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In this regime, the shrinking velocity is constant and the reaction takes place only in a thin layer at the solid surface.
It is interesting to note that the generation of vorticity for the shrinking velocity is reduced by an increase in the momentum slip at the surface (when (alpha_{1}>1)).
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Further, we note that for a shrinking sheet, the velocity in the case of a Cu-water nanofluid is larger than that of a clear fluid.
Figure 2 Effects of λ on velocity, when K = 1, Sc = 1, K s = 1, M = 0.5, f w = 1. Figure 2 shows the effects of both stretching and shrinking on the velocity profiles in the case of a Cu-water nanofluid.
Boundary mobilities (M) were measured from the boundary velocity of shrinking circular antiphase domains (APDs).
(iii) For λ < 0 (shrinking surface), the fluid velocity is initially negative, but it increases with η, and after a certain value of η, it becomes positive.
Figures 3(a) and 3(b) illustrate the effect of the magnetic parameter, nanoparticle volume fraction and stretching or shrinking parameters on the velocity profiles.
We note that for both stretching and shrinking sheets, the fluid velocity increases with λ and M. Furthermore, increasing the value of M also causes thinning of the boundary layer.
The 3 parameters can be thought of geometrically as follows: size is an up or down shift on the height axis for each individual growth curve; tempo is a corresponding left or right shift of the curve on the age axis, and velocity is a shrinking or stretching of the age axis, which affects the mean slope (ie, velocity) of the curve.
This model predicts that, apart from the very beginning and end of devolatilisation, there is an almost constant velocity for the shrinking core of raw coal.
The increasing values of nanoparticle volume fraction decrease the velocity components in stretching sheet and shrinking sheet lower branch solution and increase the velocity profile in shrinking sheet lower branch solution.
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