## 4 Results and Discussion
Thus, the temperature gradient increases, and the thermal boundary layer thickness decreases. As is well known, Figure 3 shows that the increasing values of M also cause shrinking of the surface region, and \(\lambda<0\) is bigger, which is capable of slowing down the separation of boundary layers, while the critical value \(\lambda_{c}\) becomes smaller. This is because the MHD effect acts in a way that is similar to the suction effect, \(S>0\), which controls the state of the boundary layer. Additional parameters in the problem of this case study are the heat sink/source and the thermal radiation effect, the purpose of which are to diversify the behavior of the MHD hybrid nanofluid on an exponentially shrinking surface. The parameter of \(\varepsilon\) and \(Rd\) only affect heat transfer or the Nusselt number, \(Re_{x}^{1/2}Nu_{x}\), because the local skin friction coefficient, \(Re_{x}^{1/2}C_{f}\), values are unchanged and it has been proved that they are not dependent on the effects of heat sink/source, \(\varepsilon\), and thermal radiation, \(Rd\). Figure 4a presents the reduction in \(Re_{x}^{1/2}Nu_{x}\) value based on increasing \(\varepsilon\). This is because when the heat source of hybrid nanofluid \(\varepsilon>0\), the heat flux is lower on the permeable exponentially shrinking surface, and it slows down the heat exchange process. In fact, when heat sink occurs \(\varepsilon<0\), the heat flux is higher, and speeds up the heat exchange process. As a result, with the increase in the temperature gradient, the thermal boundary layer thickness \(\delta_{\text{T}}\) becomes thin when the heat sink effect occurs \(\varepsilon<0\). An example of one application is that of a solar collector: when heat flux is higher, the heat exchange process is faster from the solar panel surface to the environment, which will increase the efficiency of the process of the solar collector. This is because the solar panel surface cools down quickly. In addition, Figure 4b shows the reduction in the \(Re_{x}^{1/2}Nu_{x}\) value over the permeable exponentially shrinking surface or region \(\lambda<0\) for the first and second solution when the thermal radiation parameter \(Rd\) is higher. In addition, the radiation effect is dominant over fluid flow. If this situation is examined in more detail, we find that it happens because inertial force resists the influence of the weak buoyancy force to overcome the temperature distribution of the MHD hybrid nanofluid flow along the permeable exponentially shrinking case. Consequently, the temperature of the hybrid nanofluid in the shrinking case is \(\lambda<0\) when the involvement of the higher thermal radiation effect decreases. Therefore, thermal boundary layer thickness increases because higher energy radiation is present in the flow velocity field. Subsequently, Figure 5a,b describes the value of \(Re_{x}^{1/2}C_{f}\) and \(Re_{x}^{1/2}Nu_{x}\) with changes in the types of hybrids and regular nanofluid. Numerical results are produced for the purpose of studying the behavior of MHD flow and heat transfer with the different types of nanofluid used and for identifying the best nanofluid types for heat transfer enhancement. Based on Figure 5a, hybrid nanofluid SWCNT/Cu-water shows the highest value of \(Re_{x}^{1/2}C_{f}\) compared with MWCNT/Cu-water and CNT-water. Regular nanofluid CNT-water, \(\varphi_{2}=0\), produces a lower value of \(Re_{x}^{1/2}C_{f}\). Hybrid nanofluid SWCNT/Cu-water causes shear stress to become higher because this nanofluid is more viscous and its momentum boundary layer thickness is thin compared with MWCNT/Cu-water and CNT-water. Moreover, Figure 5b shows that SWCNT/Cu-water has the highest value of \(Re_{x}^{1/2}Nu_{x}\) compared with MWCNT/Cu-water and CNT-water when in the region of \(\lambda<-1\). This is because nanoparticles and fluid have different thermophysical properties that affect the heat transfer process and temperature gradient on the permeable exponentially shrinking surface, which is in the region of \(\lambda<-1\).