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(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
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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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: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
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).
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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