CHEMICAL ENGINEERING

MOMENTUM, HEAT AND MASS TRANSFER 299

The heat transferred to the air Dud^2 / 4 CpT 2 T 1 

Duð 0. 0502 / 4  1. 19 Cp 313  289 D 0. 056 CpuW

This is equal to:hdlTwTmDhð 0. 050 l 373  301 D 11. 3 hlW

∴ 11. 31 hlD 0. 056 CpuorhD 0. 0050 Cpu/l (ii)

From equation (i): Cp/lD 0. 32 hu

and substituting in equation (ii):hD 0. 005 ð 0. 32 hu^2 anduD25 m/s

For this velocity, interpolation of the given data gives a value ofhD64 W/m^2 K.

∴ Cp/lD 0. 32 ð 64 ð 25 D512 J/kg K m

For air: CpD1000 J/kg K

and hence: lD 1000 / 512 D 1 .95 m

PROBLEM 12.3

Air at 330 K, flowing at 10 m/s, enters a pipe of inner diameter 25 mm, maintained at
415 K. The drop of static pressure along the pipe is 80 N/m^2 per metre length. Using the
Reynolds analogy between heat transfer and friction, estimate the temperature of the air
0.6 m along the pipe.

Solution

See Volume 1, Example 12.2.

PROBLEM 12.4

Air flows at 12 m/s through a pipe of inside diameter 25 mm. The rate of heat transfer
by convection between the pipe and the air is 60 W/m^2 K. Neglecting the effects of
temperature variation, estimate the pressure drop per metre length of pipe.

Solution

From equations 3.18 and 12.96,PD 4 h/Cpul/du^2

TakingCpD1000 J/kg K andlD1 m, then:

PD 4  60 / 1000 ð 12  1. 0 / 0. 025 ð 122 D 115 .2N/m^2 per metre