dharm
\M-therm\Th15-3.pm5
822 ENGINEERING THERMODYNAMICS
and dtc =
dQ
mc
dQ
&cpccC
=
where, Ch = m&h cph = Heat capacity or water equivalent of hot fluid, and
Cc = m&c cpc = Heat capacity or water equivalent of cold fluid.
m&h and m&c are the mass flow rates of fluids and cph and cpc are the respective specific heats.
∴ dth – dtc = – dQ 11
CChc
+
L
N
M
O
Q
P
dθ = – dQ
11
CChc
+
L
N
M
O
Q
P ...(15.50)
Cold
Cold
Hot
Annulus
surrounding
the pipe
Pipe
( ) Flow arrangement.a
1 2
dA
Area
Temperature
th 1
th 2
tc 2
tc 1
q dQ
dtc
dth
Cold fluid
Hot fluid
th
tc
q1h
1
c^1
(= t
- t )
q2h(= t 2 – t )c 2
( ) Temperature distribution.b
Subscripts h, c refer to hot and cold fluids
Subscripts 1, 2 refer to inlet and outlet conditions.
Fig. 15.38. Calculation of LMTD for a parallel-flow heat exchanger.
Substituting the value of dQ from eqn. (15.49) the above equation becomes
dθ = – U. dA (th – tc)^11
CChc
+
L
N
M
O
Q
P
or dθ = – U. dA. θ
11
CChc
+
L
N
M
O
Q
P
or dθ
θ
= – U. dA
11
CChc
+
L
N
M
O
Q
P