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MASS BALANCE: WHY MASS FLOWS?. SURROUNDING. Phase a T a , P a , m i a. Phase b T b , P b , m i b. NO. NO. ISOLATED. SYSTEM. WORK. HEAT. Ideal fixed permeable membrane. a i = i th species activity. T a = T b P a = P b m i a = m i a. EQUILIBRIUM CONDITIONS

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PowerPoint Slideshow about ' SURROUNDING' - hall-cobb


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Presentation Transcript
slide1

MASS BALANCE: WHY MASS FLOWS?

SURROUNDING

Phase a

Ta, Pa, mia

Phase b

Tb, Pb, mib

NO

NO

ISOLATED

SYSTEM

WORK

HEAT

Ideal fixed permeable membrane

ai = ith species activity

Ta = TbPa= Pb

mia = mia

EQUILIBRIUM CONDITIONS

dU=dUa+dUb = 0

slide2

MASS BALANCE: EQ.CON. ALTERATION

1

Pa increase (>Pb)

[Ta = Tb; mia = mib]

Phase a

T, Pa, mi

Phase b

T, Pb, mi

MASS TRASPORT

(CONVECTION)

permeable membrane

slide3

mia>mib

[Ta = Tb; Pa = Pb]

2

Phase a

T, P, mia

Phase b

T, P, mib

permeable membrane

MASS TRASPORT

(DIFFUSION)

Mass transport represents a possible way the system has to get new equilibrium conditions once the original ones have been altered.

slide4

MASS BALANCE

Z

X

Y

DZ

DX

(X+DX, Y+ DY, Z+ DZ)

G

(X, Y, Z)

DY

(X, Y+ DY, Z)

(X+DX, Y+ DY, Z)

slide5

MASS BALANCE: EXPRESSION

DX

DZ

(X, Y, Z)

G

DY

Ci = f(X, Y, Z, t)

slide6

DX

DZ

(X, Y, Z)

G

DY

DIVIDING FOR DV

slide8

FLUXES EXPRESSIONS

Ideal solution

Diffusion

Diffusion

Diffusion

Convection

Convection

Convection

Bi = mobility of the diffusing components

slide10

MASS BALANCE EQUATION FOR ith SPECIES

where:

Remembering the definition of the NABLA operator:

slide11

As:

… the summation of ith mass balance over all the r components yields to the well known continuity equation:

slide12

MASS BALANCE: CYLINDRICAL COORDINATES

Jir+dr

Jir+dr

Jiz

Jiz+dz

Jir

Jir

Jir

Jiz

Jiz+dz

Jir+dr

r

dr

dz

TWO DIMENSIONS

r

z

slide13

Ci = f(z, r, t)

r

dr

dz

Dividing by 2prdrdz

slide14

Constant diffusion coefficient D

Remembering the derivativedefinition

slide15

MOMENTUM BALANCE

Incoming sand

Escaping sand

Sand containing vessel

Sliding vessel motion direction

Inclinate plane

Friction

Gravity

NO

Yes

slide16

DZ

DX

(X+DX, Y+ DY, Z+ DZ)

(X, Y, Z)

DY

(X, Y+ DY, Z)

(X+DX, Y+ DY, Z)

Body forces: gravitational, electro-magnetic fields

Surface forces: viscous drag and pressure

slide17

Surface forces

gravitational field

Incoming and

exiting mass

slide18

ENERGY BALANCE

Conduction

Expansion

Viscous heating

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