Transport Phenomena

1. Transport Phenomena Fourier heat conduction law. Q = - kt A dT Δt dx

2. Transport Phenomena Fourier heat conduction law. Q = - kt A dT Δt dx kt = thermal conductivity.

3. Transport Phenomena Fourier heat conduction law. Q = - kt A dT Δt dx kt = thermal conductivity. Heat Equation ∂T = K ∂2T ∂t ∂x2

4. Transport Phenomena Fourier heat conduction law. Q = - kt A dT Δt dx kt = thermal conductivity. Heat Equation ∂T = K ∂2T ∂t ∂x2 K = kt /ρc

5. Transport Phenomena Fourier 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

6. Conductivity of an ideal gas • Mean Free Path λ = l ≈ 1/4πr2 V/N

7. Conductivity of an ideal gas • Mean Free Path λ = l ≈ 1/4πr2 V/N • in FGT  λ = 1/(√2 nσ)

8. 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

9. 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

10. 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

11. 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

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 η = 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 η = 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 η = stress = Fx / dux strain A dz η ~ √T and independent of P

17. Diffusion • Movement of particles is diffusion

18. Diffusion • Movement of particles is diffusion • Jx = - D dn/dx (Fick’s Law)

19. Diffusion • Movement of particles is diffusion • Jx = - D dn/dx (Fick’s Law) • D is the diffusion coefficient n = N/V

20. 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.

21. 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