1. Thermodynamics Solar Hydrothermal Energy
By: Aaron Vanderpool

2. Problem:
To find a cheap and easy way to heat a home.
Question:
How much heat can be obtained using the Sun and a water mass collector?
Hypothesis:
Water can be heated and transfer a significant amount of energy into a building with little to no maintenance if designed correctly using our understanding of physics.

3. My Collector
Glass donated by
Incline Tahoe Glass

4. Heat is like work and is a form of energy that can be transferred by having a difference in temperature.
Ways of transferring heat:
Radiation: Happens through empty space in the form of electromagnetic waves.
Conduction: Usually through a solid as molecules collide with one another.
Convection: Usually in a liquid of gas as lots of molecules are moving about mixing with one another.

5. Radiation We have about 5 kWh/m^2/day average (NREL)
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0.6
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196.9
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460.6
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291.9
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429.4
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245.6
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109.4
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Radiation
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639.4
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33.1
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2686.3
We have about 5 kWh/m^2/day average (NREL)
1366W/m^2 strikes Earth’s atmosphere.
1000 Watts / m^2
My collector panel m^2 = watts
Watts * Seconds = Joules
755.8 watts * 60 seconds * 60 minutes = 2721 kj in 1 hour
2721 kj = 2579 BTU’s
2579 BTUs / lb (15 Gal/56.78 kg Tank) = F (11.45 C) in 1 100% efficiency
Reverse Engineer
Q = mc ∆T
Q = kg * 4186 J/kg C (specific heat of 15C) * C = 2721 kj

6. Conductivity
A = Area, d = thickness, k = smC (thermal conductivity of glass)
∆T = change in temperature
CPVC (.95 BTU/in/hr/ft.2/°F)
Q/t = 6 smC * m^2 * C / .002 m = 8395 J/s
Radiation = 1000W/m^2 * m^2 = Watts * 1 second = J/s
The back of the collector if just wood
Q/t = .1 smC * m^2 * C / .018 m = 48 J/s
The glass glazing of the collector
Q/t = .84 smC * m^2 * C / m = 2271 J/s (8178 kj/s)
Air
Q/t = .023 smC * m^2 * C / .06 m = J/s
Water
Q/t = .56 smC * m^2 * C / .06 m = J/s
Limit convection of air Limiting factor is air.

7. Convection buoyancy Accel = 9.8 * (1-(ϱw/ϱ)) 15C
9.8*(1-(1/999.1)) =
26C
9.8*(1-(1/999.1)) =
= m/s^2
= 1.4 mm/min^2
= .053 in/min^2
(need a drag force)
4 °C

8. Flow Poiseuille's equation Non-laminar .0001131 * .762 = 0.0000861822
Boyles law
Flow
Length 15.34m of CPVC pipe
Area x 10-4 m^2
Volume x 10 ^-3 m^3 inside piping
Viscosity
η = .001 Pa*s (water at 20C)
F = η A v/l
Idea = Find velocity  Find pressure (Bernoulli’s equation)  Find flow (Poiseuille’s equation)
V = .007m/s
P1 = 1 atm
(Bernoulli’s equation) P2 = P1 + ϱg(y1-y2) + 1/2 ϱ (v1^2-v2^2)
P2 = ( N/m^2) + (996.8 kg/m^3 * 9.8 * -.5m) + ½ (996.8*.007^2 m/s) =
Q = ( ) * pi * ^4 / (8 * .001 * 1) = m^3/s = 2436 cm^3/s
P275

9. Convection
buoyancy
= 1.4 mm/min^2 * 5 min = .007mm/min * x 10-4 m^2 = 7.917×10^-7 m^3
= cm^3/min
(need a drag force of pipe and viscosity)
4 °C

10. Putting heat back into the room Thermal Radiation, conduction and convection
Stefan-Boltzman equation
Tank
Q = 1 * 5.67 x 10^-8 W/m^2*K * .759 m^2 * 299.2^4 K = 345W
Watts * Seconds = Joules
345 * Seconds = 2.721×10^6 joules
Seconds = 7887 = 2.19 hours in a vacuum
Wherever you are not putting radiation heat into the system, the system is losing heat and all those need to be added up.