CHEMICAL ENGINEERING

HEAT TRANSFER 203

PROBLEM 9.71

Liquid is heated in a vessel by means of steam which is supplied to an internal coil in
the vessel. When the vessel contains 1000 kg of liquid it takes half an hour to heat the
contents from 293 to 368 K if the coil is supplied with steam at 373 K. The process is
modified so that liquid at 293 K is continuously fed to the vessel at the rate of 0.28 kg/s.
The total contents of the vessel are always being maintained at 1000 kg. What is the
equilibrium temperature which the contents of the vessel will reach, if heat losses to the
surroundings are neglected and the overall heat transfer coefficient remains constant?

Solution

Use is made of equation 9.209:

ln



TsT 1 /

TsT 2 D

UA/mCpt

In this case:TsD373 K,T 1 D293 K,T 2 D368 K,mD1000 kg andtD 0 .5 h or 1800 s

∴ ln

373  293 /
373  368 D
UA/Cp 
1800 / 1000 D 2. 773

and: UA/CpD 1 .54 kg/s

For continuous heating, assuming
UA/Cp is constant and losses are negligible then:

QDUA

TsTDmCp

TT 1

whereTis the temperature of the contents.

∴ UA
373 TD 0. 28 Cp
T 293

UA/Cp 

373 TD 0. 28 T 82. 04

Substituting for
UA/Cp :

1. 54 ð 373  1. 54 TD 0. 28 T 82. 04

and: TD 360 .7K

PROBLEM 9.72

The heat loss through a firebrick furnace wall 0.2 m thick is to be reduced by addition of a
layer of insulating brick to the outside. What is the thickness of insulating brick necessary
to reduce the heat loss to 400 W/m^2? The inside furnace wall temperature is 1573 K, the
ambient air adjacent to the furnace exterior is at 293 K and the natural convection heat
transfer coefficient at the exterior surface is given byhoD 3. 0 T^0.^25 W/m^2 K, whereT
is the temperature difference between the surface and the ambient air. Thermal conduc-
tivity of firebrickD 1 .5 W/m K. Thermal conductivity of insulating brickD 0 .4W/mK.