By S. Friedlander, D. Serre
ISBN-10: 0444515569
ISBN-13: 9780444515568
This can be the fourth quantity in a sequence of survey articles masking many features of mathematical fluid dynamics, a necessary resource of open mathematical difficulties and interesting physics.
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Example text
Conversely, when σ = 1, the gas molecules transmit all their tangential momentum to the wall and the reflection is a diffuse reflection. 57) which is very close to the value of the mean free path λHS deduced from an HS model. 58) w which omits the second term on the right-hand side of Eq. 56). Chapter 2. Single-phase gas flow in microchannels 27 After non-dimensionalization with the characteristic length L, a reference velocity u0 and a reference temperature T0 , Eq. 59) w where us∗ = us /u0 , T ∗ = T /T0 , n∗ = n/L and s∗ = s/L.
1. According to the associated boundary conditions, they can be valid up to Knudsen numbers in the order of 10−1 or 1 (cf. Fig. 7). In the case of a plane flow in the (x, y) plane, Eq. 73) yields (1) σxx = µ δ1 (1) (1) σxy = σyx = µ (1) ∂uy ∂ux + δ2 ∂x ∂y ∂uy ∂ux + ∂y ∂x σyy = µ δ1 ∂uy ∂ux + δ2 ∂y ∂x with δ1 = 4/3 and δ2 = −2/3. 75) 32 Heat transfer and fluid flow in minichannels and microchannels As the Knudsen number becomes higher, additional higher-order terms from Eqs. 70) are required. 77) σB = σEQ + σEQ + σEQ qB = qEQ + qEQ + qEQ These new expressions for stress and heat-flux terms dramatically complicate the EHE systems.
Heat transfer in microchannels and thermally driven gas microflows are also described. They are particularly interesting for vacuum generation, using microsystems without moving parts. 1. Rarefaction and wall effects in microflows In microfluidics, theoretical knowledge for gas flows is currently more advanced than that for liquid flows (Colin, 2004). Concerning the gases, the issues are actually more clearly identified: the main micro-effect that results from shrinking down the devices size is rarefaction.
Handbook of mathematical fluid dynamics. / Vol. 1 by S. Friedlander, D. Serre
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