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Added to that, the effects of nonlinear growth of boundary layer thickness are rarely included in these models.
Boundary layer thickness are increased by Clay swelling, and flow channel are blocked by clay off and migration, that the main reason of KW smaller than K∞.
However, compared with experimental results, the discrepancies in turbulence structure in the lowest part of the boundary layer (especially for z/δ < 0.2, δ is the boundary layer thickness) are observed.
The temperature and thermal boundary layer thickness are decreased corresponding to an increase in the values of the Prandtl number.
As a general result, it should be noted that for decreasing values of the fractional coefficient α, the fluid velocity and boundary layer thickness are decreasing.
It is observed that the velocity profile (f' eta )) and momentum boundary layer thickness are enhanced when (lambda > 0) (assisting flow), while opposite behavior is noted for (lambda < 0) (opposing flow).
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The fluid boundary layer thickness is rapidly reduced when either the frequency or the amplitude is increased.
The boundary layer thickness was obtained by smoke visualization and measured by image analysis in the range 2.4×104
The thermal gradients are high near the lower portion of left wall and near upper portion of right wall for Da⩾10−4 irrespective of φ and Pr and thus, thermal boundary layer thickness is small along those zones.
It was concluded that the boundary layer thickness was affected not only by the bulk flow parallel to the membrane surface, but also by the permeation flow perpendicular to the membrane surface.
The results show that the concentration boundary layer thickness is very thin and the previous three-layer model can be further simplified.
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