Page 83 - Low Temperature Energy Systems with Applications of Renewable Energy

72 Low-Temperature Energy Systems with Applications of Renewable Energy

where h HP is an efficiency that takes into account real processes done by the working
fluid inside the heat pump; it can be assumed to be 0.6; 4 t is a theoretical heat pump
COP that can be determined by the following relation taking into account heat irre-
versibility in the evaporator and condenser:

" # 1 1
T HP 273:15 þ t out Dt ev
ev
s
4 ¼ 1 HP ¼ 1 ; (2.15)
t
T 273:15 þ t c þ Dt c
c
where T HP is the working fluid evaporating temperature, K; T HP is the working fluid
ev c
condensation temperature, K; t out is the surroundings temperature at the evaporator
s

outlet, C; Dt ev is temperature difference between the heat pump surroundings and the

working fluid at the evaporator outlet, C; Dt c is temperature difference between the
heat pump working fluid and the water at the condenser outlet. According to standard

practice, one can assume that Dt ev ¼ 10 C, 5 C, and 5 C for air, water and brine

solutions, respectively; Dt c ¼ 5 C for low-temperature water-heating systems.
The water temperature t c at the condenser outlet is specified by the needs of the heat
consumer. In the case of a HP to supply a hot water heating system, the temperature of
the heat carrier that is fed from the heat pump condenser into the low-temperature heat-
ing system can be found from the following equation [11]:
1
ð1þnÞ

c c t a t 0
t c ¼ t þ t t a ; (2.16)
hc hc c
t a t
0
c
where t is the calculated temperature of the heat carrier being heated in the heating
hc
system with calculated ambient temperature t , C; n ¼ 0 for low-temperature heating
c
0
systems.
Taking into account Eqs. (2.10)e(2.14), Eq. (2.9) for the specific external energy
losses for heating takes the following form:
" #
1 Að4 1Þ
l h ¼ 1 þ ; (2.17)
4 t t out h m:e h dr
in
s
s
s
Dp
where A ¼ is a defined factor, a function of given values, C.
r s c p
Thus, the total specific external energy loss for heating l h depends on the defined
function A, ambient temperature, the temperatures of a low-temperature energy source
at the evaporator inlet and outlet, and the calculated temperature of the heat transfer
in out c
fluid in the heating system, namely, l h ¼ f A; t 0 ; t ; t ; t .
s s hc
2.6.2 Optimum degree of cooling in heat pump evaporator
In the following sections, we consider this problem for systems that use air, water and
soil as the low-temperature energy source for the heat pump.