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Basic Review

Basic Review. Energy Budget Physics Behind Heat Pumps Definitions and Terminology. The Energy Budget. All bodies emit characteristic energy spectrum Energy Emitted Proportional to Temperature 4 Energy emitted drops as the square of the distance Emission governed by the

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Basic Review

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  1. Basic Review Energy Budget Physics Behind Heat Pumps Definitions and Terminology

  2. The Energy Budget All bodies emit characteristic energy spectrum Energy Emitted Proportional to Temperature4 Energy emitted drops as the square of the distance Emission governed by the Stefan-Boltzman Law I = σT4

  3. Sun’s Emission Rate 6000°K Energy Flux: I = (5.67 x 10-8) . (60004) =  73.5 x 106  W/m2 Total Energy: W = (energy per square meter) x (area of photosphere) = (73.5 x 106) x (4πr2);    where r = 647 x 106 m = 3.865 x 1026 W

  4. Energy Received by Earth Asphere = 4πr2  W α 1/r2 r = 150 x 109 m =  2.83 x 1023 m2 Energy Flux to Earth: W/m2 = 3.865 x 1026 Watts / 2.83 x 1023 m2 = 1367 W/m2 Solar Constant (So)

  5. Energy Received by Earth

  6. Energy Received By Earth Earth’s Disk W = (So) (π r2),

  7. Albedo 30% of incoming radiation is reflected

  8. Energy Emitted by Earth Short Wave Radiation in Peak λ = 0.47 μm Visible Light Heat Earth Long Wave Radiation out Peak λ = 10 μm Infrared = heat 239 in = 239 out

  9. Equilibrium Temperature of Earth

  10. Effects of an Atmosphere

  11. Effects of an Atmosphere

  12. Effects of an Atmosphere Equivalent to Equilibrium T of 58°C or 136°F Too Hot!

  13. Transfer Mechanisms Conduction - transfer of energy by neighboring molecules across a temperature gradient Convection - transfer of energy through larger scale motion of currents – warm air rises, cool air sink – convection Thermals and create weather Advection – Same as convection but horizontal Latent Heat – transfer of energy through a change in state – evapotranspiration (feeds our weather)

  14. The Energy Balance Energy In = Energy Out Top of Atmosphere W/m2 Sunlight In = Sunlight reflected (atmos & land) + IR emission (340) (99.5) (239.7) In Atmosphere Sunlight Absorbed + IR Absorb + Thermals + ET = IR space + IR ground (77) (358) (18) (86) (200) (340) At Earth’s Surface Sunlight Absorbed + IR Back = IR emitted + Thermals + ET (163) (340) (398) (18) (86)

  15. NASA

  16. Earth’s Other Energy Source Radioactive decay of three elements 238U, 232Th and 40K produce most of Earth’s internal heat Equivalent to 38 trillion Watts (U.S uses 0.3 trillion Watts) Spread over earth’s surface average heat flow to surface from radioactive decay produces 0.075 W/m2 Enough to light a single 75 Watt bulb on 1000 m2 lot (approximately an area = 100 x 100 ft) Energy absorbed from sun about 2200 times larger than heat flow Davies and Davies, 2010

  17. The Real World - Insolation NASA

  18. Long-Wave Radiation Out NASA

  19. Absorbed Energy NASA

  20. Average Surface Temperatures NASA

  21. Temperature Variation with Depth TTeTemperature Variation in °F VT Dept Mines, Mineral & Energy

  22. Boutt et al., 2010

  23. Mean Earth Temperatures in U.S. VT Dept Mines, Mineral & Energy

  24. Summary Energy absorbed by the earth is renewable It is stored by the soil, rock and water GSHP systems borrow this heat temporarily

  25. Physics of Heat Pumps 1060 Btu to evaporate 1 lb of water (at 60°F) 1060 Btu is released when that 1 lb of water condenses

  26. Heating Hot Liquid, High Pressure Expansion Valve Cooler Liquid/Vapor Mix Low Pressure Closed system Condenser Evaporator Compressor Heat Source (Ground) Heat Distribution (Structure) Hot Gas, High Pressure Cool Gas, Low Pressure

  27. Coupling the Heat Pump Three main components to the System Interior Air Distribution Ground Exchanger(GHEX) Heat Pump

  28. GSHP Vocabulary BTU – British Thermal Unit: energy required to raise 1 lb water 1 °F Therm – 1 Therm = 100,000 BTU Ton – 12,000 BTU/h: the amount of heat required to melt 1 ton of ice in 24 hours So, 288,000 BTU to melt 1 ton of ice

  29. L D Q µ Dh Q µ 1/L Q µ A Thermal Conductivity Thermal Conductivity equivalent to Hydraulic Conductivity Darcy’s Experiment (1857) constant head reservoir ∆h Sand Q µ (Dh/L) A Q

  30. Q/A slope = K = Hydraulic Conductivity gradient Rewrite, Q = K (Dh/L) A Darcy’s Law For heat flow: Q = heat flow in Btu/hr Dh/L = temperature gradient = ∆T/L (°F/ft) A = cross sectional area of flow = L2 (ft2) K = thermal conductivity = ʎ (Btu/hr/°F/ft)

