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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