## 4 Solutions and Results
Quantitative illustration of the results for temperature profile for different thermophysical quantities is provided, in \[-C_{1}h_{0}(\lambda)h^{{}^{\prime\prime}}_{0}(\lambda)-h^{{}^{\prime\prime \prime}}_{0}(\lambda)-C_{1}h^{{}^{\prime\prime\prime}}_{0}(\lambda)+h^{{}^{ \prime\prime\prime}}_{1}(\lambda)=0. \tag{36}\]3 The velocity profile \(h^{\prime}(\lambda)\) and temperature profile \(\Theta(\lambda)\) are also analyzed graphically as presented below. Figure 3 shows the temperature profile \(\Theta(\lambda)\) for different values of magnetic parameter \((M)\) in the case of base fluid pure water, copper-water (Cu-water), and silver-water (Ag-water). The graphs indicate that the temperature of the fluid is progressively heated up with the increase in magnetic parameters strength due to the uniform convective radiation. Hence, the increase in the magnetic strength increases the rate at which the fluid temperature is accelerating. Effect of \(M\) is observed to lessen as it drifts away from the plate, hence the resistive type of force is formed known as the Lorentz force. This force implies that the magnetic field is opposing transport of the fluid resulting in acceleration of temperature profiles. Since temperature is bound to vanish at some point, the result meets the expectation that magnetic field exerts a force on the convection flow. All the results in Figure 3 show an increasing trend. However, the parameters are differently aligned for each nanofluid type. For pure water, it is observed that the graph has magnetic parameters loosely aligned together compared to others. For Cu-water, it is observed that the temperature profiles against different values of \(M\) shows slow convergence compared to pure water. It happens due to high thermal conductivity of copper. In case of Ag-water, the temperature profiles against \(M\) have low temperature values as compared to pure water and Cu-water. These findings clearly support the fact that magnetic parameters can help control the temperature profiles. Figure 4 shows the temperature profiles \(\Theta(\lambda)\) with different values of conductive radiation parameter \((N)\) for the base fluid pure-water, Cu-water, and Ag-water. Equations (2) and (3) presents that the radiative heat flux increases the overall thermal conductivity of the base fluid which also increases the radiative heat rate of transfer of the nanofluid. This evidence adds to the fact that fluid temperature would also increase and it highlights the significance of the \(N\). \(\Theta(\lambda)\) are observed to be increasing with the increase in conductive radiation parameter. The increasing trend was observed in all the three graphs with different parametric indications in the case of pure-water, Cu-water, and Ag-water. For pure water, the conductive radiation parameters are loosely aligned. For Cu-water, \(N\) are closely aligned than in pure water. For Cu-water, it is observed that the temperature profiles against different values of \(N\) shows slow convergence compared to pure water. In case of Ag-water, the temperature profiles against \(N\) have low temperature values as compared to pure water and Cu-water. These findings support that the temperature of nanofluid can be controlled with the \(N\). Figure 5 shows the temperature profiles with different stretching rate \(m\) values for the pure-water, Cu-water and Ag-water. The results demonstrate that the temperature increases with the increase in \(m\) values. This means that the temperature and the rate of transport process of the fluid is accelerated with the increase in the \(m\). Hence, an increasing  
trend is observed in all graphs with slight differences. The increasing trend for the case of pure water has the \(m\) values within a single flow and having minimum closure compared to Cu and Ag. Cu-water, on the other hand, has the \(m\) parameter values within a single flow yet has more closure as compared to the pure water due to their high conductivity towards temperature.