CHEMICAL ENGINEERING

HEAT TRANSFER 179

When the scale has formed, the total resistance is:

0. 0003 C 1 /[2. 236 ð 10 ^6 L

Ts 3602.^5 ]D 0. 0003 C 4. 472 ð 105 L^1 

Ts 360 ^2.^5

For conduction through the scale:

GLD 

380 Ts/ 0. 0003 D 3. 33 ð 103

380 Ts (i)

For transfer through the outside film:

GLD

t 360 /[4. 472 ð 105 L^1 

Ts 360 ^2.^5 ] 2. 236 ð 10 ^6 L

Ts 3603.^5 (ii)

and for overall transfer:

GLD 

380  360 /[0. 0003 C 4. 472 ð 105 L^1 

Ts 360 ^2.^5 ] (iii)

Inspection of these equations shows that the rate of evaporationGis a function not only
of the surface temperatureTsbut also of the latent heat of the fluidL. Using equations (i)
and (ii) and selecting values ofTin the range 360 to 380 K, the following results are
obtained:

Surface temperature Mass rate of evaporation Latent heat of vaporisation

Ts(K) G(kg/s) L(kJ/kg)

362 0.000025 2,400,000

364 0.00029 186,000

366 0.0012 39,600

368 0.0033 12,200

370 0.0071 4710

372 0.013 1990

374 0.023 869

376 0.036 364

378 0.055 121

380 0.080 0

At a boiling point of 360 K it is likely that the liquid is organic with a latent heat of, say,
900 kJ/kg. This would indicate a surface temperature of 374 K and an evaporation rate
of 0.023 kg/s. A precise result requires more specific data on the latent heat.

PROBLEM 9.48

A batch of reactants of specific heat 3.8 kJ/kg K and of mass 1000 kg is heated by means
of a submerged steam coil of area 1 m^2 fed with steam at 390 K. If the overall heat
transfer coefficient is 600 W/m^2 K, calculate the time taken to heat the material from 290
to 360 K if heat losses to the surroundings are neglected.
If the external area of the vessel is 10 m^2 and the heat transfer coefficient to the
surroundings at 290 K is 8.5W/m^2 K, what will be the time taken to heat the reactants
over the same temperature range and what is the maximum temperature to which the
reactants can be raised?
What methods would you suggest for improving the rate of heat transfer?