OCTOBER 19-20, 2012 - YMCA University of Science & Technology

Proceedings of the National Conference on
Trends and Advances in Mechanical Engineering,
YMCA University of Science & Technology, Faridabad, Haryana, Oct 19-20, 2012
are the thermal capacitance rates and effectiveness of heat exchangers on evaporator side (cold) and condenser
side (hot) respectively.
Let
y = (T L1 - T Y ) (15)
So T Y = (T L1 – y)
x = (T X – T H1 ) (16)
so T X = T H1 + x
expressing A L and A H in terms of ε L & ε H
A L = -C L ln(1 - ε L ) / U L (17)
A L = -Q L ln(1 - ε L ) / (U L ε L y) (18)
Let k L = -ln(1 - ε L ) / (U L ε L ) (19)
So A L = Q L k L / y (20)
Similarly,
A H = -C H ln(1 – ε H ) / U H (21)
A H = -Q H ln(1 – ε H ) / (U H ε H y) (22)
Let k H = -ln(1 – ε H ) / (U H ε H ) (23)
So A H = Q H k H / y (24)
From the first law of thermodynamics, the power input to the heat pump is
W = Q H - Q L (25)
From the second law of thermodynamics, for an endoreversible cycle, the changes in entropies of the working
fluid for heat addition and heat removing isothermal process yields:
Q L / T Y = Q H / T X
So Q L = T Y Q H / T X
Or Q L = Q H (T L1 – y) / (T H1 + x) (26)
The coefficient of performance for endoreversible heat pump, as defined earlier is
COP hp = Q H / W = (T H1 + x) / [(T H1 + x) - (T L1 - y )] (27)
The objective function of thermoeconomic optimization as proposed by earlier researchers [9, 12-13] is given by
F hp = Q H / (C i + C e + C m ) (28)
Where C i , C e and C m are the annual investment, energy consumption cost and maintenance costs, respectively.
The investment cost includes the investment cost of the main system components which are the heat exchangers
and the compressor together with its prime movers, where the investment cost of the heat exchangers is assumed
to be proportional to the total heat transfer area, while the investment cost of the compressor and its driver is
assumed to be proportional to its compression capacity or required power input. Thus the annual investment cost
of the system can be given as:
C i = a(A H + A L ) + b 1 W (29)
Where a is the proportionality coefficient of the heat exchangers and is equal to the capital recovery factor times
investment cost per unit heat transfer are and its dimension is ncu/year-m 2 . The proportionality coefficient of the
compressor and its driver, b 1 is equal to the capital recovery factor times investment cost per unit power and its
dimension is ncu/year-kW. The unit ncu stands for the national currency unit. The initial investment cost is
converted to equivalent yearly payment using the capital recovery factor. The annual energy consumption cost is
proportional to the power input i.e.
c e = b 2 W = b 2 (Q H - Q L ) (30)
Where the coefficient, b 2 is equal to the annual operation hours times price per unit energy and its dimension is
ncu/year-m 2 .
And C m = b p (Q H - Q L ) (31)
Here b p is equal to equivalent annual operation hours per unit power input.
Substituting Eqs. (29), (30) and (31) into Eq. (28), gives
F hp = Q H / {a (A H + A L ) + b (Q H - Q L )} (32)
Where b = b 1 + b 2 + b p
Using Eqs. (20), (24), and (26) gives
F hp = Q H / Q H [a{(k H / x) + (k L (T L1 - y) / y(T H1 + x))}+ b {1 – ((T L1 - y) / (T L1 + x))}]
Or bF hp = 1 / [k{(k H / x) + (k L (T L1 - y) / y(T H1 + x))}+ b {1 – ((T L1 - y) / (T L1 + x))}] (33)
Where k = a/b; Economical parameter
30