## 4 Solutions and Results
Lastly, silver had the \(m\) values within a single flow having maximum closure to the point that the difference is negligible. For Cu-water, it is observed that the temperature profiles against different values of \(m\) shows slow convergence compared to pure water. In case of Ag-water, the temperature profiles against \(m\) have low temperature values as compared to pure water and Cu-water.This evidence indicate that the temperature profiles \(\Theta(\lambda)\) with base fluid pure water, Cu-water and Ag-water can be controlled with the values of \(m\). Figure 6 represents the different parametric values of volume fraction \(\mu\) of the nanoparticles for distributed temperature profile \(\Theta(\lambda)\). It is observed that due to the presence of nanoparticle volume fraction, a uniform magnetic field is formed that accelerates the temperature of the fluid. Boundary thermal layers maintain its sensitivity with \(\mu\), because its higher values raise the values of thermal conductivity which comes with thermal diffusivity. However, thermal diffusivity decreases the temperature gradients making room for boundary thickness behavior. To summarize, it confirms the notion that with increase in \(\mu\), \(\Theta(\lambda)\) tends to increase the thickness of thermal boundary layer. Size, shape, and material of the volume fraction parameter help in the tuning of the spectral absorption obtained from sun light energy. Figure 7 presents the temperature profiles, \(\Theta(\lambda)\), for different values of the unsteady parameter \((\eta_{u})\) against base fluid pure-water, Cu-water, and Ag-water. \(\Theta(\lambda)\) of base fluid is observed to be decreasing with the increase in \(\eta_{u}\). The dominant role of \(\eta_{u}\) for the nanofluid flow fields is facilitated by the Prandtl number \(P_{R}\), present at the boundary layers. A decreasing trend is observed in the base fluid. However, it is also observed that  
\(\eta_{u}\) affected the base fluid differently as compared to the Cu-water and Ag-water. The flow and the basic acceleration are same for all the fluids, but for Cu-water the temperature of the fluid is decreasing slowly as compared to the pure water. Similarly, in case of Ag-water the unsteady parameter decelerates the temperatures of the fluid rapidly leading in the flow to be closely aligned. This implies that the \(\eta_{u}\) can control the temperature profiles for base fluid, Cu-water, and Ag-water. Figure 8 presents the temperature profiles \(\Theta(\lambda)\) with different heat source parameters \(\varepsilon\) for base fluid (pure-water), Cu-water, and Ag-water. The figures indicates that the temperature of base fluid decreases with the increase in \(\varepsilon\). It confirms that the temperature of the fluid is affected by the \(\varepsilon\) causing decrease in the fluid's temperature due to the boundary layer. It happens due to the influence of internal heat generation of the \(\Theta(\lambda)\) to be more evident than presence of base fluid. Moreover, heat sink present in the boundary layer tends to observe all the energy resulting into the temperature decrease in the base fluid. Hence, overall a decreasing trend has been observed for all graphs (pure-water, Cu-water, and Ag-water). The faster decrease in temperature is observed for Ag-Water as compared to pure water and Cu-water. Slow decreasing trend in temperature is illustrated by Cu-Water as compared to pure water and Ag-Water. This indicated that the \(\varepsilon\) can control the temperature profile for base fluid, Cu-water and Ag-water. Figure 9 presents the temperature profiles \(\Theta(\lambda)\) with different wedge angles \(\chi\) for base fluid (pure-water), Cu-water, and Ag-water. The figures indicates that the temperature of base fluid increases with the increase in \(\chi\). It confirms that the temperature of the fluid is affected by the \(\chi\) causing increase in the fluid's temperature due to the slow fluid movement.