# MHD Stagnation Point Flow of Nanofluid on a Plate with Anisotropic Slip

## Abstract

**:**

## 1. Introduction

## 2. Mathematical Formulation

## 3. Result and Discussion

## 4. Conclusions

- An increase in the magnetic field M and slip parameter ${\lambda}_{1}$ causes an increase in the velocity profile and decrease in the boundary layer thickness near the stagnation point.
- It is observed that in the absence of magnetic parameter M the boundary layer thickness is larger than while M is present.
- The thermal boundary layer increases with an increase in the thermophoresis parameter ${N}_{t}$ and Brownian motion parameter ${N}_{b}$. It is observed that the thermal boundary layer is achieved earlier compared to the momentum boundary layer.
- It is observed that with the increase in ${S}_{c}$ and ${N}_{t}$ the nanoconcentration $\varphi $ decreases and vice versa.

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

$(u,v)$ | velocity Components |

$\nu $ | kinematic viscosity |

${N}_{1},{N}_{2}$ | slip coefficient |

T | temperature |

${\alpha}_{m}$ | thermal diffusivity |

C | volume of nano particles |

${(\rho C)}_{f}$ | heat capacity of fluid |

${D}_{B}$ | Brownian diffusion coefficient |

${D}_{T}$ | thermophoretic diffusion coefficient |

${\lambda}_{1},{\lambda}_{2}$ | slip parameters |

${N}_{t}$ | thermophoresis parameter |

${N}_{b}$ | browning motion parameter |

${C}_{f}$ | skin friction coefficient |

$N{u}_{x}$ | local Nusselt number |

$S{h}_{x}$ | Sherwood number |

$R{e}_{x}$ | local Reynolds number |

${S}_{c}$ | Schmidt number |

$Pr$ | prantle number |

$\gamma $ | ratio of slip parameters |

$\varphi $ | nano concentration |

M | magnetic parameter |

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**Figure 13.**${f}^{\prime}(\eta )$ solid curves and ${g}^{\prime}(\eta )$ dashed curves for $\gamma =\frac{{\lambda}_{2}}{{\lambda}_{1}}=0.5$. From top: ${\lambda}_{1}=10,1,0.1$.

**Figure 14.**$h(\eta )$ solid curves and $k(\eta )$ dashed curves for $\gamma =\frac{{\lambda}_{2}}{{\lambda}_{1}}=0.5$. From top: ${\lambda}_{1}=10,1,0.1$.

**Table 1.**Variation of Local Nusselt number $N{u}_{x}$ and Sherwood number $S{h}_{x}$ for different ${N}_{b}$ and ${P}_{r}$.

${\mathit{\lambda}}_{1}=1$, ${\mathit{\lambda}}_{2}=1,{\mathit{S}}_{\mathit{c}}=2,\mathit{M}=2,{\mathit{N}}_{\mathit{t}}=0.5$ | ||||||
---|---|---|---|---|---|---|

${\mathit{N}}_{\mathit{b}}=\mathbf{0.1}$ | ${\mathit{N}}_{\mathit{b}}=\mathbf{0.3}$ | ${\mathit{N}}_{\mathit{b}}=\mathbf{0.5}$ | ||||

${\mathit{P}}_{\mathit{r}}$ | ${\mathit{Nu}}_{\mathit{x}}$ | ${\mathit{Sh}}_{\mathit{x}}$ | ${\mathit{Nu}}_{\mathit{x}}$ | ${\mathit{Sh}}_{\mathit{x}}$ | ${\mathit{Nu}}_{\mathit{x}}$ | ${\mathit{Sh}}_{\mathit{x}}$ |

5.5 | 0.67084 | 1.47332 | 0.45477 | 1.58078 | 0.30641 | 1.77542 |

5.6 | 0.66527 | 1.47440 | 0.44833 | 1.58438 | 0.29987 | 1.78168 |

5.7 | 0.65976 | 1.47546 | 0.44197 | 1.58792 | 0.29346 | 1.78781 |

5.8 | 0.65431 | 1.47651 | 0.43570 | 1.59139 | 0.28716 | 1.79381 |

5.9 | 0.64890 | 1.47754 | 0.42950 | 1.59481 | 0.28098 | 1.79968 |

6.0 | 0.64355 | 1.47856 | 0.42343 | 1.59816 | 0.27492 | 1.80543 |

6.1 | 0.63826 | 1.47956 | 0.41742 | 1.60145 | 0.26897 | 1.81105 |

6.2 | 0.63302 | 1.48055 | 0.41150 | 1.60468 | 0.26314 | 1.81655 |

6.3 | 0.62784 | 1.48152 | 0.40566 | 1.60785 | 0.25742 | 1.82192 |

6.4 | 0.62272 | 1.48248 | 0.39992 | 1.61096 | 0.25181 | 1.82718 |

6.5 | 0.61766 | 1.48342 | 0.39425 | 1.61401 | 0.24631 | 1.83232 |

**Table 2.**Variation of Local Nusselt number $N{u}_{x}$ and Sherwood number $S{h}_{x}$ for different M and ${\lambda}_{1}$.

