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Nq

T

x

evaporation

q

T

x

condensation

NN

T

x

drying

q

liquid vapour

Three times Mass & Heat Transfer

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T

T

2COCO2

H2O H2+ CO

H2O + CO

H2+ CO2

q

Reactions and Heat Transfer

gasification of coal

endothermic

reaction

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1

2

3

1 mol of iat T,p

add heat

samep

H

dq

H dHenthalpy change

Enthalpy

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H

0

TTref

liquid H c T T pL ref

molar heat capacity

H= 0 at the reference temperature

H

Hrefvap

0

TTref

gas H c T T H pG ref refvap

enthalpy of vaporisation,

(depends on choice of Tref)

Effect of Temperature

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mixture H x Hi iH f T x i i ( , )species enthalpies

effect of composition often small: H Hi i

pure i

Enthalpy in Mixtures

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Enthalpy of

Reaction

12N H NH2

32 2 3

(1) (2) (3)

H

T

Tref 298c cp p1 2 29

J mol K

1 1

cp 3 41 J mol K1 1

12 1 32 2c c T T p p ref

NH3(3)

reactants

H Treaction

Hrefreaction 46 1 1. (mol )kJ NH3

H H c T T refreaction

p ref3 3

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changes are not

very important

Temperature Effects

MS-equation

)termsdiffusionthermal()(, jijjii uuxFsmall

driving force

dz

dx

x

RT

dz

dF i

iT

ii

difference form:

zx

xTRF i

i

i

at constant

temperature

average film

temperature

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E

Ni

T

driftthermal

conduction

iiHNdz

dTE

thermal conductivity species enthalpies

difference equation:

E h T N H i i

at the average Theat transfer coefficient hz

differential equation:

z

T

Energy Flux Relation

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E EE E

calculated with the

energy transport relation

calculated by

other means

the film other phase

Continuity of Energy Flux

a Bootstrap

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Condensation with Inert Gascondensate wall coolant

T

y1

vapour

inert (1) accumulates at interface

y H

R T T

vap

b2

1 1

exp

y2

interfacial equilibrium of (2)

low temperature for condensation

boiling point

E E

E N H T h T T L2 2

methanol

nitrogen

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Reaction with Convection

(1) (2) (3)

catalyst

1

2 2N

32H2

NH3

bootstraps:

N N N N 2 1 3 13 2

no net energy flux through film:

h T T N H T N H T N H T

1 1 2 2 3 3 0

1

2N H NH23

2 2 3

T T T 0 5.

conduction thermal drift

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water (1)

air (2) + ammonia (3)

gas

liquid

10 30 50T

o

C

condensation of 1

co-diffusion

absorption of 2

evaporation of 1

counter diffusion

Ammonia Absorber

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T

T

y1

y1

E

N

N H T E L1 1

water hot air (2)

water (1)

N2 0

THNTThE G11

y y N y N

k c1

2 1 1 2

1 2,

bootstraps transport relations

(much) lower than

bulk temperature

T

y1

Drop in a Spray Drier