the storage unit)

• Heat water to 130 F and extract heat from it until it cools to 80 F. Total volume of water required is:
  500,000/(62.4*50) = 160 cubic feet = 1250 gallons
• For Stones:
  500,000/20*50 = 500 cubic feet = 25 tons of stones !

Energy losses in a flat plate collector system:

• Not all solar photons penetrate black collector surface
• Once the collector becomes hotter than the environment heat loss by conduction, convection (aided by wind) and radiation
• Transmission/reflectance depends on incident angle
• efficiency starts to rapidly go down if the collector becomes too hot as the thermal radiation (which goes as temperature to the fourth power) dramatically increases

• Overall effect is that the collector system has an efficiency which decreases with higher temperatures. But the effect is not dramatic:
  • Temp. difference between collector and surroundings = 20 F efficiency is 74%
  • Temp. difference between collector and surroundings = 100 F efficiency is 48%

  Single glass cover admits most sunlight but also most re-radiated infrared radiation. Best at low temp differences

  Three layers of glass -> admits fewer photons but also inhibits radiative losses best at high temperature differences Can fiddle with number of glass covers on the front of the collector:

Orientation of collector with respect to sun is crucial part of overall efficiency

Focusing Collectors:

Not practical for the homeowner somewhat dangerous due to high temperatures.

Parabolic reflectors (heliostats) are pretty expensive

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