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
2.OPTIMIZATION ANALYSIS :
2.1 Optimization for Endoreversible Heat Pump system
Taking the finite thermal capacity of reservoir makes the cycle realistic, conceptual heat pump cycle. The
schematic model and T-S diagram of an endoreversible heat pump system, coupled to a variable temperature heat
reservoir are shown in Fig 1. The system operates steadily between two variable reservoirs, i.e. between heat
source of temperature range (T L1 -T L2 ) and heat sink of temperature range (T H2 -T H1 ). The working fluid in the
heat pump, exchanges heat with the reservoirs, has two constant temperature limits T y and T x . Assuming that the
heat exchangers are counter flow, and the heat conductance (heat transfer co-efficient and area product) of hot
and cold side heat exchangers are U H A H and U L A L , respectively.
From the heat transfer theory, the steady rate of heat flow (Q L ) from heat source to the working fluid of heat
pump and the rate (Q H ) at which the heat is rejected from the working fluid of heat pump to the heat sink in the
heat exchangers, during the two isothermal processes are, respectively, given by:
Q H
T H
1/U H A H
T X
T H2
T H1
3
2
T X
Q H
Heat Pump
Q L
Q L
T Y
T L
W
T X
T L1
TL2
T Y 4
1/U L A L
1
Fig 1 Endo-reversible Carnot heat pump model and its T-S diagram
Q L = U L A L (LMTD) L = m L C pL (T L1 – T L2 ) (1)
Q H = U H A H (LMTD) H = m H C pH (T H2 – T H1 ) (2)
Where U L and U H are the overall heat transfer coefficients on evaporator and condenser side; and A L , A H are the
heat transfer area of the heat exchangers on evaporator and condenser side, respectively.
LMTD is the logarithmic mean temperature difference and is defined as
(LMTD) L = {(T L1 - T Y ) – (T L2 - T Y )} / ln {(T L1 - T Y ) / (T L2 - T Y )} (3)
(LMTD) H = {(T X – T H1 ) – (T X – T H2 )} / ln {(T X – T H1 ) / (T X – T H2 )} (4)
Using above equations, the following expressions are obtained
T L2 = T Y + (T L1 - T Y ) exp (-U L A L / m L C pL ) (5)
T H2 = T X - (T X – T H1 ) exp (-U H A H / m H C pH ) (6)
Further, Eq. (1) - (6) gives
Q L = C L ε L (T L1 - T Y ) (7)
Q H = C H ε H (T X – T H1 ) (8)
On rearranging,
C L = Q L / ε L (T L1 - T Y ) (9)
Where,
C L = m L C pL (10)
ε L = 1 - exp (-U L A L / m L C pL ) (11)
and,
C H = Q H / ε H (T X – T H1 ) (12)
Where,
C H = m H C pH (13)
ε H = 1 - exp (-U H A H / m H C pH ) (14)
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