Transportation Processes Of the Gases 2007/05/10

Three typical transportation processes of the gases  Viscosity phenomenon  Heat Transfer  Diffusion

Viscosity phenomenon Direction of flux ofmomentum

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:

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.

Momentum flux

Newton’s Law of Viscosity  The internal friction f:  Viscosity  Momentum flux

Heat Transfer  Heat conductivity  Convection  Heat 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 flow

 Quantity of heat  Heat flux  Coefficient of thermal conductivity

Fourior Law of Heat Conduction  Heat flux is proportional to the temperature gradient.

Convection Newton’s law of cooling: h is coefficient of heat convection

Heat Radiation  Wien’s displacement law:  Wien’s formula:  Rayleigh – jeans’ formula

Heat Radiation  Plank’s formula:

Rayleigh-Jeans ’ law Plank ’ s law Wien ’ s law

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:

 Inter-diffusion Inter-diffusion flux: Inter-diffusion coefficient:

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:

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

The Relationship Between Transport Coefficient and Pressure 、 Temperature

Relationships Between Transport Coefficients

Ultra-thin gas  Vaccum 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 !