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In this paper, He’s homotopy perturbation method (HPM) is used, which is an approximate analytical method for solving numerically the problem of Newtonian fluid flow past a porous exponentially stretching sheet with Joule heating and convective boundary condition. The major feature of HPM is that it does not need the small parameters in the equations and hence the determination of classical perturbation can be discarded. Due to the complete efficiency of the HPM, it becomes practically well suited for use in this field of study. Also, the obtained solutions for both the velocity and temperature field are graphically sketched. The results reveal that the proposed method is very effective, convenient, and quite accurate to systems of nonlinear differential equations. Results of this study shed light on the accuracy and efficiency of the HPM in solving these types of nonlinear boundary layer equations.

In this work, an approximate analytical solution for the problem of non-Newtonian Casson fluid flow past a porous exponentially stretching sheet with Joule heating and convective boundary condition is obtained using a relatively new technique; He’s homotopy perturbation (HPM). The major feature of HPM is that it does not need the small parameters in the equations, and hence the determination of classical perturbation can be discarded. Due to the complete efficiency of the HPM, it becomes practically well suited for use in this field of study. Also, the obtained solutions for both the velocity and temperature field are graphically sketched. The results reveal that the method is very effective, convenient and quite accurate to systems of nonlinear equations.

The analysis of Boundary Layer Flows (BLFs) is of huge significance due to its large-scale applications most likely in aerodynamics, manufacturing of vehicles front faces and many other advanced research areas. Therefore, this study is organized by exercising significant important engineering parameters like surface convection, radiative flux, MHD and thermal and mass diffusion. The developed model embedded the concrete effects of velocity slip, diffusion convection, thermal radiations, magnetic field, chemical reaction and thermo-mass gradients. Later, the numerical treatment is made via RK scheme and the model efficaciously is tackled with desired accuracy. Then the results are decorated over the region (wedge and sheet) and deeply examined. It is observed that slippery surface of wedge and sheet $(S_1=0.1,0.3,0.5,0.7,0.9)$ enlarges the fluid movement rapidly. The directed magnetic field ($M=0.0,0.1,0.2,0.3,0.4)$ controlled the fluid motion which can be beneficial from industrial view point. Further, temperature and concentration distributions upsurge by strengthening convective heat ($B_i=0.1,0.2,0.3,0.4,0.5)$ and diffusion convection processes. Moreover, skin friction and Nusselt number improved against the parameters under consideration.

This research is focused on the examination of an unsteady flow of an electromagnetic nanofluid close to a stagnation point over an expanded sheet kept horizontally. Buongiorno’s nanofluid model is revised with the combined influence of the externally applied electric and magnetic fluxes. Moreover, the underneath surface offers multiple slips into the nanofluid flow. The leading partial differential equations (PDE) are renovated to the nonlinear ordinary differential equations (ODE) with the assistance of similarity transformations. Thus, the outcomes are received numerically by using the RK-6 with Nachtsheim–Swigert shooting technique. The enlistment of the outcomes for the momentum, energy and concentration profiles along with the skin-friction coefficient $(C_{fx}^{\ast })$, Nusselt number $({\text{Nu}}_x^{\ast })$ and Sherwood number $({\text{Sh}}_x^{\ast })$ for several parametric values are presented in a graphical and tabular form and discussed in detail. The variation of streamlines with respect to the unsteadiness parameter is also recorded. Statistical inspection reveals that the flow parameters are highly correlated with the wall shear stress, wall heat and mass fluxes. Findings indicate that the escalation of electric flux tries to intensify the hydrodynamic boundary layer meanwhile the magnetic flux assists to stabilize the growth by reducing it for both the steady and unsteady flow patterns. Influence of velocity slip parameter $\xi$ from 0.0 to 1.5 causes the reduction in ${\text{Nu}}_x^{\ast }$ by 16.98% for steady flow while 60.27% for time-dependent flow case. Moreover, we expect that these theoretical findings are very much helpful for several engineering and industrial applications such as polymer sheet productions, manufacturing automobile machines, cooling microelectronic chips, etc.