Transportation Processes

Of the Gases

2007/05/10

Three typical transportation processes of the gases

Viscosity phenomenon

Heat Transfer

Diffusion

Viscosity phenomenon

t

0u

0zu0z

s

z

Direction of flux

of m

omentum

When an impulse is transport from layer to layer ,the impose of these layer changes (grows or diminishes).This means that a force equal to the change in the impulse in a unit time acts on each of layers.

This force is the force of friction between layers of a gas moving with different velocities,hence the name internal friction( f ).

Newton’s Law of Viscosity

Velocity gradient :which characterizes the rate of change in the velocity along

this axis

Viscosity coefficient:

sdz

duf

z

0

dzdu /

v3

1

Other expressions for Newton Law of viscosity

The momentum K transported during through of a cross section perpendicular to the z-axis will be determined by the equation :

Newton’s Law of Viscosity

The minus sign signifies that the momentum is transport in the direction of a reduction in velocity.

tsdz

dudK

z

0

Momentum flux sdt

dKJK

0Zk dz

dvJ

Newton’s Law of Viscosity

The internal friction f:

Viscosity

Momentum flux

sdz

dvf

0

0

dz

dvJ k

v3

1

Heat Transfer

Heat conductivityConvectionHeat radiation

Heat Conductivity

If a gas is heated unevenly,i.e. the temperature in one portion of it is higher or lower than in another portion,leveling out of the temperature is observed:the hotter portion cools and the cold part becomes heated .

This is evidently connected with the flow of heat from the warmer portion to the the colder one .this phenomenon of the appearance of a heat flux in a gas or in any other substance is called thermal conductivity.

Heat Conductivity

Assume that ,along the x-axis ,the temperature changes from point to point ,i.e. Is a function of x whereas the temperature is identical at any point in a plane at right angles to this axis.

Direction of flow1T 2T

1x 2x x

Quantity of heat

Heat flux Coefficient of thermal conductivity

sdtdz

dTdQ

比vcv

3

1

sdt

dQjQ

Fourior Law of Heat Conduction

Heat flux is proportional to the temperature gradient.

dz

dTjQ

Convection

Newton’s law of cooling:

h is coefficient of heat convection

fs tthAq

Heat Radiation

Wien’s displacement law:

Wien’s formula:

Rayleigh – jeans’ formula

bTm

Tcb e

cTM

2

51

4

2

ckT

M b

Heat Radiation

Plank’s formula:

1

185

kThcb e

hc

Rayleigh-Jeans’ law

Plank’s law

Wien’s law

T

max

L

L

Diffusion

The penetration of two or more contacting substances into one another : diffusion.

Appears if it is not homogeneous in composition.

The motion of a component under the action of a concentration gradient is called diffusion flux of this component.

Fick Diffusion Law

Self-diffusion

• Diffusion flux:

• Diffusion coefficient:

• Mass diffusion flux:

dz

dnDj

vD 3

1

dz

dDjM

Inter-diffusion

• Inter-diffusion flux:

• Inter-diffusion coefficient:

dz

dnDj

dz

dnDj

2212

1121

dz

dDj

dz

dDj

M

M

2212

1121

The microscopic explanations to the transportation process

Particle number passing through the considering area s with time dt along z axis

The average distance of last collision place far away from the considering cross-section is the mean free path:

sdtvndNdN 6

1

z

With the simple microscopic model, we can explain the macroscopic transportation processes.

vD

cv

v

v

3

13

13

1

/2

1

8

,VmV Cc

kTpnn

m

kTvmn

The Relationship Between Transport Coefficient and

Pressure 、 Temperature

pTmkD

tCkm

tkm

v

233

21

21

3

23

2

比

Relationships Between Transport Coefficients

vv cDc

D

Ultra-thin gasVaccum Gas

Transport phenomena are closely related to collisions between molecules.The quantitative characteristics of these phenomena therefore depend on the free path of the molecules.

For the ultra-thin gases, the pressure is very low

Heat transfer in gases at very low pressure

The mean free path of its molecules > the dimensions of the

vessel containing the gas. The molecules collide only with the walls of the vessel , When molecules of a gas collide with the hotter

surface ,they acquire energy correspond to the temperature of this surface.After rebounding from it

High Vacuum Gas

For high vacuum gas ,viscosity and coefficient of thermal conductivity are both proportion to pressure.

Thank You !