7/27/2019 Transport Phenomena...Steady State Diffusion Problems

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DepartmentofMaterialsScienceandEngineering

MSE626N:Assignment6(Problemonmasstransfer:steadydiffusion)Problem 1: In studying the rate of leaching of a substance A from solid particles by a solvent we may postulate

that that the rate controlling step is the diffusion of A from the particle surface through a liquid film ( essentially

stagnant) out into the main liquid stream. The solubility of A in B is CAo g-moles/cc and the concentration in themain stream beyond the liquid film of thickness is CA

(i) Obtain a differential equation for CA as a function of y by making a mass balance over a thin slab ofthickness z. Assume that diffusivity DAB is constant and that A is only slightly soluble in B

(ii) Show that in the absence of any chemical reaction concentration profile of A in the liquid is linear(iii) Show that the rate of leaching is then given by:

)( AoAAB

AZ

CCDN

Problem 2:A droplet of a substance is suspended in a stream of gas B that is essentially quiescent. The droplet

radius is r1 . We postulate that there is a spherical stagnant gas film of radius rg. The concentration of A in the gas

phase is XA1 at r=r1 and XAg at r =rg.

(i) By shell balance show that for steady state diffusion ArNr2

is a constant and set the constant equal to

1

2

1 ArNr the value at the droplet surface.

(ii) Derive the following relationship from (i) abovedr

dxr

x

CDNr A

A

ABAr

2

1

2

11

.

(iii) Integrate the above relationship between r1 and r2 to get1

2

1

2

12

1 lnB

BABAr

x

x

r

r

rr

CDN

(iv) If a mass transfer coefficient Kp is defined as NAr1=Kp(pA1-pA2) show that r2 tends to ,ln)(

2

B

ABp

p

DCDk

in which D is the droplet diameter.

Problem 3: Moth balls are made from naphthalene, a volatile substance that sublimes with time. Given

that initial ball diameter is 1mm, diffusion coefficient of naphthalene in air at room temperature is 8x10-6

m2/s, its molar volume is 1.83x10

-4m

3and the equilibrium partial pressure of Naphthalene vapour in

contact with solid Naphthalene is 30 Pa

(a)Estimate mass transfer coefficient and flux of naphthalene vapour away from the surface instagnant air.

(b)Suppose that the moth balls are left in a drafty room in which air flows past them with anaverage velocity of 0.1m/s , Estimate the mass transfer coefficient and the corresponding flux.

You may carry out calculations based on the initial diameter, since the latter is small.Problem 4:On the basis of the relationship )/( RTQExpCC sat

sat

o

sat , calculate the concentration of hydrogen

dissolved in -iron at room temperature in equilibrium with a hydrogen gas partial pressure of 0.15 atm. Given that

Csat=370 and corresponding activation energy 27100 J/mol

Problem 5:On the basis of the above determine the steady state rate of diffusion of hydrogen through an iron

plate of 0.5mm thickness, 0.25 m2 area. Given that Do is =2.3x10-9 m2/s and corresponding activation energy is

660 J/mol. Assume an Arrhenius type expression for diffusion coefficient.