# Interaction of Wu’s Slip Features in Bioconvection of Eyring Powell Nanoparticles with Activation Energy

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## Abstract

**:**

## 1. Introduction

## 2. Mathematical Modeling

## 3. Numerical Solution

^{−6}is obtained.

## 4. Validation of Solution

## 5. Analysis of Results

## 6. Concluding Remarks

- ❖
- A devaluate distribution of velocity has been observed for higher values of combine parameter, first order slip parameter and second order slip parameter.
- ❖
- The distribution of velocity attains maximum values with mixed convection parameter.
- ❖
- The nanoparticles temperature rises with thermophoresis parameter, Biot number and radiation parameter.
- ❖
- A decreasing variation in nanoparticles concentration has been figured out for mixed convection parameter and Brownian motion constant.
- ❖
- Both Peclet number and the bio-convection Lewis number retarded the motile microorganism distribution.
- ❖
- The observations presented here can be simulated to enhance the performances of various thermo-extrusion systems.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Table 1.**Comparison of solution for ${f}^{\u2033}\left(0\right)$ with various values of $Ha$ when $K=\lambda =Rb=Rc=\Gamma =\alpha =\beta =0$.

$\mathit{H}\mathit{a}$ | Wubshet Ibrahim [35] | Ali et al. [36] | Present Results |
---|---|---|---|

0.0 | 1.0000 | 1.0000 | 1.0000 |

1.0 | 1.4142 | 1.41421 | 1.4142 |

5.0 | 2.4495 | 2.44948 | 2.4496 |

**Table 2.**Variation of skin friction coefficient $-{f}^{\u2033}\left(0\right)$ for $Ha$, $K$, $\alpha $, $\beta $, $\Gamma $, $Rb$ and $Rc$.

$\mathit{H}\mathit{a}$ | $\mathit{K}$ | $\mathit{\alpha}$ | $\mathit{\beta}$ | $\mathsf{\Gamma}$ | $\mathit{R}\mathit{b}$ | $\mathit{R}\mathit{c}$ | $\mathbf{-}{\mathit{f}}^{\u2033}\mathbf{\left(}\mathbf{0}\mathbf{\right)}$ |
---|---|---|---|---|---|---|---|

0.1 0.4 0.7 | 0.3 | 1.0 | −1.0 | 0.1 | 0.1 | 0.1 | 0.3648 0.4027 0.4335 |

0.1 0.4 0.7 | 0.4297 0.4093 0.3924 | ||||||

2.0 3.0 4.0 | 0.2567 0.1959 1.1589 | ||||||

−2 −3 −4 | 0.2489 0.1872 0.1532 | ||||||

0.2 0.5 0.7 | 0.3646 0.3273 0.2941 | ||||||

0.2 0.3 0.4 | 0.3784 0.3816 0.3876 | ||||||

0.2 0.3 0.4 | 0.3804 0.3864 0.3927 |

**Table 3.**Variation in local Nusselt number $-{\theta}^{\prime}\left(0\right)$ for $Ha$, $Rb$, $Rc$, $\Gamma $, $\mathrm{Pr}$, $Bi$, $Rd$, $Nt$ and $Nb$.

$\mathit{H}\mathit{a}$ | $\mathit{R}\mathit{b}$ | $\mathit{R}\mathit{c}$ | $\mathsf{\Gamma}$ | $\mathbf{Pr}$ | $\mathit{B}\mathit{i}$ | $\mathit{R}\mathit{d}$ | $\mathit{N}\mathit{t}$ | $\mathit{N}\mathit{b}$ | $-{\mathit{\theta}}^{\prime}(0)$ |
---|---|---|---|---|---|---|---|---|---|

0.1 0.4 0.7 | 0.1 | 0.1 | 0.1 | 0.7 | 2.0 | 0.8 | 0.3 | 0.2 | 0.4022 0.3775 0.3558 |

0.2 0.5 0.8 | 0.3935 0.3933 0.3931 | ||||||||

0.2 0.5 0.8 | 0.3923 0.3885 0.3845 | ||||||||

0.2 0.5 0.8 | 0.4016 0.4211 0.4364 | ||||||||

1.0 3.0 5.0 | 0.2865 0.4637 0.5521 | ||||||||

1.0 1.5 1.5 | 0.3306 0.3640 0.3855 | ||||||||

0.1 0.5 0.8 | 0.4848 0.4262 0.3754 | ||||||||

0.1 0.4 0.7 | 0.4104 0.3852 0.3604 | ||||||||

0.1 0.3 0.4 | 0.5521 0.3935 0.3926 |

**Table 4.**Variation in local Sherwood number $-{\varphi}^{\prime}\left(0\right)$ for $\alpha $, $\beta $, $\Gamma $, $Le$, $Nb$, $Nt$ and $\mathrm{Pr}$.

