**4. Results**

A magneto-hydrodynamic nanofluid flow over an exponential stretching sheet with joule heating and viscous dissipation effects was modeled. The reduced modeled Equations (9)–(15) were solved by HAM. The graphical interpretation of the modeled problem is articulated in Figure 1. The impacts of important physical parameters such as *M*, *S*, Ω, *Sc*, *Nt*, *Nb* and Pr are discussed with the help of Figures 2–17.

**Figure 2.** Impact of *M* on *f*(η) when *k* = 1.

**Figure 3.** Impact of *M* on *g*(η) when *k* = 2.

**Figure 4.** Impact of *M* on *k*(η) when *k* = 1.

**Figure 5.** The effect of *M* on *s*(η) when *k* = 0.5.

**Figure 6.** Effect of *K* on *f*(η) while *M* = 0.3.

**Figure 7.** Effect of *K* on *g*(η) when *M* = 0.5.

**Figure 8.** Effect of *K* on *k*(η) for *M* = 0.3.

**Figure 9.** Impact of *K* on *s*(η) for *M* = 0.5.

**Figure 10.** Impact of Pr on θ (η) for *M* = 0.3, Ω = 0.4, *S* = 0.5, *Nt* = 0.8, *Sc* = 0.7, *Nb* = 0.6.

**Figure 11.** The effect of *Nb* on θ (η) when *M* = 0.3, Ω = 1, *S* = 0.5, Pr = 2, *Sc* = 0.7, *Nt* = 0.5.

**Figure 12.** The influence of *Nt* on θ (η) when *Sc* = 0.7, *S* = 0.5, Ω = 1, *Nb* = 0.6, *M* = 0.3, Pr = 0.6.

**Figure 13.** The impact of Ω on θ (η) while *Nt* = 0.8, Pr = 0.5, *S* = 0.5, *Nb* = 0.6, *Sc* = 0.7, *M* = 0.3.

**Figure 14.** The effect of *Nb* on θ (η) when *M* = 0.3, *Nt* = 0.7, *S* = 0.5, Pr = 1, *Sc* = 0.5, Ω = 1.

**Figure 15.** Impact of *Nt* on θ (η) for *M* = 0.3, *Nb* = 0.7, *S* = 0.5, Pr = 1, *Sc* = 0.5, Ω = 1.

**Figure 16.** Impact of *S* over θ (η), when *M* = 0.3, *Nb* = 0.6, *Nt* = 0.7, Pr = 2, *Sc* = 0.5, Ω = 1.

**Figure 17.** Impact of *Sc* on θ (η), when Ω = 1, Pr = 1, *S* = 0.5, *Nb* = 0.7, *Nt* = 0.6, *M* = 0.3.
