numerical results and
discussions
Numerical solutions to the dimensionless Eqs. (9) – (13) are obtained
using the Runge-Kutta-Gills method with the shooting technique and the
embedded parameters are varied to study their effects on the
dimensionless velocity \(\left(f^{{}^{\prime}}\right)\), temperature\(\left(\theta\right)\) and concentration \(\left(\phi\right)\)functions. Numerical results are obtained for the local skin-friction
coefficient \(f^{{}^{\prime\prime}}\left(0\right)\), local Nusselt number\(-\theta^{{}^{\prime}}\left(0\right)\), local Sherwood number\(-\phi^{{}^{\prime}}\left(0\right)\) and results displayed in Tables (1) –
(3).
Effects of various parameters on velocity
profiles
The influence of the flow parameters on velocity profiles are
illustrated in Figures (1) to (6). Figure 1 (a-b) shows that Dufour
number \(\left(D_{f}\right)\) has similar effect on the velocity
profile of both Blasius flow and Sakiadis flow. It is observed that the
velocity profile decreases with increase in \(D_{f}\) for both the
Blasius and the Sakiadis flows. As can be seen from Figure 2 (a-b),
Eckert number \(\left(\text{Ec}\right)\) has opposite effects on the
velocity profiles of Blasius and Sakiadis flows. For Blasius flow, the
velocity profile decreases with increase in Ec whereas, the
velocity profiles increase in Sakiadis flow with increase inEc. Effect of the local Grashof number\(\left(Gr_{x}\right)\) on the velocity profiles is shown in Figure 3
(a-b) and it is observed that the velocity profiles increase with
increase in the Grashof number \(\left(\text{Gr}\right)\) for both the
Blasius flow and the Sakiadis flow. In Figure 4 (a-b), we observed that
increase in the local magnetic field parameter \(\left(M_{x}\right)\)causes a decrease in the velocity profile for both the Blasius flow and
the Sakiadis flow due to the presence of Lorentz force which acts
against the flow and Schmidt number due to low molecular diffusivity.
Figure 5 (a-b) shows the influence of Prandtl number\(\left(\Pr\right)\) on the velocity profiles and it is observed that
the velocity profile increases with increase in \(\Pr\) for both the
Blasius flow and the Sakiadis flow. The influence of Soret number\(\left(\text{Sr}\right)\) is illustrated in Figure 6 (a-b). Soret
number \((Sr)\) has opposite effects on the Blasius and Sakiadis flows
such that velocity profile decreases with increase in Sr for
the Blasius flow but increase for the Sakiadis flow.