The main aim of the current study is to determine the effects of the temperature dependent viscosity and thermal conductivity on magnetohydrodynamics (MHD) flow of a non-Newtonian fluid over a nonlinear stretching sheet. The viscosity of the fluid depends on stratifications. Moreover, Powell–Eyring fluid is electrically conducted subject to a non-uniform applied magnetic field. Assume a small magnetic reynolds number and boundary layer approximation are applied in the mathematical formulation. Zero nano-particles mass flux condition to the sheet is considered. The governing model is transformed into the system of nonlinear Ordinary Differential Equation (ODE) system by using suitable transformations so-called similarity transformation. In order to calculate the solution of the problem, we use the higher order convergence method, so-called shooting method followed by Runge-Kutta Fehlberg (RK45) method. The impacts of different physical parameters on velocity, temperature and concentration profiles are analyzed and discussed. The parameters of engineering interest, i.e., skin fraction, Nusselt and Sherwood numbers are studied numerically as well. We concluded that the velocity profile decreases by increasing the values of S t , H and M. Also, we have analyzed the variation of temperature and concentration profiles for different physical parameters.

In this work, radioactive heat transfer analysis in non-Newtonian Ferrofluid over a stretchable sheet is considered. Furthermore, the effects of Arrhenius activation energy, magnetic dipole, velocity slip, and mass convective boundary condition are taken into account. The governing model is transformed into coupled ordinary equations (ODEs) via a similarity transformation. The solution of these resulting ODEs systems are computed by Runge–Kutta method (RK-45). The influence of beneficial physical parameters on momentum, pressure, energy, and concentration profiles are presented. The major finding of this study is the variation of the velocity field is reduced for the higher values of velocity slip parameters A 1 and β 2 and fluid material parameter H . The temperature field increases for higher values of Rd and decreases for Pr . Here we concluded that, the increasing or decreasing of the concentration, temperature, and velocity field for various physical parameters can be seen in the result and discussion section in detail. The physical quantities such as skin friction, Nusselt, and Sherwood numbers are examined.

In this work, the combined effects of velocity slip and convective heat boundary conditions on a hybrid nano-fluid over a nonlinear curved stretching surface were considered. Two kinds of fluids, namely, hybrid nano-fluid and aluminum oxide (Al2O3)- and iron oxide (Fe3O4)-based nano-fluid, were also taken into account. We transformed the governing model into a nonlinear system of ordinary differential equations (ODEs). For this we used the similarity transformation method. The solution of the transformed ODE system was computed via a higher-order numerical approximation scheme known as the shooting method with the Runge–Kutta method of order four (RK-4). It is noticed that the fluid velocity was reduced for the magnetic parameter, curvature parameter, and slip parameters, while the temperature declined with higher values of the magnetic parameter, Prandtl number, and convective heat transfer. Furthermore, the physical quantities of engineering interest, i.e., the behavior of the skin fraction and the Nusselt number, are presented. These behaviors are also illustrated graphically along with the numerical values in a comparison with previous work in numerical tabular form.

In this study, we considered heterogeneous and homogeneous chemical reactions in Eyring-Powell ferrofluid past a stretchable surface. In addition, thermal radiation and magnetic dipole impacts are also considered. The direct numerical solution of the governing model is complex. For this, we simplified the model into coupled ordinary differential equations (ODEs) with the dimensionless variables. Then, we determined the computational solution of the resulting transformed ODE system via the Runge-Kutta (RK) method. The impacts of interesting engineering parameters on temperature, velocity, and concatenation behaviors are presented through graphs. We concluded that the velocity field is reduced for higher values of ferromagnetic parameter β and fluid material parameters ß and H and arises the temperature field for higher values of thermal radiation R while the temperature field is reduced for Prandtl number Pr and dissipation parameter λ 1 . The obtained results of the current work are compared with published work, and we found that between them a good agreement can be seen in the table. The characteristics of skin fraction and Nusselt number are presented.