# A Model for the Generalised Dispersion of Synovial Fluids on Nutritional Transport with Joint Impacts of Electric and Magnetic Field

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## Abstract

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## 1. Introduction

## 2. Formulation of the Problem

- A 2D, electrically conducting, viscous and incompressible synovial fluid is considered.
- Flow of fluid is laminar and steady.
- A constant magnetic field of strength ${B}_{0}$ is applied in the transverse direction.

## 3. Method of Solution

#### 3.1. Velocity Distribution

#### 3.2. Generalized Dispersion Model (GDM)

## 4. Results and Discussion

## 5. Conclusions

- Dispersion is accelerated by electromagnetic fields and other physical factors.
- In contrast to electromagnetic fields and other physical factors, the mean concentration drops as axial distance and time increase.
- Cells in the centre receive more nutrients than those in the periphery.
- The dispersion mechanism formula is used by orthopaedic surgeons to assess how well joints function.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

$(\widehat{u},\widehat{v})$ | Horizontal and normal components of the fluid velocity |

$(\widehat{x},\widehat{y})$ | Cartesian coordinates |

$\widehat{p}$ | Pressure |

$\tilde{u}$ | average velocity |

${B}_{0}$ | Magnetic induction |

k | Permeability of porous medium |

$\widehat{{E}_{x}}$ | x component of electric field |

$\widehat{C}$ | Species concentration |

$\widehat{{C}_{0}}$ | Initial species concentration |

$\widehat{D}$ | Diffusion coefficient |

${K}_{k}$ | Dispersion coefficient |

M | Hartmann number |

$We$ | Electric number |

$Re$ | Reynolds number |

$Pe$ | Peclet number |

$Da$ | Darcy number |

Greek Symbols | |

$\mu $ | Dynamic viscosity |

$\widehat{\eta}$ | Kinematic viscosity |

$\alpha $ | Slip parameter |

${\sigma}_{0}$ | Electrical conductivity |

$\sigma $ | Porous parameter |

$\u03f5$ | Viscoelastic parameter |

$\varphi $ | Concentration |

${\varphi}_{m}$ | Mean concentration |

${\rho}_{e}$ | Dimensionless charge density |

$\tau $ | Dimensionless time |

$\xi $ | Dimensionless axial distance |

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**MDPI and ACS Style**

Kumar, B.R.; Vijayakumar, R.; Rani, A.J.
A Model for the Generalised Dispersion of Synovial Fluids on Nutritional Transport with Joint Impacts of Electric and Magnetic Field. *Math. Comput. Appl.* **2023**, *28*, 3.
https://doi.org/10.3390/mca28010003

**AMA Style**

Kumar BR, Vijayakumar R, Rani AJ.
A Model for the Generalised Dispersion of Synovial Fluids on Nutritional Transport with Joint Impacts of Electric and Magnetic Field. *Mathematical and Computational Applications*. 2023; 28(1):3.
https://doi.org/10.3390/mca28010003

**Chicago/Turabian Style**

Kumar, B. Rushi, R. Vijayakumar, and A. Jancy Rani.
2023. "A Model for the Generalised Dispersion of Synovial Fluids on Nutritional Transport with Joint Impacts of Electric and Magnetic Field" *Mathematical and Computational Applications* 28, no. 1: 3.
https://doi.org/10.3390/mca28010003