In order to apply the fitting procedure (28) together with (26) and (27), experimental values are converted into dimensionless form and the following values of model parameters are obtained: [alpha] = 0.999, [[tau].sub.x[alpha]] = 24.886, and [[tau].sub.f[alpha]] = 0.047, where the parameter [[alpha].sub.1] is taken to be equal, [[epsilon].sub.1] = 1, for simplicity reasons, without loss of generality, because the cross sectional area, the modulus of elasticity, and the length of the rod, which form the dimensionless group
[[epsilon].sub.1] (see [(6).sub.6]), are not explicitly included into the nondimensional numerical algorithm.
It was found that entropy generation increases with Hartman number, Brinkman number, and the dimensionless group
. Irreversibility due to the magnetic field, the conduction heat in the transverse direction, and the fluid friction increases by the increase of Hartman number, Brinkman number, and the dimensionless group
17 and 18 show the influences of dimensionless group
parameter Br[[OMEGA].sup.-1] and Reynolds number on entropy generation number respectively.
The derivation of a dimensionless group
called blade flexibility* is outlined and its effect on coating thickness and blade behavior is studied.
Each dimensionless group
is expressed as a natural logarithm of the dimensionless group
in order to keep the values of the dimensionless groups
from getting excessively large, and to facilitate the visualization of the surface fitting procedure described in the next subsection.
3 we have plotted the variation in dimensionless group
velocity U/[[beta].sub.2] with respect to scaled wave number k/s.
This procedure provides one dimensionless group
for each concept.
A dimensionless group
, as follows, is used to include a dependency upon surface tension:
He proposed that a dimensionless group
be developed to characterize the freezing range of the alloy, as compared to thermal conditions in the mold, in order to establish the validity of the models.
They concluded that the approach to temperature equilibrium would be expected to correlate with the dimensionless group
. (1) [Alpha] [Theta]/[r.sup.2] where [Alpha] is thermal diffusivity, [Theta] is the contact time and r is the distance over which heat is transferred.
One such chart exists for each value of the dimensionless group
M = (k/[lambda]).sup.1/2.Pr.sup.-1/6., where k and [lambda] are the thermal conductivities of the fin and fluid, respectively.
A new dimensionless group
, Q, the sheet bowability, was uncovered which governs how much a heated sheet will bow.