Page 77 - Low Temperature Energy Systems with Applications of Renewable Energy

66 Low-Temperature Energy Systems with Applications of Renewable Energy

transfer will not decline provided there is a balance between heat extraction for heat
supply in winter and heat replacement in summer during operation of the air condi-
tioning system.
The analysis that leads to the empirical equation to estimate the heat flow from the
soil to a horizontal pipe heat exchanger, given below Eq. (2.4), is developed in
Ref. [5]:

W c
q s ¼ð1:4l 0:5Þ$ þ 1 $ðt s t c Þ; (2.4)
W w
where l is the soil thermal conductivity, W/m$ C; W c and W w are amount of cooling

and heating used per year; t s is soil temperature in the natural state, C; t c is the mean
fluid temperature that cools the soil, C. Data on thermal conductivity of some soils are

given in Table 2.5.
Horizontal heat exchanger pipes are arranged so that there is no thermal
interference with adjacent pipe temperature fields. It is generally assumed that
when the distance between pipes is 1 m, the interference between adjacent pipes
is negligible. If the pipe spacing is taken to be 1 m, then its area in square meters
will be numerically equal to the common pipe length that is determined by Eq.
(2.3).
As for the heat exchanger pipe diameter (typ. 27e34 mm), its value does not prac-
tically affect the specific heat flow value q s because only a small range of polymer pipe
diameters are deployed. The heat transfer coefficient from the pipe wall to fluid flow is
sufficient provided the mode of fluid flow in the pipe is both turbulent and transient.
The transient mode is desirable when the heat pump operates periodically as the soil
somehow manages to return to its initial temperature state. Fully turbulent flow is ob-
tained in polyethylene pipe at Re > 3000. The corresponding minimal fluid flow
values are given in Table 2.6.
If fluid flow in the pipe exceeds the minimum, its diameter or discharge capacity
of the circulation loop is chosen based on the hydraulic head. When using
polyethylene pipe of the widely used diameters, one can refer to the curves shown
in Fig. 2.15.
Being aware of the circulation discharge capacity and total fluid flow in the lower
loop of the heat pump system, one can determine the number of parallel loops of the
soil collector. Total fluid flow is defined by the equation:

3600$Q HP 4 1
G sc ¼ (2.5)
c p $r $Dt io 4
f
where Q HP is the heat pump thermal power, kW; 4 is the COP; c p is the fluid specific
3

heat circulating in the loop, kJ/kg$ C; r f is fluid density, kg/m ; Dt io is fluid tem-

perature difference at the soil collector input and output that is taken equal to 5 C,
according the data in Ref. [5].