The results showed that, when the buoyancy is added, the flow separation diminishes gradually and at some value of the buoyancy parameter
it completely disappears.
In the above, [lambda] is an important dimensionless parameter signifying the relative importance of rotation rate to stretching rate, [gamma] is the buoyancy parameter
, [sigma] is the concentration buoyancy parameter
, Pr is the Prandtl number, and Sc the Schmidt number given by
It can be seen that as the buoyancy parameter
N increases, the temperature profiles decrease.
Figures 4 and 5 are depicted for positive values of the buoyancy parameter
Gr which corresponds to the cooling problem.
The influence of buoyancy parameter
Nr on the local temperature and nanoparticle profiles is displayed in Figure 2.
In the above equations, the parameters Pr, [N.sub.b], [N.sub.r], and [N.sub.t] are the Prandtl number, the Brownian motion parameter, the buoyancy parameter
, and the thermophoresis parameter, respectively, which are defined by
 studied the above mention heat transfer over a stretching surface with variable heat flux in micropolar fluids in the absence of the magnetic field (H = 0), the temperature buoyancy parameter
(G = 0), and the local heat generation parameter (Q = 0).
Results of velocity and temperature profiles investigated for laminar developing mixed convection in vertical channel with different buoyancy parameter
Gr/Re are shown in figures 3 and 6.
 investigated theoretically the problem of free convection boundary layer flow of nanofluids over a non-linear stretching sheet, incorporating the effects of buoyancy parameter
, the solutal buoyancy parameter
and the power law velocity parameter.
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].
), and [[lambda].sub.T] = g[[beta].sub.T]([T.sub.w] - [T.sub.[infinity]])x/([a.sup.2] [x.sup.(2m-1)]x) = [Gr.sub.x]/[Re.sup.2.sub.x] is the buoyancy parameter
, where [Gr.sub.x] = g[[beta].sub.T]([T.sub.w] - [T.sub.[infinity]])[x.sup.3]/[v.sup.2] is the Grashof number, [R.sub.ex] = [u.sub.e]x/v = [ax.sup.m+1]/v is the Reynolds number, and Pr = [mu][c.sub.P]/k is the Prandtl number.
The influence of suction parameter, unsteadiness parameter, buoyancy parameter
, and Eckert number has been depicted graphically.