## 4 Results and Discussion
In all cases, we found that \(\theta(\eta)\) decreases and that becomes constant to zero at a certain point of \(\eta\). The temperature profile has the same value at \(\eta=0\) irrespective of the parameters' values. Moreover, as the thermal rate increases upon adding nanoparticles to the base fluid, we can see from the figures that \(\theta(\eta)\) becomes more of an HNF than a base fluid. Figure 7 shows the temperature profile \(\theta(\eta)\) for different values \(\Lambda\). We observe that \(\theta(\eta)\) decreases with the enhancement in \(\Lambda\). Panels (a)-(c) show the regimens of \(S\). In panel (a) for \(S=0\), there is no permeability, whereas in panel (b) suction \((S=1)\) and finally in panel (c) for injection case \((S=-1)\). We found that there is an achievement of enhancement of heat transfer upon using HNF and that Casson fluid will suppress the temperature distribution. Figure 8 shows the temperature profile as a function of \(\eta\) for different values of \(M\). We see that \(\theta(\eta)\) increases as \(M\) increases. Panels (a)-(c) show \(\theta\) for \(S=0\), \(S=1\), and \(S=-1\), respectively. We observe that HNF has much more thermal conductivity than the base fluid. Furthermore, we observe that as the value of S increases, the domain of the temperature distribution decreases. Figure 5: The axial velocity as a function of \(\eta\) for various values of \(S\), (**a**) for suction case and (**b**) for injection case. The other fixed parameters are: \(\Lambda=Da^{-1}=M=1\), \(\phi_{1}=0.1\), \(\phi_{2}=0.04\). Figure 6: _Cont._  
Figure 7: The temperature distribution \(\theta(\eta)\) as a function of \(\eta\) for various values of \(\Lambda\) and for three different regimes of S: (**a**) \(S=0\), (**b**) \(S=1\) and (**c**) \(S=-1\). The other fixed parameters are: \(M=Da^{-1}=N_{B}=1\), \(\phi_{1}=0.1\), \(\phi_{2}=0.04\). Figure 3:0 Cont. Figure 9 shows the temperature distribution \(\theta(\eta)\) for various values of the radiation parameter \(N_{R}\). We can observe that \(\theta(\eta)\) increases as the effect of radiation increases. Panels (a)-(c) show the profile for cases with no permeability, with suction and injection. We note that the domain of the temperature is larger in the case of injection and smaller in the case of no-permeability. Furthermore, by observing each plot of temperature distribution, the effect of radiation on the change of heat transfer rate is less than those of the magnetic field and Casson fluid, i.e., the difference in temperature distribution between base fluid and HNF is not that much more significant. Finally, the effect of various values of \(S\) on the temperature profile is shown in Figure 10 for suction and injection cases. \(\theta(\eta)\) decreases when as \(S\) increases, as shown in the figure. The domain of \(\theta(\eta)\) is larger in the case of injection than in suction. Figure 3:1 Cont. Figure 3:2 _Cont._  
Figure 3:3 The temperature distribution \(\theta(\eta)\) as a function of \(\eta\) for different values of \(N_{R}\) and for three different regimes of \(S\): (**a**) \(S=0\), (**b**) \(S=1\), and (**c**) \(S=-1\). The other fixed parameters are: \(M=\Lambda=Da^{-1}=N_{R}=1\), \(\phi_{1}=0.1\), \(\phi_{2}=0.04\).