By N.N.Bogoliubov

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0 as y ! 33b) x is the stretching velocity; Tw ¼ T0 e2L is the temperature at the sheet; U0 x and T0 are the reference velocity and temperature, respectively; N¼ N1 eÀ 2L is the velocity slip factor, which changes with x; N1 is the initial value of velocity slip factor; x D ¼ D eÀ 2L is the thermal slip factor which also changes with x; and D is the initial 1 1 value of thermal slip factor. The no-slip case is recovered for N ¼ 0 ¼ D. V(x) >0 is the x velocity of suction and V(x) <0 is the velocity of blowing.

115] is also extended by considering non-Newtonian fluid obeying the Casson fluid model. The existence of dual solutions to nonlinear equations representing physical problems is important from theoretical as well as practical points of view. This gives the fundamental mechanism of the flow problem under investigation. We shall present here the dual solutions and its range of existence for stagnation-point flow of a nonNewtonian fluid over a stretching sheet. 1 Formulation of the mathematical problem The rheological equation of state for an isotropic and incompressible flow of a Casson fluid is given by ( À pﬃﬃﬃﬃﬃÁ 2 μB + py = 2π eij , π > π c , τij ¼ À pﬃﬃﬃﬃﬃﬃﬃÁ 2 μB + py = 2π c eij , π < π c : 36 Fluid Flow, Heat and Mass Transfer at Bodies of Different Shapes Here π ¼ eij eij and eij is the (i,j)-th component of the deformation rate, π is the product of the component of deformation rate with itself, π c is a critical value of this product based on the non-Newtonian model, μB is plastic dynamic viscosity of the nonNewtonian fluid, and py is the yield stress of the fluid.

It is found that skin-friction coefficient increases with M whereas it decreases in the presence of slip at the boundary. 4(b) displays the behavior of the skin-friction coefficient against the suction parameter S for a nonlinearly stretching sheet for two values of the slip parameter B. The skin-friction coefficient decreases with slip and increases with suction. 3 Effects of (a) nonlinear stretching parameter and (b) slip parameter on velocity profiles [22]. 4 Skin friction coefficient against (a) nonlinearly stretching and (b) suction parameter [22].

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