Radiation and MHD Boundary Layer Stagnation-Point of Nanofluid Flow towards a Stretching Sheet Embedded in a Porous Medium: Analysis of Suction/Injection and Heat Generation/Absorption with Effect of the Slip Model

Abstract

In existence of the velocity slip model, suction/injection, and heat source/sink, the boundary layer flow near a stagnation-point over a heated stretching sheet in a porous medium saturated by a nanofluid, with effect of the thermal radiation and magnetic field, has been studied. The governing system of partial differential equations was transformed into a system of nonlinear ordinary equations using the appropriate similarity transforms. Then, the obtained system has been numerically solved by the Chebyshev pseudospectral differentiation matrix (ChPDM) approach. It was found that, at some special cases, the current results are in a very good agreement with those presented in the literature. In addition, the flow velocity, surface shear stress, temperature, and concentration are strongly influenced on applying the slip model, which is, therefore, extremely important to predict the flow characteristics accurately in the nanofluid mechanics. It was proved that this velocity slip condition is mandatory and should be taken into account in nanoscale research; otherwise, false results and a spurious physical sight are to be gained. Further, it was deduced that the influence of the stream velocity and shear stress reaches very rapidly the stable manner for both cases of the velocity ratio. However, when this ratio is equal to one, the skin friction coefficient, reduced Nusselt number, and reduced Sherwood number are constant and equal to zero, 0.721082, and 3.06155, respectively. Furthermore, it was proved that the reduced Nusselt number decreases with increase of Brownian motion and thermophoresis; has a very weak effect on increasing Lewis number; increases with increase of Prandtl number; and is higher in the cases of suction, velocity ratio > 1 and heat source in comparison with injection, velocity ratio < 1, and heat sink, respectively. Moreover, the reduced Sherwood number increases with increase of Brownian motion, thermophoresis, and Lewis number; decreases with increase of Prandtl number; is higher in the cases of suction and velocity ratio > 1 in comparison with injection and velocity ratio < 1, respectively; and is approximately the same in the heat source and heat sink cases. Finally, it was shown that the most effective region for radiation effect is[0,1].

MHD flow and heat transfer over a permeable stretching/shrinking sheet in a hybrid nanofluid with a convective boundary condition

“…Further, from equation ( 24) in equation ( 21), the resulting non-linear ordinary differential equation of f 1 (h ) subject to the boundary conditions ( 22) is solved by the method of Chebyshev pseudospectral differentiation matrix (ChPDM). For details of this technique, see Aly and Vajravelu (2014), Aly (2015) and Aly and Sayed (2017). Therefore, f(h ) and, then, Sr in equations ( 18) and ( 23), respectively, are to be evaluated.…”

Combined effects of Coriolis force and nanoparticle properties on the dynamics of gold–water nanofluid across nonuniform surface

“…The system of partial differential equations (8)(9)(10)(11)(12) with the boundary conditions (13,14) are rendered dimensionless and reduced to a system of ordinary differential equations with the boundary values by using the similarity variables…”

Flow and Heat Transfer Past a Stretching/Shrinking Sheet Using Modified Buongiorno Nanoliquid Model

“…where S is the constant mass flux parameter with S > 0 for suction and S < 0 for injection or withdrawal, respectively. Invoking the similarity variables (7), Equations ( 2)-( 4) along with the boundary conditions (5a) are transformed into the following ordinary (similarity) differential equations (see for e.g., Aly [35])…”