CHEMICAL ENGINEERING

316 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

and: uŁ

2

D

(





CE

)

duC

dyC

uŁ

/uŁ

Hence:





D

(





CE

)

duC

dyC

D

(





CE

)

5

yC

WhenyCD15, then:/D/CE/ 3

and: ED 2 /

iii)For heat transfer in buffer zone:qDkCCpEH

dT

dy

WritingEHDEgives:qDkCCpE

dT

dy

WhenyCD15, then puttingED 2 /gives:

qDkC 2 Cp

dT

dy

Dk 1 C 2 Pr

dT

dy

Thus:

dT

dy

D

q

k 1 C 2 Pr

Putting: kD 0 .62 W/m K,PrD7andqD1000 W

then: dT/dyD108 deg K/m or 0.108 deg K/mm

PROBLEM 12.23

Derive an expression relating the pressure drop for the turbulent flow of a fluid in a pipe
to the heat transfer coefficient at the walls on the basis of the simple Reynolds analogy.
Indicate the assumptions which are made and the conditions under which it would be
expected to apply closely.
Air at 320 K and atmospheric pressure is flowing through a smooth pipe of 50 mm
internal diameter and the pressure drop over a 4 m length is found to be 150 mm water
gauge. By how much would the air temperature be expected to fall over the first metre
if the wall temperature there is 290 K? Viscosity of airD 0 .018 mN s/m^2. Specific heat
capacityCpD 1 .05 kJ/kg K. Molecular volumeD 22 .4m^3 /kmol at 1 bar and 273 K.

Solution

If a mass of fluid,m, situated at a distance from a surface, is moving parallel to the
surface with a velocity ofus, and it then moves to the surface, where the velocity is zero,
it will give up its momentummusin timet. If the temperature difference between the

mass of fluid and the surface is (^0) s, then the heat transferred to the surface ismCp (^0) sand
over a surface of area,A:
mCp (^0) s/tDqA
whereqis the heat transferred from the surface per unit area per unit time.