Chapter 6 Scaling Laws in Miniaturization

More documents

Recommendations

Info

where V is the applied voltage ∝ l0• Electric field energy density:1 2 −2u = ε E ∝ l(6.20)20−1where the dielectric permittivity ε ∝ l , and the electric field E ∝ l .3• Example: For a system that carries its own power, the available power E av ∝ l .P −2⇒ ∝ l . (6.21)Eav- That is, a 10 times reduction of l leads to 100 times greater power lossdue to the resistance increase.- Disadvantage of scaling down of power supply systems.6.7 Scaling in Fluid Mechanics• In Fig. 6.7, moving the top plate to the right induces the motion of the fluid.- Newtonian flow:dθτ ∝ , ordtdθdVτ = µ = µdt dywhere τ: shear stress; μ: coefficient of viscosity ( 黏滯性 ); dθ/dt:strain rate; V: fluid velocity.-τThus, µ =R s(6.22)where R s =V max /h- Rate of volumetric fluid flow: Q =A s V ave (6.23)where A s : cross-sectional area for the flow; V ave : average velocity ofthe fluid.8
• Renolds number:ρVLRe =µwhere ρ: fluid density; V & L: characteristic velocity and length scales of theflow.- Re ∝ (inertial forces)/(viscous force)- Macro flows: high inertial forces → high Re → turbulence flow- Micro flows: high viscosity → low Re → laminar flowp.s.: (1) turbulence flow: fluctuating and agitated;(2) laminar flow: smooth and steady;(3) transition from laminar to turbulent: 10 3 ~10 5(from “Micromachines: A New Era in Mechanical Engineering,” by Iwao Fujimasa,Oxford University Press, 1996)• In Fig. 6.8, with the pressure drop ΔP over the length L, the rate of volumetricflow of the fluid is (Hagen-Poiseuille law),πa4 ∆PQ = (6.24)8µL9
Page 1 and 2: Chapter 6 Scaling Laws in Miniaturi
Page 3 and 4: ‣ An elephant and a flea have cel
Page 5 and 6: • Power Density P/V 0 : from Eq.
Page 7: nearly as favorably as electrostati
Page 11 and 12: Scaling in Effect of Heat Conductio

Chapter 6 Scaling Laws in Miniaturization

Create successful ePaper yourself

Delete template?

Save as template?