# Magnetohydrodynamic Nanoliquid Thin Film Sprayed on a Stretching Cylinder with Heat Transfer
## 5 Discussion
### Temperature Profile  
The thermal investigation has a prominent application in the cooling of the cylinder. The thin film parameter \(\beta_{1}\) has a special role in the temperature distribution. The non-dimensional temperature \(\theta(\zeta)\) is high at the surface and it is growing small along the transversely distance within the thermal boundary layer. The dimensional temperature \(\theta(\zeta)\) decelerates for greater quantities of film thickness parameter \(\beta_{1}\) which is obvious in Figure 8. Transfer of heat is improved for the thinning of the nanofluid film. But in the present case, it is depreciating. The reason is that with the thickness of the fluid film the mass of the fluid is greater which exhaust the amount of temperature. Heat penetrates in the fluid as a result the environment is cool down. Thick film fluid needs more heat as compared to the thin film fluid. The volume fraction parameter \(\phi\) is displayed in Figure 9. No sensitivity occurs in temperature for greater quantities of the volume fraction parameter \(\phi\). Figure 10 predicts that the temperature \(\theta(\zeta)\) depreciates for the big quantities of Reynolds number \(Re\). It is due to the fact that greater Reynolds number signifies that inertial forces exist as the overcoming agents in contrasting the the viscous forces. These inertial forces are very powerful and due to these forces the particles (atoms and molecules) of the fluid remains tightly. Too much heat energy is required in order to break down the bonds between atoms and molecules of the fluids. Due to these forces the boiling point of fluids increase. Figure 11 indicates that temperature distribution enhances with various values of magnetic field parameter \(M\). Due to the application of magnetic the Lorentz force is generated which increases the temperature of the fluid. This force supports and favors the temperature. Since the magnetic field is imposed perpendicularly so with the increasing magnetic field effect the fluid is controlled and bounded. Figure 12 witnesses the influence of Prandtl number \(Pr\) describing that \(\theta(\zeta)\) decreases with larger values of \(Pr\) since for the larger quantities of \(Pr\) the thermal boundary layer decreases which displays that effective cooling is achieved quickly for nanofluid. The influence is even more clear for high Prandtl number because the motion layer size is comparatively small. For the greater quantities of \(Pr\) the liquid keeps low thermal conductivity which causes thinner thermal boundary layer resulting in the enhancement of the rate of transfer of heat at the surface. Prandtl number defines the ratio of momentum diffusivity to thermal diffusivity. Those liquids which have minimum Prandtl number have good thermal conductivity consequently, possess thick boundary layer structures for diffusing heat.  
Figure 8: Non-dimensional temperature \(\theta(\zeta)\) sketch for \(h=-0.10\), \(M=2.00\), \(Re=5.00\), \(\phi=0.04\), \(Pr=6.80\) and various values of \(\beta_{1}\) (CuO-H\({}_{2}\)O).  
Figure 11: Non-dimensional temperature \(\theta(\zeta)\) sketch for \(h=-2.50\), \(\beta_{1}=1.70\), \(\phi=0.04\), \(M=0.10\), \(Pr=6.80\) and greater quantities of \(M\) (CuO-H\({}_{2}\)O).  
Figure 10: Non-dimensional temperature \(\theta(\zeta)\) sketch for \(h=-1.10\), \(\beta_{1}=1.10\), \(\phi=0.04\), \(M=0.10\), \(Pr=6.80\) and greater quantities of \(Re\) (CuO-H\({}_{2}\)O).  
Figure 9: Non-dimensional temperature \(\theta(\zeta)\) sketch for \(h=-1.10\), \(\beta_{1}=1.70\), \(M=0.10\), \(Re=0.70\), \(Pr=6.80\) and various values of \(\phi\) (CuO-H\({}_{2}\)O).