Explanation For Column G
and H Calculations
Wi = Work or electricity consumption of the Indoor R/F.
Ww = Work or electricity consumption of the Window R/F.
Qi = Heat absorbed by the evaporator of the Indoor R/F.
Qw = Heat absorbed by the evaporator of the Window R/F.
Ti = temperature difference between Indoor R/F's condenser and evaporator.
Tw = temperature difference between Window R/F's condenser and evaporator.
G = The Energy (electricity) Savings % = (Wi - Ww) / Wi
COP = Q / W (or W = Q / COP). The higher the COP the better,
because more heat can be transferred with less work (electricity). The COP depends primarily on the
temperature of the evaporator (inside the R/F) and the condenser (the back of
the R/F). The closer the two
temperatures, the higher the COP.
Therefore the colder the outside temperature gets, the closer it gets to
the inside temperature of the R/F and the higher the efficiency of the Window
R/F.
Although the COP of
the Window R/F is higher whenever the outside is colder than the inside, column G's calculation is based on simplistic (incorrect)
assumption that both R/Fs have the same COP.
Then after simple math
(multiplying top & bottom of the fraction by the constant COP) :
G = (Wi - Ww) / Wi = (Qi - Qw) / Qi
Calculating the heat energy being absorbed or released in a system may be accomplished using the formula:
Heat gain or loss = Mass x Change in Temperature x Specific Heat (for air, this is 0.25)
Again using simple math (dividing top & bottom of the fraction by the constant (0.25 x Mass)) we get:
G = (Qi - Qw) / Qi = (Ti - Tw) / Ti
Column H Calculations:
Calculations for the coefficient of performance (COP).
H = The Energy
(electricity) Savings % = (Wi - Ww) / Wi =
1 - Ww / Wi
W = Q / COP therefore substituting in the above equation: Ww / Wi = (Qw / COPw) / (Qi / COPi)
Ww / Wi = (Qw x COPi) / (Qi x COPw)
As stated above, Heat gain or loss = Mass x Change in Temperature x Specific Heat (for air, this is 0.25)
Again using simple math (dividing top & bottom of the fraction by the constant (0.25 x Mass)) we get:
Ww / Wi = (Qw x COPi) / (Qi x COPw) = (Tw x COPi) / (Ti x COPw)
COP = cold temperature (Tc) or the temperature of the evaporator, divided by
the temperature difference of the evaporator and the condenser (Td).
COP = Tc / Td
Going back to our original
table column definitions:
B = Outdoor Temperature = the temperature of Window R/F's condenser.
C = Indoor Temperature = the temperature of Indoor R/F's condenser.
D = Temperature inside the R/F = the temperature of Indoor and Window R/F's evaporator.
Ti = C - D = Temperature difference between the Indoor R/F's evaporator and condenser.
Tw = B - D = Temperature difference between the Window R/F's evaporator and condenser.
Substituting these variables in our formula, we get:
COPi = D / Ti and COPw = D / Tw
Therefore H
= 1 - Ww / Wi = 1 - (Tw x COPi) / (Ti x COPw)
Or
alternatively:
Ww / Wi = (Tw x COPi) / (Ti x COPw) = (Tw x (D / Ti)) / (Ti x (D / Tw)) = (Tw x Tw x D) / (D x Ti x Ti)
H = 1 - Ww / Wi =
1 - (Tw x Tw x D) /
(D x Ti x Ti) = 1 - ((Tw x Tw ) / (Ti x Ti))