# MHD convective stagnation-point flow of nanofluids over a non-isothermal stretching sheet with induced magnetic field

## Abstract

This paper is concern with the investigation of buoyancy-driven hydromagnetic mixed convection stagnation-point flow of nanofluids over a stretching sheet in the presence of induced magnetic field. Three types of nanofluids namely, Cu–water, \(\hbox {Al}_2\hbox {O}_3\)–water, \(\hbox {TiO}_2\)–water are considered. The resulting system is solved numerically by a fifth-order Runge–Kutta–Fehlberg scheme with shooting technique. Numerical results are validated by comparing the present results with previously published results. Investigations predict that the effects of magnetic field is to increase induced magnetic field, whereas reverse effects is seen by increasing the volume fraction of the nanoparticles.

## Keywords

Nanofluids Stagnation-point flow Induced magnetic field Mixed convection Nanoparticles Stretching sheet## List of symbols

- \(C_f\)
Skin friction coefficient

- \(Gr\)
Grashof number

- \(\overrightarrow{H}\)
Magnetic induction vector

- \(H_0\)
Uniform magnetic field at infinity upstream

- \(H_1\)
Magnetic component at x-direction

- \(H_2\)
Magnetic component at y-direction

- \(\overrightarrow{J}\)
Current density

- \(L\)
Characteristic length

- \(M\)
Magnetic parameter

- \({Nu_x}\)
Local Nusselt number

- \(p\)
Fluid pressure

- \(P\)
Magnetohydrodynamic pressure

- \(Pr\)
Thermal Prandtl number

- \(Pr_m\)
Magnetic Prandtl number

- \({Re}\)
Reynolds number

- \(S\)
Suction/injection parameter

- \(T\)
Temperature of the fluid

- \(T_{\infty }\)
Free stream temperature

- \(T_w\)
Temperature at the wall

- \(u\)
Velocity component in

*x*-direction- \({u_w}\)
Stretching/shrinking sheet velocity

- \({u_e}\)
Free stream velocity of the nanofluid

- \(\overrightarrow{V}\)
Fluid velocity

- \(v\)
Velocity component in

*y*-direction- \(x,y\)
Direction along and perpendicular to the sheet, respectively

## Greek symbols

- \({\alpha _{nf}}\)
Effective thermal diffusivity of the nanofluid

- \({\alpha _f}\)
Fluid thermal diffusivity

- \(\alpha _1\)
Magnetic diffusivity

- \({\beta }\)
Coefficient of thermal expansion

- \({{\beta }_{nf}}\)
Thermal expansion of nanofluid

- \({\beta _f}\)
Thermal expansion coefficient of the fluid

- \({\beta _s}\)
Thermal expansion coefficient of the nanoparticles

- \({\phi } \)
Solid volume fraction of the nanoparticles

- \({\eta }\)
Similarity variable

- \({\varLambda }\)
Buoyancy parameter

- \(\mu _0\)
Magnetic permeability

- \({\mu _{nf}}\)
Effective dynamic viscosity of the nanofluid

- \({\mu _f}\)
Dynamic viscosity of the fluid

- \({\nu _f}\)
Kinematic viscosity of the fluid

- \({\rho _{nf}}\)
Effective density of the nanofluid

- \(\theta \)
Dimensionless temperature of the fluid

- \({\psi }\)
Stream function

- \(\sigma \)
Electric conductivity

- \(\kappa _{nf}\)
Effective thermal conductivity of the nanofluid

- \(\kappa _f\)
Thermal conductivity of the fluid

## Superscript

- \('\)
Differentiation with respect to

*y*

## Subscripts

- \({nf}\)
Nanofluid

- \({f}\)
Fluid

- \({s}\)
Solid

## Notes

### Acknowledgments

We are very thankful to the Editor and the referees for their valuable comments and suggestions, which have definitely improved the quality of the paper considerably.

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