CHEMICAL ENGINEERING

HEAT TRANSFER 189

PROBLEM 9.57

A liquid hydrocarbon is fed at 295 K to a heat exchanger consisting of a 25 mm diameter
tube heated on the outside by condensing steam at atmospheric pressure. The flowrate of
hydrocarbon is measured by means of a 19 mm orifice fitted to the 25 mm feed pipe. The
reading on a differential manometer containing hydrocarbon-over-water is 450 mm and
the coefficient of discharge of the meter is 0.6.
Calculate the initial rate of rise of temperature (deg K/s) of the hydrocarbon as it enters
the heat exchanger.
The outside film coefficientD 6 .0W/m^2 K.
The inside film coefficienthis given by:

hd/kD 0. 023 

ud/^0.^8 

Cp/k^0.^4

where:uDlinear velocity of hydrocarbon (m/s).dDtube diameter (m),Dliquid density
800 kg/m^3 ,Dliquid viscosity
9 ð 10 ^4 Ns/m^2 ,CpDspecific heat of liquid (1. 7 ð
103 J/kgK), andkDthermal conductivity of liquid (0.17 W/mK).

Solution

The effective manometer fluid density, is 200 kg/m^3.

The pressure difference across the orificeD450 mm water

or:
450 ð 800 / 200 D1800 mm hydrocarbon

that is: HD 1 .80 m

The area of the orificeD
$/ 40. 0192 D 2. 835 ð 10 ^4 m^2

In equation 6.21: GD
0. 6 ð 2. 835 ð 10 ^4 ð 800

√

2 ð 9. 81 ð 1. 80

D 1. 36

√

35. 3 D 0 .808 kg/s

The volume flowD
0. 808 / 800 D 0 .00101 m^3 /s.
Cross-sectional area of a 0.025 m diameter pipeD
$/ 40. 0252 D 0 .000491 m^2 and
hence the velocity,uD
0. 00101 / 0. 000491 D 2 .06 m/s.
The inside film coefficient is given by:

hið 0. 025 / 0. 17 D 0. 023



2. 06 ð 0. 025 ð 800 / 9 ð 10 ^40.^8

ð 



1. 7 ð 103 ð 9 ð 10 ^4 / 0. 170.^4

or: hiD 0. 1564
4. 58 ð 1040.^8
9. 00.^4 D2016 W/m^2 Kor2.02 kW/m^2 K

Neglecting scale and wall resistances:

1 /UD 

1 / 6. 0 C 

1 / 2. 02 andUD 1 .511 kW/m^2 K

For steam at atmospheric pressure, the saturation temperatureD373 K and at the inlet
the temperature driving forceD
373  295 D78 deg K.