Micro/ Nanofluidics and Heat transfer

1. Micro/Nanofluidics and Heat transfer 27 Oct 2011 In Joo Hwang

2. Contents 1. The Knudsen number and flow regimes 2. Velocity slip and temperature jump 3. Gas conduction from the continuum to the free molecule regime

3. 1. The Knudsen number and flow regimes

4. The Knudsen number and flow regimes Lc : Characteristic dimension Λ : Mean free path Lc ~ Λ Not valid for continuum model Lc < Λ Ex) low pressure (rarefied gases) micro or nano channel

5. The Knudsen number and flow regimes Λ Kn ≡ ─ : Knudsen number L Kn : The ratio of the mean free path to the characteristic length Kn : determining the degree of deviation from the continuum assumption and method of calculation

6. The Knudsen number and flow regimes x Centerline 1 y 2 vx(y) T(y) yb 3 Tw Velocity profiles vx(y) Temperature profiles T(y)

7. 2. Velocity slip and temperature jump

8. Velocity slip and temperature jump Momentum accommodation coefficient For tangential components For normal components Specular reflection : Diffuse reflection : Thermal accommodation coefficient Monatomic molecules Kinetic energy ∝ K Often extended to polyatomic molecule

9. Velocity slip and temperature jump Velocity slip boundary condition thermal creep due to the temperature gradient Temperature jump boundary condition viscous dissipation caused by the slip velocity usually negligibly small

10. Velocity slip and temperature jump Poiseuille flow with heat transfer W 2H y Λ x vx Kn = ─ 2L W ≥ 2H velocity slip condition velocity distribution bulk velocity defining velocity slip ratio

11. Velocity slip and temperature jump energy equation temperature jump condition temperature – jump distance Nusselt number ,

12. 3. Gas conduction from the continuum to the free molecule regime

13. Gas conduction from the continuum to the free molecule regime Diffusion T1 Jump T1 T2 Free molecule T2 x x L L 0 0 Λ diffusion Kn = ─ << 1 Fourier’s law L Effective mean temperature Temperature distribution by integrating

14. Gas conduction from the continuum to the free molecule regime • collide with the wall > collide with each other • mean free path > actual distance • neglect the collisions between molecules • heat transfer by the molecules Λ Kn = ─ >> 1 L Thermal accommodation coefficients : Flux temperatures assumption Effective mean temperature in the free molecule regime Net heat flux heat flux∝ P independent of L

15. Thank You !