  31. Conceptually, Temperature Gradient = 1 1 1 ʎ = Heat Flow in Btu/hr through a unit length of material per unit area under a unit temperature gradient 1 Unit Volume 1 1 Pulling terms together, Q = ʎ (∆T/L) A ʎ = QL/∆TA Units are: Btu/hr/°F/ft

  32. Specific Heat Capacity cp - Specific heat capacity is the amount heat energy a unit mass of material takes into storage or releases from storage per unit change in T 1Btu/lb/°F This is equivalent to specific storage in hydrogeology

  33. Heat Out or In Conceptual Meaning of Specific Heat Capacity 1 unit ∆ in T 1 unit Mass Earth

  34. Volumetric Heat Capacity Volumetric Heat Capacity is also equivalent to specific storage s is the amount of heat energy a unit volume of material takes into storage or releases from storage per unit change in T. s has units of Btu/ft3/°F Specific and Volumetric Heat Capacity are related by s = cpρ

  35. Heat Out or In Conceptual Meaning of Volumetric Heat Capacity 1 unit ∆ in T 1 unit Volume earth

  36. Heat Capacity Heat Capacity is equivalent to Storage used in hydrogeology C = ∆Q/ ∆T C = Heat Capacity in Btu/°F ∆Q = heat energy in Btu ∆T = temperature in °F

  37. Heat Capacity and Specific Heat Capacity Two important relationships: C = cp x total mass of material being heated C = s x total volume of material being heated

  38. Thermal Diffusivity Thermal Diffusivity equivalent to Transmissivity D = ʎ/ cpρ Thermal conductivity / volumetric heat capacity D is a measure of the rate at which a temperature disturbance at one point in a body travels to another point in the body – similar to transmissivity English Units are: ft2/hr

  39. GSHP Efficiency Terminology Coefficient of Performance – COP energy in or energy output (Btu/h) electrical energy needed (Btu/h) at a specific T Energy Efficiency Ratio – EER (steady state cooling eff.) cooling capacity (BTU/h) electrical energy input (Btu/h) at a specific T Seasonal Energy Efficiency Ratio (SEER) total cooling over entire cooling season (BTU/h) electrical energy used over cooling season (Btu/h) EER = 0.875 x SEER

  40. GSHP Acronyms EAT Entering Air Temperature EWT Entering Water Temperature LWT Leaving Water Temperature HC Total Heating Capacity TC Total Cooling Capacity CFM Cubic Feet per Minute GPM Gallons per Minute GSHP Ground Source Heat Pump

  41. Important Conversions & Calculations 1 Watt = 1 Joule/sec 1 Watt = 3.412 BTU/hr 1 Btu = heat to raise 1 lb of water 1 degree Farenheit 12,000 Btu’s per hour = 1 ton

  42. A Useful Calculation Flow (gpm) x T difference (°F) x 500 = Q (Btu/hr) Eg., ((1 gpm x 60 min/hr)/7.481 gal/ft3) x 62.4 lbs/ft3 = 498 lbs water/hr (~500 lbs/hr) In a closed loop system: for a 10 degree temperature difference 1 gpm x 500 lbs/hr x 10 °F temp diff. = 5000 Btu/hr Therefore, 1 gpm adds 5000 Btu’s of heat per hour 5000 Btu/hr / 12,000 Btu/hr/ton = 0.42 tons or 1 gpm flow needed per 0.42 tons or 2.4 gpm required per ton of heating or cooling when you have a 10° temp. diff.

  43. The Thermodynamics of it All:Do GSHPs Work in Cold Climates? Coefficient of Performance (COP) = Heat Energy Output Electric Energy Input Industry claims COP ranging from 3 to 6 From the Second Law of Thermodynamics and the Carnot cycle: COP theoretical limit = Indoor Temperature (Indoor Temperature - Temperature of Heat Source/Sink) 44

  44. Thermodynamics (continued) Degrees Farenheit to degrees Kelvin conversion: °K = 5/9 (°F - 32) + 273 Example: • Heat a dwelling to 70 °F ~ 294 °K • Ambient groundwater temperature in Massachusetts is typically about 54 °F ~ 285 °K From the Carnot cycle: COP theoretical limit = 294 °K = 33 294 °K – 285 °K

  45. Thermodynamics (continued) What happens to the theoretical efficiency toward the end of the heating season if the entering water temperature has dropped to 35 °F? 35 °F ~ 275 °K COP theoretical limit = 294 °K = 15 294 °K – 275 °K

  46. Thermodynamics (continued) Why is the theoretical heat pump efficiency many times greater than the actual COP? • No heat pump is 100% efficient - Not all of the energy put into the heat pump is converted into the work of pumping heat – some energy “lost” as waste heat • It takes energy to pump the heat transfer fluid through the ground coupled part of the system and the air or water through the building’s heating ducts

  47. Ground Exchange vs. Air Exchange Heating season Cooling season Heating season °F

  48. Entering Heat Pump Temperature vs. Theoretical Maximum COP Entering Temperature °F Theoretical Coefficient of Performance

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