492
Chapter 11
Heat transfer correlations
We will first consider heat transfer through the reactor wall. The rate of heat transfer,
QHE,
(W) is
proportional to surface area,
A he,
and the temperature difference,
A T,
across the surface over
which transfer occurs as described by Eq (11.12)
Qhe = ^ he A
(11.12)
In the chemical engineering literature, the proportionality constant,
Uhe,
(W m"2 K'E
) is called the
overall heat transfer coefficient. The overall heat transfer can be decomposed into heat transfer
through a boundary layer on the inside of the wall, through the wall itself and through a
boundary layer on the outside of the wall. It can be shown that the overall heat transfer
coefficient can be calculated from:
1
1
dw
1
----- ™---- 1
------1----
UHE
a 0
(11.13)
where cti is the heat transfer coefficient on the inside (W m"2 K"1), a 0 is the heat transfer
coefficient on the outside, dw is the wall thickness and kw (W m 1
K'1) is the heat conductivity of
the wall material. In many cases, the first term of Eq. (11.13) will be the largest, i.e. the heat
transfer rate will be largely determined by the heat transfer coefficient on the inside. However,
stainless steel has a rather low heat conductivity (<20 W m'1
K'1), which is several times lower
than that of steel. The resistance for conduction through the wall (the second term on right hand
side of Eq. 11.13) must be taken into account when dw
> 5 mm. Fouling of the wall, i.e.
deposition of a biofilm on the wall, will give a further decreased value of
Uhe-
Fouling not only
results in a thickening of the wall - the thermal conductivity of the deposited film is typically
significantly lower than that of the wall material.
The values of the internal and external heat transfer coefficient depend on the flow rate and
material properties such as viscosity,
rj,
heat conductivity,
A\,
and heat capacity,
Cp
(J kg' K'1), of the fluid. Correlations are normally based on dimensionless numbers, which
give
the Nusselt number, Nu,
as a function of the Reynolds number,
Res,
(cf. Eq. 11.6) and
the
Prandtl number
,
Pr.
In addition, a correction is sometimes made for viscosity changes that may
occur close to the reactor wall due to temperature effects or lower shear rate (see further 11.3.5.).
One correlation given for a stirred baffled tank of standard geometry (ds/dt = 1/3) is (Chilton et
al., 1944)
Nu=0.36
Ref66 Pr033
n. 0 .1 4
m
Vwalt J
(11.14)
where
Tjwaii
is the viscosity close to the wall, and
rji
is the bulk viscosity. (For a low viscosity
fluid like water the last factor will be 1.) The dimensionless numbers are defined as
previous page 514 Bioreaction Engineering Principles, Second Edition  read online next page 516 Bioreaction Engineering Principles, Second Edition  read online Home Toggle text on/off