The

nondimensional forms of the boundary and interface conditions (2) become

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are

nondimensional shears at wall.

When drive voltage is applied with [V.sub.d] = 5 V, [V.sub.a] = 0.5 V, and [f.sub.d] = 3315 Hz, the phase plane portrait of (9) is illustrated in Figure 9, in which the arrow tells the progressing trend of the

nondimensional displacement and velocity along with time [18].

where [E.sub.yi] is

nondimensional annual average children trajectory exposure due to trajectory i (all year) and [C.sub.i] is the concentration of [PM.sub.10] ([micro]g [m.sup.-3]) in the cell, i; [t.sub.i] is the permanency time in cell (s); and [f.sub.i] is the wind direction frequency for one year, as discussed in Section 4.1.

In

nondimensional form [13], the transformation [bar.w] = [bar.W] - c becomes w = W - 1.

By introducing new

nondimensional parameters, (1) can be equivalently written in the following dimensionless form:

Modified (Solutal) Grashof number [G.sub.m] = g[beta]*([C.sub.w] - [C.sub.[infinity]])[[delta].sup.2]/v[U.sub.0]; Prandtl number [P.sub.r] = [rho]v[c.sub.p]/[kappa]; magnetic interaction parameter M = [sigma][[delta].sup.2][B.sup.2.sub.0]/[mu]; schmidt number [S.sub.c] = v/[D.sub.M]; the

nondimensional activation energy E = [E.sub.a]/k([T.sub.w] - [T.sub.[infinity]]); the dimensionless chemical reaction rate constant [[lambda].sup.2] = [k.sup.2.sub.r][[delta].sup.2]/v; radiation parameter N = 16[[sigma].sub.1][T.sup.3.sub.[infinity]]/3[kappa][k.sub.1].

where TIP is temperature in engine cylinder at the moment of fuel injection, K; [K.sub.Q] is

nondimensional heat transfer characteristic; [V.sub.IP] is cylinder volume at the moment of fuel injection, [m.sup.3]; [V.sub.C] is the volume of cylinder combustion chamber, [m.sup.3]; [n.sub.1] is compression ratio of polytrophic; CV is air specific heat (heat capacity), KJ/kg K; [[lambda].sub.0] is excess air ratio at an altitude H = 0 m; l0D is the quantity of air needed to completely burn one kilogram of the fuel, kg; [q.sub.T] is the quantity of heat required to vaporize and overheat a kilogram of fuel by injection into the compressed air in engine cylinder at temperature [T.sub.c].

The vertical and the horizontal axes are the

nondimensional sound speed a' and [omega][tau], respectively.

The left term of equation (6) and (7) are thus the

nondimensional meridional tangential and circumferential stresses, respectively.

Proceeding from the discussion of fluid properties and animal strategies, I offer a basic mode l that uses

nondimensional parameters to establish the dynamic similarity between animals in different flow environments.

[tau]* =

nondimensional parameter relating to time, dimensionless