$\mathit{\alpha}$ | $\mathit{\beta}$ | $\mathsf{\Gamma}$ | $\mathit{L}\mathit{e}$ | $\mathit{N}\mathit{b}$ | $\mathit{N}\mathit{t}$ | $\mathbf{Pr}$ | $-{\mathit{\varphi}}^{\prime}(0)$ |
---|---|---|---|---|---|---|---|

1.0 2.0 3.0 | −1 | 0.1 | 0.5 | 0.2 | 0.2 | 0.7 | 0.5348 0.5004 0.4766 |

0.1 | −2.0 −3.0 −4.0 | 0.5307 0.4950 0.4727 | |||||

0.2 0.5 0.8 | 0.6024 0.6316 0.6545 | ||||||

1.0 2.0 3.0 | 0.6069 0.5995 0.5954 | ||||||

0.2 0.3 0.5 | 0.2052 0.7703 1.2613 | ||||||

0.4 0.5 0.6 | 1.1806 0.2952 0.1687 | ||||||

2.0 3.0 4.0 | 0.4297 0.6956 0.8282 |

**Table 5.**Variation of motile density number $-{\chi}^{\prime}(0)$ for of $Pb$, $Lp$, $K$, $\alpha $, $\beta $, $\Gamma $, $\Omega $, $Rb$ and $Rc$.

$\mathit{P}\mathit{b}$ | $\mathit{L}\mathit{p}$ | $\mathit{K}$ | $\mathit{\alpha}$ | $\mathit{\beta}$ | $\mathsf{\Gamma}$ | $\mathsf{\Omega}$ | $\mathit{R}\mathit{b}$ | $\mathit{R}\mathit{c}$ | $-{\mathit{\chi}}^{\prime}(0)$ |
---|---|---|---|---|---|---|---|---|---|

0.2 0.6 0.8 | 1.02 | 0.2 | 1.0 | −1.0 | 0.1 | 0.1 | 0.1 | 0.1 | 0.6076 0.8312 1.0577 |

0.5 1.0 1.5 | 0.6115 0.7172 0.8105 | ||||||||

0.1 0.4 0.7 | 0.7759 0.8061 0.8307 | ||||||||

2.0 3.0 4.0 | 0.4911 0.4545 0.4297 | ||||||||

−1.0 −2.0 −3.0 | 0.4866 0.4488 0.4256 | ||||||||

0.2 0.5 0.8 | 0.5657 0.5990 0.6257 | ||||||||

0.2 0.6 1.0 | 0.8150 0.8330 0.8512 | ||||||||

0.2 0.5 0.8 | 0.5521 0.5518 0.5515 | ||||||||

0.2 0.5 0.8 | 0.5502 0.5438 0.5371 |

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**MDPI and ACS Style**

Alwatban, A.M.; Khan, S.U.; Waqas, H.; Tlili, I.
Interaction of Wu’s Slip Features in Bioconvection of Eyring Powell Nanoparticles with Activation Energy. *Processes* **2019**, *7*, 859.
https://doi.org/10.3390/pr7110859

**AMA Style**

Alwatban AM, Khan SU, Waqas H, Tlili I.
Interaction of Wu’s Slip Features in Bioconvection of Eyring Powell Nanoparticles with Activation Energy. *Processes*. 2019; 7(11):859.
https://doi.org/10.3390/pr7110859

**Chicago/Turabian Style**

Alwatban, Anas M., Sami Ullah Khan, Hassan Waqas, and Iskander Tlili.
2019. "Interaction of Wu’s Slip Features in Bioconvection of Eyring Powell Nanoparticles with Activation Energy" *Processes* 7, no. 11: 859.
https://doi.org/10.3390/pr7110859