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How Water Heaters • Heated water is used in bathing and cleaning periodically throughout the day. • Energy is required to heat the water. • If not used immediately, energy is also required to keep the water hot!
Types of Water Heaters: Tank • Water is … • heated and stored • delivered to user when needed • replaced in the tank by municipal connection • Reheated as needed • Sizes: • 60 – 90 gal. whole home • 3 – 10 gal. point of use • Energy Use • Electric • Natural gas • Solar • Heat pump Homedepot.com Heaterdetails.info unitedinspection.com
Types of Hot Water Heaters: Tankless Heaterinsigt.info • Water is … • run through the heater when needed • brought up to desired temperature • delivered to user • not stored • Energy used • Natural gas • Electric A-archer.net
How to Choose? • Not an unimportant decision • 22% of US energy use is residential • 20% of that is heating water • Things to consider • Size • Fuel type • Overall cost • First hour rating
Tankless water heat ratings • Primary consideration: want hot water at a desired flow rate • Appliances are rated by the maximum temperature rise possible at a given flow rate • Amperage (amps) : 29 A • Element Wattage (watts) : 7KW • Flow Rate @ 35°F Rise (gallons/min) : 2.2 gal (US)/min • Flow Rate @ 45°F Rise (gallons/min) : 1.5 gal (US)/min • Flow Rate @ 77°F Rise (gallons/min) : 0.5 gal (US)/min • Fuel Type : Electric • Maximum temperature (F) : 125 • Voltage (volts) : 240 V RheemEcosense 7kW
Sizing a tankless water heater • To size one we must estimate the peak usage flowrate, dV/dt, (usage) in volume/time • Then, we must determine if the system can heat that amount of water per unit time from the starting to the final temperature. • Finally total daily usage tells us how much energy is used • Assume • you live alone and just want a hot shower. • a low flow 1.5 GPM showerhead (Federal Regulation from 1992 is 2.2 GPM max) • 50 F inlet water • You want a 95F shower. • Is this possible with the 7kW Rheem?
How much energy is required? • Assume we take a shower at 1.5 gpm • The outlet temperature will be 95F (50F+45F) • How much power (dQ/dt) is required to achieve this change in water temperature? Hmmm!! Someone is not telling the truth! Where are their ethics?! If your luxury shower takes 10 minutes how much energy is used? Q=10,100 J/s * (600 sec) = 6.01 MJ (or 2.5 Big macs)
What about your dorm room or apt.? • Peak usage • 1 shower at a time • 1 bathroom sink • 1 Kitchen sink (or not?) • The power required at peak would be the sum required from all sources used at the same time. • EX: Two 1.5 GPM showers at 95F (from 50F) would require a unit capable of 20.2kW by our calculations. • Total Daily Usage • # of people bathing • Dishwasher, sink, clothes washing • The daily energy required is found by integrating (summing) power usages throughout the day • If one bather took 5 and the other 10 minute showers, you would use 6MJ +3MJ=9MJ of energy.
What About your parents home? • Your parent’s home • Peak usage • ~2 showers concurrently in the morning (possibly multiple sets of two) • ~2 sinks in the morning (possibly multiple sets of two) • Total Daily Usage • #of people bathing • Dishwasher, sink, clothes washing Total daily use tells the amount of energy used per day. Peak power tells the size of the unit required.
Sizing a tank (storage) water heater 40 gal GE hot water heater • primary consideration: the tank should not run out of hot water; examine the “first our demand” • Important specifications include • size (gal.) • Energy used (often in BTUs) • Recovery rate: time to reheat water and “First Hour” rating • energy factor (EF): relative measure of hot water produced per unit energy • “R” value of tank insulation (sometimes not given) • Fuel Type : Gas • Gas Type : Natural Gas • Total BTU : 40000 Btu (per hour) • Maximum temperature (F) : 160 • Minimum Temperature : 60 °F • Recovery Rate at 90F Rise (GPM GPH) : 40.4 • Tank Capacity (gallons) : 40 gal (US) • First Hour Rating (GPH):68.0 • Tank Diameter (in.) : 20.25 • Tank Height (in.) : 62 • Beware of faulty information
How much energy is required to heat the water in the tank? • Assume the water enters the tank at 50 F. • The energy required to heat 47 gallons to make it available? • But if we do not use it immediately, then it will cool off and we will have to heat it again!!
How much heat is lost by the water in the tank? • Convection will occur at outer surface of the tank. • Difference between air temperature and surface temperature drives convection. • We know Tsurface > Tair so we draw convection leaving tank. • Since heat is being lost, dQH/dt, we must reheat dQgen/dt, to maintain temperature. Want dT/dt=0 • We set TH20 and we can measure Tair. This is all we need to find heat flux. Water heater tank, @ Th20 Tair Tsurface
Combined convection, conduction problem • Examine control volume (dotted line) and boundaries. Heat flow is constant. • Examine Water/insulation surface • Examine conduction thru insulation • Examine insulation/air interface Water insulation Th20 Tair Tinner Touter d
Conduction+Convection Through multiple thermal “resistances” (R-values) • If we sum the boxed equations • In general the thermal resistance for conduction is • Thermal resistance for convection is • And for any thermal pathway in 1D, the heat flux from the interior to the exterior is (where a negative sign means a reversal of direction) Note: In applications, traditionally “R-values” are given per unit Area, With units of area-temp/power Note that in our problem, this is the power required to maintain the temperature of a full tank. This is why you insulate your water heater!!! If water is used, then additional heat is required to increase the replacement water’s temperature from ambient, to our set point.
Water Heater Heat Loss • If the water heater is well insulated, k=0.05 W/m-C how much power on average is required to maintain the temperature in the tank for 24 hours assuming worst case natural convections? • Assume the tank has Ainner~= Aouter=A=2pr*height+2pr2 • Where r~=10.125 inches, height=62 inches • How much energy is used in that 24 hours?
Costs? • Energy use cost: • Electricity: 0.18 kW-hr • Gas: • Installation • Tankless • Gas: $2200 • Electric: 240 V ($2200) or 110V ($1350) • Tank • Gas:$800 • Electric: 110V ($150) (or 240V ($800) • Given our average daily usage, we can determine the recurring costs. • Given the installation costs, we can determine the initial costs. • Given a prevailing interest rate, we can determine present and future values.