Page 671 - Bird R.B. Transport phenomena

Problems 651

(b) The catalyst particle of Problem 18B.14, in time-dependent operation with the boundary
conditions as given before, but with the initial condition that c A = 0 at t = 0. The differential
equation for c is
A

(20B.6-1)
at дг~
where e is the interior void fraction for the particle. The necessary solution with \i\a = 0 may
be found from the result of Example 12.1-2.
(c) Diffusion and reaction of a solute, A, injected at t = 0 at the point r - 0 (in spherical coor-
dinates) in an infinite stationary medium. Here the function g of Eq. 20.1-43 is given as
1 -ехр(-г /4& 0 (20B.6-2)
2
лв
and the function / vanishes.
206.7. Simultaneous momentum, heat, and mass transfer: alternate boundary conditions (Fig.
20B.7). The dimensionless profiles Щ17, Л, К) in Eq. 20.2-43 are applicable to a variety of situ-
ations. Use Eqs. 20.2-49 to 52 to obtain equations for the evaluation of the dimensionless net
mass flux К for the following cases:
(a) Evaporation of pure liquid A from a saturated porous plate into a gaseous stream of A
and B. Substance В is insoluble in liquid A.
(b) Instantaneous irreversible reaction of gas A with a solid plate of С to give gaseous B, ac-
cording to the reaction A + С —> 2B. The molecular weights of A and В are equal.
(c) Transpiration cooling of a porous-walled hollow plate, as shown in the figure. The fluid is
pure A throughout, and the injected fluid is distributed so as to maintain the whole outer sur-
face of the plate at a uniform temperature T . o

Approaching stream of
gas A at temperature
T^ and velocity у ж
Injection velocity v (x)
0
У Surface at uniform
temperature T
o

Gas Л at uniform temperature T (? Gas Л in

Fig. 20B.7.
A transpiration-cooled
porous plate.

Answers: (а) К = — -h'(O,Sc,K);(b)K = J- — n'(O,Sc,K)
S c V - i -
(с)К = ^~\ П'(0,Рг,Ю