## 4 Results and Discussion  
Steady two-dimensional nanofluid hydrothermal treatment between two parallel vertical permeable plates is studied considering induced magnetic field. The Runge-Kutta integration scheme is utilized to solve this problem. MAPLE code has been validated by comparison with a previously published paper [28]. Table 3 indicates good accuracy of present code. The influences of important parameters such as magnetic Prandtl number \(\left(Pm\right)\), Hartmann number \(\left(Ha\right)\), suction parameter \(\left(V_{0}\right)\) and nanoparticle volume fraction \(\left(\phi\right)\) on flow style are examined. Impact of \(\phi\) on induced magnetic field, current density, temperature and velocity distributions is shown in Figure 2. As volume fraction of nanofluid augments, nanofluid velocity and temperature are enhanced due to an increase in fluid motion by adding nanoparticles. Induced current density increases with an augment of \(\phi\) while the opposite behavior is shown for induced magnetic field. Influence of suction parameter on hydrothermal behavior is depicted in Figure 3. Velocity, temperature and induced current density decreases, with an augment of suction parameter while induced magnetic field enhances with rise of \(V_{0}\). Therefore, this parameter can be considered as control parameter for engineering designs. \begin{table}
\begin{tabular}{c c c c c c} \hline \(\mathbf{V_{0}}\) & **Pr** & \(\mathbf{\Pr_{m}}\) & \(\mathbf{Ha}\) & **[PERSON] and [PERSON] [21]** & **Present Work** \\ \hline
0.5 & 0.7 & 0.5 & 5 & 0.016 & 0.015 \\
0.75 & 0.7 & 0.5 & 5 & 0.011 & 0.011 \\
1 & 0.7 & 1 & 5 & 0.018 & 0.018 \\
1 & 0.015 & 0.5 & 0.5 & 2.695 & 2.700 \\ \hline \end{tabular}
\end{table} 
Table 3: Comparison of skin friction tension over the upper wall between the present results and previous work. \(H_{a}\), Hartmann number; \(V_{0}\), suction parameter; Pr, Prandtl number. Figure 3: _Cont._  
Figure 2: Effect of nanoparticle volume fraction on velocity (**U**); induced magnetic field (**B**); induced current density (**J**) and temperature field (\(\theta\)) distributions when \(V_{0}=1,\ Ha=5,\ Pm=1,\ \Pr=6.8\). Magnetic Prandtl number: _Pm_; nanoparticle volume fraction: \(\phi\). Figure 4 depicts the impacts of Lorentz forces on induced magnetic field, induced current density and velocity distributions. As Lorentz forces augments, the back flow appears and in turn velocity of nanofluid decreases. In addition, it can be seen that the maximum velocity point shifts to the hot wall. Induced magnetic field decreases with rise of magnetic field strength but induced current density is enhanced with the rise of Lorentz forces. Influence of \(Pm\) on induced magnetic field, induced current density and velocity profiles is depicted in Figure 5. Without the magnetic field, the shape of the velocity profiles is parabolic but in the existence of the magnetic field its shape changes to being flattened. The nanofluid motion and induced magnetic field reduces with an augment of \(Pm\). Induced current density rises with augment of \(Pm\). Figure 4: _Cont._  
Figure 3: Effect of suction parameter on velocity (**U**); induced magnetic field (**B**); induced current density (**J**) and induced temperature field (\(\theta\)) distributions when \(Ha=5,\ Pm=1,\ \phi=0.04,\ \mathrm{Pr}=6.8\). Figure 4: Effect of Hartmann number (Ha) on velocity (U); induced magnetic field (**B**) and induced current density (**J**) distributions when \(V_{0}=1,\ Pm=1,\ \phi=0.04,\ \Pr=6.8\). Figure 5: Effect of magnetic Prandtl number (Pm) on velocity (**U**); induced magnetic field (**B**) and induced current density (**J**) distributions when \(V_{0}=1,\ Ha=5,\ \phi=0.04,\ \Pr=6.8\). Influences of magnetic Prandtl number \((Pm)\), Hartmann number \((Ha)\), suction parameter \((V_{0})\) and nanoparticle volume fraction \((\phi)\) on skin friction coefficient are depicted in Figures 6 and 7.