# Effects MHD and Heat Generation on Mixed Convection Flow of Jeffrey Fluid in Microgravity Environment over an Inclined Stretching Sheet

## Abstract

**:**

## 1. Introduction

## 2. Mathematical Formulation

_{x}and the skin friction coefficient, C

_{f}, are defined as

## 3. Numerical Method

_{m}at the heat source. A very good arrangement is established among the results.

## 4. Results and Discussion

## 5. Conclusions

- The velocity profile is higher for dimensionless boundary layer thickness η = 0 then decreases significantly along the inclined stretching sheet to reach zero. In the absence of a magnetic field, the velocity profile is maximum and declines with the application of a magnetic field
- The temperature profile is higher for dimensionless boundary layer thickness η = 0 then decreases significantly along the inclined stretching sheet to reach zero. The thermal expansion coefficient and g-Jitter frequency have an insignificant effect on the temperature profile. Therefore, the thickness of the thermal boundary layer remains uniform in respect to the studied parameters.
- The dimensionless skin friction increases with both magnetic field and thermal expansion whereas it lessens with g-Jitter frequency. The g-Jitter frequency period reduces skin friction; this effect can be physically elucidated by the fact that g-Jitter generates flow creating buoyancy forces due to the effect of the vibration frequency distribution and density gradients which results to increase the acceleration of the fluid flow.
- The local Nusselt number increases with both the thermal expansion coefficient and g-Jitter frequency period. Whereas, it decreases with magnetic field. The Nusselt number at the inclined sheet surface with Jeffrey fluid and in microgravity environment lessens with magnetic field and augments with the thermal expansion coefficient and g-Jitter frequency period.

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Bi | Biot number |

C | Nanoparticle volume fraction |

C_{p} | Specific heat at constant pressure |

C_{f} | Local skin-friction coefficient |

Dn | Diffusivity of the microorganisms |

D_{B} | Brownian diffusion coefficient |

D_{T} | Thermophoretic diffusion coefficient of the microorganisms |

${f}^{\prime}$ | Dimensionless velocity |

g | Gravitational acceleration |

$G{r}_{{x}^{*}}$ | Local Grashof number |

h_{f} | Convective heat transfer coefficient |

k | Thermal conductivity |

Le | Lewis number |

Lb | Bioconvection Lewis number |

Nb | Brownian motion number |

Nr | Buoyancy ratio parameter |

Nt | Thermophoresis number |

$N{u}_{{x}^{*}}$ | Local Nusselt number |

n | Density of motile microorganisms |

Nn_{x} | Local density number |

Pe | Bioconvection Péclet number |

Pe_{x} | Local Péclet number |

Pr | Prandtl number, ν/α |

q_{w} | Wall heat flux |

r | Local radius of the truncated cone |

Ra_{x} | Modified Rayleigh number |

Rb | Bioconvection Rayleigh number |

Sh_{x} | Local Sherwood number |

T | Temperature |

u | Velocity component in the x-direction |

U_{r} | Reference velocity |

v | Velocity component in the y-direction |

w_{c} | Maximum cell swimming speed |

x | Streamwise coordinate |

x_{o} | Distance of the leading edge of truncated cone measured fromthe origin |

x* | Distance measured from the leading edge of the truncated cone, x-x_{o} |

y | Transverse coordinate |

α | Thermal diffusivity |

β | Coefficient of thermal expansion |

γ | Average volume of a microorganism |

σ | Motile parameter |

η | Pseudo-similarity variable |

θ | Dimensionless temperature |

ϕ | Dimensionless nanoparticle volume fraction |

ψ | Stream function |

χ | Dimensionless density of motile microorganisms |

ξ | Dimensionless distance |

μ | Dynamic viscosity |

ν | Kinematic viscosity |

Ω | Half angle of the truncated cone |

ρ_{f} | Density of the fluid |

ρ_{f∞} | Density of the base fluid |

ρ_{p} | Density of the particles |

ρ_{m∞} | Density of the microorganism |

(ρc)_{f} | Heat capacity of the fluid |

(ρc)_{p} | Effective heat capacity of the nanoparticle material |

ρ | Density |

ψ | Stream function |

w | Condition at the wall |

∞ | Condition at infinity |

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**Figure 1.**Variation of dimensionless velocity with (

**a**) magnetic field and g-Jitter frequency period and with (

**b**) thermal expansion coefficient and mixed convection parameter.

**Figure 2.**Variation of dimensionless temperature with (

**a**) magnetic field and g-Jitter frequency period and with (

**b**) thermal expansion coefficient and mixed convection parameter.

**Figure 3.**Variation of dimensionless skin friction with magnetic field and g-Jitter frequency period. (

**a**) Assisting flow; (

**b**) Opposing flow.

**Figure 4.**Variation of dimensionless heat transfer rate with several parameters in the presence of heat source for (

**a**) assisting flow and (

**b**) opposing flow.

Ra | Hayat et al. [5] | Current |
---|---|---|

1000 | 5.321 | 5.332 |

10,000 | 5.487 | 5.496 |

100,000 | 7.212 | 7.223 |

1,000,000 | 13.946 | 14.101 |

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**MDPI and ACS Style**

Tlili, I.
Effects MHD and Heat Generation on Mixed Convection Flow of Jeffrey Fluid in Microgravity Environment over an Inclined Stretching Sheet. *Symmetry* **2019**, *11*, 438.
https://doi.org/10.3390/sym11030438

**AMA Style**

Tlili I.
Effects MHD and Heat Generation on Mixed Convection Flow of Jeffrey Fluid in Microgravity Environment over an Inclined Stretching Sheet. *Symmetry*. 2019; 11(3):438.
https://doi.org/10.3390/sym11030438

**Chicago/Turabian Style**

Tlili, Iskander.
2019. "Effects MHD and Heat Generation on Mixed Convection Flow of Jeffrey Fluid in Microgravity Environment over an Inclined Stretching Sheet" *Symmetry* 11, no. 3: 438.
https://doi.org/10.3390/sym11030438