Transport PhenomenaFourier heat conduction law.

Q = - kt A dT

Δt dx

Transport PhenomenaFourier heat conduction law.

Q = - kt A dT

Δt dx

kt = thermal conductivity.

Transport PhenomenaFourier heat conduction law.

Q = - kt A dT

Δt dx

kt = thermal conductivity.

Heat Equation

∂T = K ∂2T

∂t ∂x2

Transport PhenomenaFourier heat conduction law.

Q = - kt A dT

Δt dx

kt = thermal conductivity.

Heat Equation

∂T = K ∂2T

∂t ∂x2

K = kt /ρc

Transport PhenomenaFourier heat conduction law.

Q = - kt A dT Δt dx

kt = thermal conductivity. Heat Equation ∂T = K ∂2T ∂t ∂x2

K = kt /ρc ρ= density, c =specific heat

Conductivity of an ideal gas

• Mean Free Path λ = l ≈ 1/4πr2 V/N

•

Conductivity of an ideal gas

• Mean Free Path λ = l ≈ 1/4πr2 V/N

• in FGT λ = 1/(√2 nσ)

Conductivity of an ideal gas

• Mean Free Path λ = l ≈ 1/4πr2 V/N

• in FGT λ = 1/(√2 nσ) where σ= 4πr2

• and n =N/V

Conductivity of an ideal gas

• Mean Free Path λ = l ≈ 1/4πr2 V/N

• in FGT λ = 1/(√2 nσ) where σ= 4πr2

• and n =N/V

• Thermal conductivity of an ideal gas is

kt = ½ CV l vave V

Conductivity of an ideal gas

• Mean Free Path λ = l ≈ 1/4πr2 V/N

• in FGT λ = 1/(√2 nσ) where σ= 4πr2

• and n =N/V

• Thermal conductivity of an ideal gas is

kt = ½ CV l vave vave ~ √T

V

Conductivity of an ideal gas

• Mean Free Path λ = l ≈ 1/4πr2 V/N• in FGT λ = 1/(√2 nσ) where σ= 4πr2

• and n =N/V• Thermal conductivity of an ideal gas is

kt = ½ CV l vave vave ~ √T V

where CV = f Nk = f P V 2 V 2T

Viscosity

• Viscosity transfers momentum in a fluid.

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

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 η = stress =

strain

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 η = stress = Fx / dux

strain A dz

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 η = stress = Fx / dux

strain A dz

η ~ √T and independent of P

Diffusion• Movement of particles is diffusion

•

Diffusion• Movement of particles is diffusion

• Jx = - D dn/dx (Fick’s Law)

•

Diffusion• Movement of particles is diffusion

• Jx = - D dn/dx (Fick’s Law)

• D is the diffusion coefficient n = N/V

Diffusion• Movement of particles is diffusion

• Jx = - D dn/dx (Fick’s 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.

Diffusion• Movement of particles is diffusion

• Jx = - D dn/dx (Fick’s 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/ΔT ~ dT/dx heat

l ~ n number

η ~ dux/dz velocity

Jx ~ dn/dx number