Page 210 - Chemical Process Equipment - Selection and Design

182 HEAT TRANSFER AND HEAT EXCHANGERS

transfer units is
EXAMPLE 8.5
Application of the Effectiveness and the B Method N = UA/Cmin = 2000/800 = 2.5,
Operating data of an exchanger are shown on the sketch. These C = Cmin/Cmax = 0.8,
data include
D = = 1.2806,
UA = 2000, P= 2 = 0.6271,
m'c' = 1000, mc = 800, 1 + C + D[1+ exp(-ND)]/l- exp(-ND)
C = Cmin/Cmax = 0.8. 0 = PIN = 0.2508,
AT, = 0(200 - 80) = 30.1,
Q = UA(AT), = 2000(30.1) = 60,200,
= 800(200 - &) = 1000(T; - SO),
m'c' = 1000
:. T2 = 124.75,
Ti = 140.2.
T, also may be found from the definition of P:
UA = 2000
T; P= actual AT 2oo - T2 = 0.6271,
max possible AT - 200 - 80
:. T,= 124.78.
The equation for effectiveness P is given by item 6 of Table 8.3 or it
can be read off Figure 8.4(a). Both P and 0 also can be read off With this method, unknown terminal temperatures are found
Figure 8.4(a) at known N and R = C,/C, = 0.8. The number of without trial calculations.

compared with a normal value of The Nusselt number, hL/k = h/(k/L), is the ratio of effective
heat transfer to that which would take place by conduction through
U = 10,000/(57 + 50) = 93, a film of thickness L.
The Peclet number, DGC/k = GC/(k/D) and its modification,
where the averages of the listed numbers in Table 8.6 are taken in the Graetz number wC/kL, are ratios of sensible heat change of the
each case. flowing fluid to the rate of heat conduction through a film of
thickness D or L.
METAL WALL RESISTANCE The Prandtl number, Cp/k = (y/p)/(k/pC), compares the rate
of momentum transfer through friction to the thermal diffusivity or
With the usual materials of construction of heat transfer surfaces, the transport of heat by conduction.
the magnitudes of their thermal resistances may he comparable with The Grashof number is interpreted as the ratio of the product
the other prevailing resistances. For example, heat exchanger of the buoyancy and inertial forces to the square of the viscous
tubing of 1/16 in. wall thickness has these values of l/h, = L/k for forces.
several common materials: The Stanton number is a ratio of the temperature change of a
fluid to the temperature drop between fluid and wall. Also,
Carbon steel l/h, = 1.76 x St = (Nu)/(Re)(Pr).
Stainless steel 5.54 x An analogy exists between the transfers of heat and mass in
Aluminum 0.40 x 1 o-~ moving fluids, such that correlations of heat transfer involving the
Glass 79.0 x Prandtl number are valid for mass transfer when the Prandtl
which are in the range of the given film and fouling resistances, and number Cp/k is replaced by the Schmidt number p/pk,. This is of
should not be neglected in evaluating the overall coefficient. For particular value in correlating heat transfer from small particles to
example, with the data of this list a coefficient of 93 with carbon fluids where particle temperatures are hard to measure but
steel tubing is reduced to 88.9 when stainless steel tubing is measurement of mass transfer may be feasible, for example, in
substituted. vaporization of naphthalene.

DIMENSIONLESS GROUPS
8.4. DATA OF HEAT TRANSFER COEFFICIENTS
The effects of the many variables that bear on the magnitudes of
individual heat transfer coefficients are represented most logically Specific correlations of individual film coefficients necessarily are
and compactly in terms of dimensionless groups. The ones most restricted in scope. Among the distinctions that are made are those
pertinent to heat transfer are listed in Table 8.8. Some groups have of geometry, whether inside or outside of tubes for instance, or the
ready physical interpretations that may assist in selecting the ones shapes of the heat transfer surfaces; free or forced convection;
appropriate to particular heat transfer processes. Such interpreta- laminar or turbulent flow; liquids, gases, liquid metals, non-
tions are discussed for example by Grober et al. (1961, pp. Newtonian fluids; pure substances or mixtures; completely or
193-198). A few are given here. partially condensable; air, water, refrigerants, or other specific
The Reynolds number, Dup/p = pu2/(pu/D), is a measure of substances; fluidized or fixed particles; combined convection and
the ratio of inertial to viscous forces. radiation; and others. In spite of such qualifications, it should be