## 4 Results and Discussions
Figure 14 designates for the distribution of the concentration profile for various values of (Lewis number \(Le\)). The results shows that decreases in concentration profile is noticed for large valves of \(Le\). This is because of the fact that there is a reduction in the nano-particle volume fraction boundary layer thickness with the raise in the Lewis number. Figure 15 indicates the variation of concentration profile for the chemical reaction parameter \(Kr\). The result has shown that concentration profile reduces by enhancing the values of \(Kr\), a decreases in concentration is observed with increasing values of \(Kr\). Figure 16 designates the temperature profile for the unlike values of the (Brownian motion parameters \(Nb\)). The result has shown that temperature distribution reduces by incrementing values of \(Nb\). Figure 17 represents the distribution of the temperature profile for the various values of the \(Nt\). The result has shown that temperature profile decreases by increasing values of thermophoresis \(Nt\). The impact of (wall thickness parameter \(\alpha\)) on velocity gradient is plotted in Figure 2.0 It is found that the velocity profile is increases for higher values of \(\alpha\). Figure 19 represents the effects of and fitted rate constant \(n\) on the nano-particle volume fraction. The antiparticles volume fraction profile decreases with an increasing value of fitted rate constant \(n\) which leads to considerable thinning with in the boundary layer. Figure 20 is plotted to represent the distribution of concentration profile for (temperature difference parameter \(\delta\)). The result has shown that concentration profile is reduces by improving values of \(\delta\). Figure 21 is the distribution of temperature profile for different values of (variable thermal conductivity \(\varepsilon\)). The temperature profile increases by increasing values of \(\varepsilon\). Figure 22 is plotted for the distinction of the temperature profile for the different values thermal slip parameter \(Lt\) The result has shown that the temperature profile increases by increasing value of \(Lt\). Figure 23 is plotted for the impact of thickness parameter \(d\) on velocity gradient. For steps up values of thickness parameter \(d\) the velocity distribution enhances. Next we calculate the numerical variation for different physical parameters through tables. Tables 2 and 3 are calculated to show the numerical aspects of skin fraction, Nusselt and Sherwood numbers for unlike values of different physical parameter. Tables 2 and 3 shows that the skin friction behavior increases for unlike values of \(M\), \(m\), \(\beta\), \(St\) and \(\lambda\). Skin friction steps down by the incrementing values of \(H\), \(d\) (is shown in Tables 2 and 3). \(Nu_{x}\) increases with an increase in \(d\), \(Lt\), \(M\), \(Pr\) and \(St\). \(Nu_{x}\) steps down by increasing values of \(\varepsilon\), \(m\) and \(R\). Sherwood number \(Sh_{x}\) enhancement by steps up values of \(\xi\), and \(Kr\). Sherwood numbers \(Sh_{x}\) reduces by enlarging values of \(M\)\(\delta\), \(Pr\), \(E\)\(m\) and \(Lc\). Figure 2.1 Influence of \(m\) on \(f^{\prime}\). Figure 2.2 Variation of \(\phi\) for distinct values of \(Le\). Figure 2.3 Variation of \(\theta\). Figure 2.4 Variation of \(\phi\) for distinct values of \(Nb\). Figure 2.5 Variation of \(\phi\) for distinct values of \(Nt\). Figure 2.6 Variation of \(\phi\) for distinct values of \(E\). Figure 2.7 The behaviour of \(Nb\) on \(\theta\). Figure 2.8 Variation of \(\phi\) for distinct values of \(Le\). Figure 2.9 Variation of \(f^{\prime}\). Figure 4:0 Variation of \(\phi\) for distinct values of \(n\). Figure 4:1 Influence of \(Nt\) on \(\theta\). Figure 4:2 Variation of \(\theta\) for distinct values of \(\varepsilon\). Figure 4:3 Variation of momentum profile for distinct values of \(d\).