Page 47 - Design and Operation of Heat Exchangers and their Networks

34 Design and operation of heat exchangers and their networks

Q Q 1 δ
Δt ¼ ¼ +
kA 2Nh fs + s fs ÞL η α
ð
0 λ f
100 1 0:0025
¼ + ¼ 34:2K
2 13 0:025 + 0:0035Þ 0:15 0:9503 27:69 230
ð
The highest temperature of the printed circuit board appears near the air
outlet:
t max ¼ t out + Δt ¼ 42:0+ 34:2 ¼ 76:2°C
The detailed calculation can be found in the MatLab code for Example
2.3 in the appendix.

2.1.2 Basic equations for steady-state operations of heat
exchangers
The first law of thermodynamics should be satisfied in any heat exchanger
both at macro- and microlevel. Taking the overall “macro” energy balance
for a heat exchanger in a steady state, we have

_
0
Q ¼ C m,h t t 00 (2.66)
h h

_
00
Q ¼ C m,c t t 0 (2.67)
c c
The general heat exchange rate equation is given by
A
Z
ð
Q ¼ kt h t c ÞdA ¼ k m Δt m A (2.68)
0
The mean thermal capacity rate of a fluid can be calculated according to
the enthalpy change
_ 0 00 0 00
C m ¼ _mh hð Þ= t t Þ (2.69)
ð
or be calculated approximately according to the specific isobaric thermal
capacity at its mean temperature:
_ 0 00
C m ¼ _mc p,m ¼ _mc p T + Tð½ Þ=2, pŠ (2.70)
The mean temperature difference is defined by

Z A
1
Δt m ¼ ð t h t c ÞdA (2.71)
A 0