Page 414 - Design and Operation of Heat Exchangers and their Networks

Experimental methods for thermal performance of heat exchangers 397

voltage and current of the electric power supply. The heat flux based on the
tube inner area can be obtained by
Q el
q ¼ (8.17)
πd i L
As the fluid flows into the tube, it is heated by the tube wall, and its tem-
perature increases linearly along the tube by assuming that the thermal con-
duction along the tube wall can be neglected:
z
ð
tzðÞ ¼ t 1 + t 2 t 1 Þ (8.18)
L
where L is the tube length and t 1 and t 2 are the measured inlet and outlet fluid
temperatures, respectively.
The wall temperatures are measured with the thermocouples welded on
the tube outside surface by spot welding technique, located with specified
intervals along the tube at z 1 , z 2 , …, z N . By solving the thermal conduction
problem for the temperature distribution in the tube wall,

1 d dt w Q el
r ¼ (8.19)
2
r dr dr π r r Lλ
2
o i
dt w
r ¼ r o : ¼ 0 (8.20)
dr
(8.21)
r ¼ r i : t w ¼ t w,i
the wall temperature at the tube inside surface for small wall thickness can be
expressed as
" #
ð
Q el 2ln d i =d o Þ Q el δ t
t w,i ¼ t w,o 1+ t w,o (8.22)
2
4πLλ t 1 d i =d o Þ 4πd o Lλ t
ð
where δ t is the tube wall thickness and λ t the thermal conductivity of the
tube wall.
When the fluid leaves the tube, it flows through a cooler where the fluid
is cooled by the cooling water. The valve controls the flow rate of the cool-
ing water to keep the inlet fluid temperature t 1 at the specified value. The
energy balance error is evaluated by

Q el

ε ¼ 1 (8.23)

_ mc p,m t 2 t 1 Þ
ð
where c p,m is determined with the mean fluid temperature (t 1 +t 2 )/2. If the
energy balance error is smaller than the expected accuracy (e.g., 5%),