dimensionless group

dimensionless group

[də′men·chən·ləs ′grüp]
(physics)
Any combination of dimensional or dimensionless quantities possessing zero overall dimensions; an example is the Reynolds number.
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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, 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.
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.