CHEMICAL ENGINEERING

SECTION 12

Momentum, Heat and Mass Transfer

PROBLEM 12.1

If the temperature rise per metre length along a pipe carrying air at 12.2 m/s is 66 deg K,
what will be the corresponding pressure drop for a pipe temperature of 420 K and an air
temperature of 310 K? The density of air at 310 K is 1.14 kg/m^3.

Solution

For a pipe of diameterd,themassflowDud^2 / 4
and the rate of heat transfer,qDud^2 / 4 CpTwhereTis the temperature rise.

AlsoqDhATwTmDhdlTwTmW
whereTwandTmare the mean wall and fluid temperatures.

Thus, h/CpuDdT/ 4 lTwTm

From equation 12.102: R/u^2 DdT/ 4 TwTml

Substituting in equation 3.18:

PD 4 dTl/du^2 / 4 TwTmDTu^2 l/TwTm

D 66 ð 1. 14 ð 12. 22 ð 1. 0 / 420  310 

D 101. 8 N/m^2 /m

PROBLEM 12.2

It is required to warm a quantity of air from 289 K to 313 K by passing it through
a number of parallel metal tubes of inner diameter 50 mm maintained at 373 K. The
pressure drop must not exceed 250 N/m^2. How long should the individual tubes be?
The density of air at 301 K is 1.19 kg/m^3 and the coefficients of heat transfer by
convection from the tube to air are 45, 62, and 77 W/m^2 K for velocities of 20, 24, and
30 m/s at 301 K respectively.

Solution

From equations 12.102 and 3.18:

PD 4 h/Cpul/du^2 D 4 hlu/Cpd

∴ 250 D 4 hlu/Cpð 0. 050 orhD 3. 125 Cp/luW/m^2 K(i)

298