${\mathit{\lambda}}_{2}=1,$${\mathit{S}}_{\mathit{c}}=2,{\mathit{N}}_{\mathit{b}}=0.5,{\mathit{N}}_{\mathit{t}}=0.5,{\mathit{P}}_{\mathit{r}}=6.2$ | ||||||
---|---|---|---|---|---|---|

$\mathit{M}=\mathbf{2}$ | $\mathit{M}=\mathbf{4}$ | $\mathit{M}=\mathbf{6}$ | ||||

${\mathit{\lambda}}_{\mathbf{1}}$ | ${\mathit{Nu}}_{\mathit{x}}$ | ${\mathit{Sh}}_{\mathit{x}}$ | ${\mathit{Nu}}_{\mathit{x}}$ | ${\mathit{Sh}}_{\mathit{x}}$ | ${\mathit{Nu}}_{\mathit{x}}$ | ${\mathit{Sh}}_{\mathit{x}}$ |

0.5 | 0.25129 | 1.78860 | 0.27363 | 1.85616 | 0.28527 | 1.88559 |

0.6 | 0.25465 | 1.79657 | 0.27603 | 1.86128 | 0.28698 | 1.88892 |

0.7 | 0.25737 | 1.80301 | 0.27791 | 1.86529 | 0.28829 | 1.89145 |

0.8 | 0.25962 | 1.80831 | 0.27943 | 1.86850 | 0.28933 | 1.89350 |

0.9 | 0.26152 | 1.81276 | 0.28068 | 1.87114 | 0.29018 | 1.89513 |

1.0 | 0.26314 | 1.81655 | 0.28172 | 1.87335 | 0.29087 | 1.89648 |

1.1 | 0.26453 | 1.81980 | 0.28261 | 1.87522 | 0.29146 | 1.89762 |

1.2 | 0.26575 | 1.82263 | 0.28337 | 1.87683 | 0.29196 | 1.89859 |

1.3 | 0.26682 | 1.82511 | 0.28403 | 1.87822 | 0.29239 | 1.89942 |

1.4 | 0.26776 | 1.82731 | 0.28461 | 1.87944 | 0.29277 | 1.90015 |

1.5 | 0.26861 | 1.82926 | 0.28513 | 1.88052 | 0.29310 | 1.90079 |

${\mathit{\lambda}}_{2}=1$, ${\mathit{S}}_{\mathit{c}}=2,{\mathit{N}}_{\mathit{b}}=0.5,{\mathit{N}}_{\mathit{t}}=0.5,{\mathit{P}}_{\mathit{r}}=6.2$ | |||
---|---|---|---|

$\mathit{M}=\mathbf{2}$ | $\mathit{M}=\mathbf{4}$ | $\mathit{M}=\mathbf{6}$ | |

${\mathit{\lambda}}_{\mathbf{1}}$ | ${\mathit{C}}_{\mathit{f}}$ | ${\mathit{C}}_{\mathit{f}}$ | ${\mathit{C}}_{\mathit{f}}$ |

0.5 | 1.12177 | 1.36687 | 1.51354 |

0.6 | 1.00998 | 1.20285 | 1.31469 |

0.7 | 0.91823 | 1.07391 | 1..16200 |

0.8 | 0.84163 | 0.96991 | 1.04108 |

0.9 | 0.77675 | 0.88425 | 0.94294 |

1.0 | 0.72109 | 0.81248 | 0.86171 |

1.1 | 0.67283 | 0.75148 | 0.79336 |

1.2 | 0.63060 | 0.69899 | 0.73505 |

1.3 | 0.59334 | 0.65335 | 0.68473 |

1.4 | 0.56022 | 0.61330 | 0.64086 |

1.5 | 0.53059 | 0.57788 | 0.60227 |

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**MDPI and ACS Style**

Sadiq, M.A.
MHD Stagnation Point Flow of Nanofluid on a Plate with Anisotropic Slip. *Symmetry* **2019**, *11*, 132.
https://doi.org/10.3390/sym11020132

**AMA Style**

Sadiq MA.
MHD Stagnation Point Flow of Nanofluid on a Plate with Anisotropic Slip. *Symmetry*. 2019; 11(2):132.
https://doi.org/10.3390/sym11020132

**Chicago/Turabian Style**

Sadiq, Muhammad Adil.
2019. "MHD Stagnation Point Flow of Nanofluid on a Plate with Anisotropic Slip" *Symmetry* 11, no. 2: 132.
https://doi.org/10.3390/sym11020132