Page 187 - Mechanical Engineers' Handbook (Volume 4)

176 Heat-Transfer Fundamentals

number of correlations, each designed for a specific geometry. For all of these, the fluid
properties are evaluated at the average temperature of the two walls.

Cavities between Two Horizontal Walls at Temperatures T and T Separated by
1
2
Distance (T for Lower Wall, T T )
1
2
1
q h(T T )
2
1
Nu 0.069Ra 1 / 3 Pr 0.074 for 3 10 Ra 7 10 9
5

1.0 for Ra 1700

3
where Ra g (T T )
/ v;
is the thickness of the space. 16

1
2
Cavities between Two Vertical Walls of Height H at Temperatures by Distance T and T 2
1
Separated by Distance 17,18
q h(T T )
1
2
Nu 0.22 Pr Ra 0.25
0.28

0.2 Pr
H
5
10
for 2 H/
10, Pr 10 Ra 10 ;

Nu 0.18 Pr Ra 0.29

0.2 Pr
5
3
for 1 H/
2, 10 Pr 10 , and 10 Ra Pr/(0.2 Pr); and
3

Nu 0.42Ra 0.25 Pr 0.012 (
/H) 0.3

4
4
7
for 10 H/
40, 1 Pr 2 10 , and 10 Ra 10 .

2.4 The Log-Mean Temperature Difference
The simplest and most common type of heat exchanger is the double-pipe heat exchanger
illustrated in Fig. 15. For this type of heat exchanger, the heat transfer between the two
fluids can be found by assuming a constant overall heat transfer coefficient found from Table
8 and a constant fluid specific heat. For this type, the heat transfer is given by
q UA T m
where
T T
T 2 1
m
ln( T / T )
2
1
In this expression, the temperature difference, T , is referred to as the log-mean temperature
m
difference (LMTD); T represents the temperature difference between the two fluids at one
1
end and T at the other end. For the case where the ratio T / T is less than two, the
2 2 1
arithmetic mean temperature difference, ( T T )/2, may be used to calculate heat-
2 1
transfer rate without introducing any significant error. As shown in Fig. 15,
T T h,i T c,i T T h,o T c,o for parallel flow
1
2
T T h,i T c,o T T h,o T c,i for counterflow
2
1