Transport Phenomena

1
Transport Phenomena

• Fourier heat conduction law.
• Q - kt A dT
• ?t dx

2
Transport Phenomena

• Fourier heat conduction law.
• Q - kt A dT
• ?t dx
• kt thermal conductivity.

3
Transport Phenomena

• Fourier heat conduction law.
• Q - kt A dT
• ?t dx
• kt thermal conductivity.
• Heat Equation
• ?T K ?2T
• ?t ?x2

4
Transport Phenomena

• Fourier heat conduction law.
• Q - kt A dT
• ?t dx
• kt thermal conductivity.
• Heat Equation
• ?T K ?2T
• ?t ?x2
• K kt /?c

5
Transport Phenomena

• Fourier heat conduction law.
• Q - kt A dT
• ?t dx
• kt thermal conductivity.
• Heat Equation
• ?T K ?2T
• ?t ?x2
• K kt /?c ? density, c specific heat

6
Conductivity of an ideal gas

• Mean Free Path ? l 1/4pr2 V/N

7
Conductivity of an ideal gas

• Mean Free Path ? l 1/4pr2 V/N
• in FGT ? ? 1/(v2 ns)

8
Conductivity of an ideal gas

• Mean Free Path ? l 1/4pr2 V/N
• in FGT ? ? 1/(v2 ns) where s 4pr2
• and n
  N/V

9
Conductivity of an ideal gas

• Mean Free Path ? l 1/4pr2 V/N
• in FGT ? ? 1/(v2 ns) where s 4pr2
• and n
  N/V
• Thermal conductivity of an ideal gas is
• kt ½ CV l vave V

10
Conductivity of an ideal gas

• Mean Free Path ? l 1/4pr2 V/N
• in FGT ? ? 1/(v2 ns) where s 4pr2
• and n
  N/V
• Thermal conductivity of an ideal gas is
• kt ½ CV l vave vave vT
• V

11
Conductivity of an ideal gas

• Mean Free Path ? l 1/4pr2 V/N
• in FGT ? ? 1/(v2 ns) where s 4pr2
• and n
  N/V
• Thermal conductivity of an ideal gas is
• kt ½ CV l vave vave vT
• V
• where CV f Nk f P
• V 2 V 2T

12
Viscosity

• Viscosity transfers momentum in a fluid.

13
Viscosity

• Viscosity transfers momentum in a fluid.
• Motion of one layer sliding on another, if slow
  and the motion is laminar the resistance to
  shearing is viscosity

14
Viscosity

• Viscosity transfers momentum in a fluid.
• Motion of one layer sliding on another, if slow
  and the motion is laminar the resistance to
  shearing is viscosity
• The equation for the coefficient is similar
• to a modulus ? stress
• strain

15
Viscosity

• Viscosity transfers momentum in a fluid.
• Motion of one layer sliding on another, if slow
  and the motion is laminar the resistance to
  shearing is viscosity
• The equation for the coefficient is similar
• to a modulus ? stress Fx / dux
• strain A
  dz

16
Viscosity

• Viscosity transfers momentum in a fluid.
• Motion of one layer sliding on another, if slow
  and the motion is laminar the resistance to
  shearing is viscosity
• The equation for the coefficient is similar
• to a modulus ? stress Fx / dux
• strain A
  dz
• ? vT and independent of P

17
Diffusion

• Movement of particles is diffusion

18
Diffusion

• Movement of particles is diffusion
• Jx - D dn/dx (Ficks Law)

19
Diffusion

• Movement of particles is diffusion
• Jx - D dn/dx (Ficks Law)
• D is the diffusion coefficient n N/V

20
Diffusion

• Movement of particles is diffusion
• Jx - D dn/dx (Ficks Law)
• D is the diffusion coefficient n N/V
• D ranges from 10-5 for CO to 10-11 for
  large molecules SI unit is m2 /s.

21
Diffusion

• Movement of particles is diffusion
• Jx - D dn/dx (Ficks Law)
• D is the diffusion coefficient n N/V
• D ranges from 10-5 for CO to 10-11 for
  large molecules SI unit is m2 /s.
• Summary Q/?T dT/dx heat
• l n
  number
• ? dux/dz
  velocity
• Jx dn/dx
  number