9; Ec - Eckert number
; g - gravitational acceleration, m/[s.sup.2]; [Gr.sub.x] - Grashof number, [Gr.sub.x] = [g[beta][DELTA]T[x.sup.3]/[v.sup.2]]; L - plate length, m; M - dimensionless magnetic parameter; [Nu.sub.x] - local Nusselt number, [Nu.sub.x] = [hx/[lambda]]; P - Pressure, Pa; Pr - Prandtl number, Pr = [[nu]/[alpha]]; [Ra.sub.x] - Rayleigh number [Ra.sub.x] = [g[beta][DELTA]T[x.sup.3]/[nu][alpha]]; T - temperature, [degrees]C; [U.sub.c] - characteristic velocity; u, v - direction velocity, m/s; x, y - axial, normal coordinates
It is noticed that the heat transfer reduces with increasing Eckert number
, Ec, whereas the reverse trend is seen in the mass transfer.
Motsumi and Makinde  examined the effects of viscous dissipation parameter (i.e., Eckert number
), thermal diffusion, and thermal radiation on boundary layer flow of Cu-water and [Al.sub.2][O.sub.3]-water nanofluids over a moving flat plate.
The results have been computed for several values of the parameters namely magnetic parameter Ha, velocity ratio parameter , Prandtl number Pr, Eckert number
Ec and the non dimensional micropolar parameters C , C and C .
The influence of suction parameter, unsteadiness parameter, buoyancy parameter, and Eckert number
has been depicted graphically.
The [E.sub.c], the Eckert number
, is a measure of the dissipation effects in the flow.
These results are obtained to illustrate the influence of the magnetic field M, the radiation parameter R, the Prandtl number [P.sub.r] and the Eckert number
Figures 1 to 6 represent the velocity profiles u0 against y for various values of Prandtl number [P.sub.r], Hartmann number M, sink strength S, Grashoff number G and Eckert number
[E.sub.c] with [omega]=5, [epsilon]=0.2, [omega]t = [pi] to observe the non-Newtonian effects.
where [G.sub.r] is the Grashof number for heat transfer, [G.sub.m] is the Grashof number for mass transfer, E is the Eckert number
, M is the Hartmann number, P is the Prandtl number, [S.sub.c] is the Schmidt number, [S.sub.0] is the Soret number, [alpha] is the permeability parameter, [omega] is the frequency parameter and the other symbols have their usual meanings.
The effect of viscous dissipation is usually characterized by the Eckert number
and has played a very important role in geophysical flow and in nuclear engineering that was studied by Alim et al.
Numerical computations are performed for various values of the physical parameters involved, for example, the magnetic parameter M, the mass suction parameter S, the Prandtl number Pr, the Eckert number
Ec, and the heat source/sink parameter [lambda].
The nondimensional parameters appearing in (10)-(11) and defined in (12) are the magnetic parameter M, the mass concentration of dust particles I, the fluid particle interaction parameter [alpha], the local thermal buoyancy parameter [lambda], the local Grashof number [Gr.sub.x] , the local Reynolds number [Re.sub.x], the Prandtl number Pr, the Eckert number
Ec, the suction parameter S, the Biot number Bi, the heat absorption parameter [[beta].sub.h], the local fluid particle interaction parameters for heat transfer [c.sub.1] and [c.sub.3], and the local fluid particle interaction parameter for velocity [c.sub.2].