Heat and Mass Transfer

Question 1

When does internal or intraphase transport occur?

Answer 1

The reactant diffuses into the pores of the
particle.

Question 2

Where does external or interphase transport occur?

Answer 2

The reactant diffuses through the stagnant boundary layer surrounding the particle.

Question 3

Fick’s first law equation

Answer 3

N(a)=-D(ab) ∇Ca

Question 4

Molar flux of ‘A’ through the film (external mass transport)

Answer 4

Na=Kc( C(ab)-C(as) )

Question 5

Present the rate equation for a 1st order reaction in terms of measurable quantities

Answer 5

r=C(ab)/(1/Kc +1/Ks)

Question 6

Observable rate constant

Answer 6

1/Kobs = 1/Kc +1/Ks

Question 7

What is the Sherwood number definition

Answer 7

The Sherwood number relates the mass transfer coefficient of a species A to its diffusivity and the radius of a catalyst particle, Rp

Question 8

Sherwood number equation

Answer 8

Sh=Kc2Rp/D(AB)

Question 9

Sherwood number for flow around spherical particles

Answer 9

Sh=2+0.6(Re^0.5)(Sc^1/3)

Question 10

Reynolds number

Answer 10

Re= (velocitydensitydiameter)/viscosity

Question 11

Schmidt number

Answer 11

Sc=viscosity/(density*diffusivity)

Question 12

Heat transfer equation

Answer 12

q=h( T(b)-T(s) )

Question 13

When will the max temperature change occur

Answer 13

C(as)=0

This is when the max observable rate occurs

Question 14

What is molecular diffusion?

Answer 14

This occurs in external mass transfer.

Occurs in macropores (>50nm)

Collisions with other molecules are more frequent than with the wall.

Question 15

What is Knudsen diffusion?

Answer 15

Occurs in internal mass transfer.

Occurs in mesopores (2-50nm)

Molecule-wall collisions are dominant.

Diffusivity decreases with pore size.

Question 16

What is single file diffusion?

Answer 16

Occurs in micropores (<2nm).

Pores are too small to allow molecules to pass each other.

Question 17

Transition diffusivity

Answer 17

Bosanquet equation

1/D(ta)= 1/D(ab) + 1/D(ka)

Question 18

Knudsen diffusivity equation

Answer 18

D(ka)=(9.710^3)Rpore*(T/Ma)^0.5

Question 19

Thiele modulus equation

Answer 19

Φ=L (k/D(ta))^0.5

Question 20

Small Φ

Answer 20

The diffusional resistance is insufficient to
limit the rate of reaction

Question 21

Big Φ

Answer 21

A significant diffusional resistance
prevents a constant concentration profile

Question 22

Porosity definition

Answer 22

The ratio of void volume within the pellet to the total pellet volume

Question 23

Tortuosity definition

Answer 23

Accounts for the deviations in the path length of the pores.

Question 24

Effective Knudsen or molecular diffusivity

Answer 24

De = (porosity/tortuosity)*D

Question 25

Effectiveness factor general

Answer 25

η=robs / rmax

Question 26

Effectiveness factor sphere

Answer 26

η= 3/Φ [1/tanh(Φ) - 1/Φ]

Question 27

Effectiveness factor for a slab

Answer 27

η= tanh(Φ)/Φ

Question 28

Length parameter

Answer 28

L(p) =V(p)/S(p)

Question 29

What is the observed order of reaction in terms of true order ‘n’, under severe diffusional limitations?

Answer 29

=(n+1)/2

Question 30

What is the observed activation energy in terms of actual activation energy Ea?

Answer 30

=Ea/2

Question 31

How does temperature affect diffusional resistances and then rate?

Answer 31

At low temperatures, the reaction
rate is not limited by diffusional
resistances.

At high temperatures, the reaction
rate is inhibited by diffusional
resistances. The observed activation
energy is half the true value.

Question 32

Prater number

Answer 32

β= (-ΔHrDeC(as) )/ (lambda*Ts)

Question 33

Prater relationship for temperature and concentration.

Answer 33

T= T(s)+ β( C(as)-C(a) )

Question 34

Max temperature rise in catalyst pellet

Answer 34

(Tmax-Ts)/Ts=β

Question 35

Damkohler number

Answer 35

Da=ks/kc

Question 36

What does the Damkohler number indicate?

Answer 36

The Damkohler number indicates which characteristic first order process is faster: external diffusion or reaction.

For large values of Da the surface concentration of reactant approaches zero.

For small values of Da the surface concentration approaches the bulk fluid concentration.

Question 37

Biot number for mass

Answer 37

Bi=x(p)*kc/De

Question 38

Biot number for heat

Answer 38

Bi=x(p)*h(t)/Lambda

Question 39

Overall effectiveness factor

Answer 39

η=η(interphase)*η(intraphase)