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nano boundary-layer flows

The resulting profiles of the dimensionless velocity f ′ ηð Þ and the temperature distribution θ(η) for various values of the Deborah number β and γ when Pr¼0.7, λ¼1 and M¼1, are displayed in Figures 5 and 6, respectively. It is observed that the velocity and boundary layer thickness are increasing functions of the Deborah number β. It should be pointed out that β¼0 represents Newtonian fluid and β40 represents the Jeffrey fluid parameter. However, opposing phenomenon is observed for the temperature profile. The

Figure 4 Variations of -θ′(0) with λ at selected values of M and γ when Pr¼0.7 and β¼1.

Figure 1 Variations of f″(0) with γ at selected values of M and β when Pr¼0.7 and λ¼1.

Figure 2 Variations of -θ′(0) with γ at selected values of M and β when Pr¼0.7 and λ¼1.

Figure 3 Variations of f″(0) with λ at selected values of M and γ when Pr¼0.7 and β¼1.

effect of γ is found to decrease the velocity distribution and increase temperature distribution, respectively.

The effects of the MHD parameter M on the velocity f ′ ηð Þ and the temperature profiles θ(η) are shown in Figures 7 and 8, respectively. Velocity is found to decrease with the increase of M. The introduction of the transverse magnetic field will result in a restrictive force (Lorenz force), which tends to resist the motion of the fluid flow and hence, lead to the decrement of velocity. However, the opposite trend is observed in the increment of M, which results in the increment of temperature distribution across the boundary layer. The effect of the porous medium γ on flow velocity and temperature can also be garnered from the same figures. It is obvious that an increase in the porosity γ causes greater obstruction to the fluid flow, which culmi- nates in the decrement of velocity, whereas the opposite