(vii) From (vi) and the integrated form for Na(r), obtain a differential equation for the mole fraction of "A" in the stream (viii) Integrate the equation in (vii) in terms of a second constant c2. (ix) Obtain the two constants from the boundary conditions on the mole fraction of "A" at the boundaries of the film. (x) Obtain an expression for Nar(r) and the evaporative flux of "A" at the surface r=r1, XA(r).
(vii) From (vi) and the integrated form for Na(r), obtain a differential equation for the mole fraction of "A" in the stream (viii) Integrate the equation in (vii) in terms of a second constant c2. (ix) Obtain the two constants from the boundary conditions on the mole fraction of "A" at the boundaries of the film. (x) Obtain an expression for Nar(r) and the evaporative flux of "A" at the surface r=r1, XA(r).
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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Please help me only 7,8,9,10 please....
Transcribed Image Text:r dinectlon
Steady state
NO reaction.
0 = -V.nA
dnar
dnxe
anat
dr
do
dnar
Nar = Consteant
dr
Cil S
dNar
%3D
dr
NAr
() Nor Cr= Constant
(iv)
ar
Nor Cr) = C
(v) means thent
at ravo
So C220
(vi)
Fick's
Caw
Na= Jat + XA (Na+ ) =-C DA VXa+XA (NAt NB)
NAr = -CDAB
dXA
+ XANAY
dr
(vii)
dXA
+X4NA-
dr
C-XANAr= -CD axA
ar
Transcribed Image Text:1. A droplet of liquid A of radius ra is suspended and is evaporating in a stream of gas B.
We assume that there is a gas film of A and B of radius r2 surrounding the droplet. In this
film B is stagnant. The concentration of A in the gas phase is XA1 at r=r1 and xa2 at the
edge of the stagnant layer r=r2. XA1 > XA2. The temperature T and the pressure P are
constant. The aim of the problem is to calculate the evaporative flux of A into the
stagnant gas layer assuming the radius of the droplet remains constant.
sagrant fim of gas
dropet of
Awth ed
us
Assuming diffusive transport of A only in the "r" direction and steady state, what
does the conservation equation for species "A" become in terms of NAr(r) in
spherical coordinates?
Integrate the equation in (i) to obtain the flux Na-(r) as a function of r in terms of
an unknown constant "c,".
Formulate a similar equation for the flux of species "B" in the layer, NBr(r).
Integrate the equation in (iii) to obtain the flux of species "B", Na-(r) in terms of
a constant c2
Species "B" is not soluble in droplet "A". What does this tell you about the
(i)
(ii)
(iii)
(iv)
(v)
boundary condition for the flux of "B" at r=r1. What is the constant c2?
What is the form for Fick's law for species "A"; do not assume the mole fraction
(vi)
of "A" is small and write Fick's law for the mole fraction of "A". The diffusion
coefficient of A in B is denoted as D
(vii) From (vi) and the integrated form for Na(r), obtain a differential equation for the
mole fraction of “A" in the stream
(viii) Integrate the equation in (vii) in terms of a second constant c2.
Obtain the two constants from the boundary conditions on the mole fraction of
"A" at the boundaries of the film.
(ix)
(x)
Obtain an expression for Nar(r) and the evaporative flux of "A" at the surface
r=r1, XA(r).
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