# Entropy Analysis for Hydromagnetic Darcy–Forchheimer Flow Subject to Soret and Dufour Effects

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## Abstract

**:**

## 1. Introduction

## 2. Formulation

## 3. Engineering Contents of Interest

#### 3.1. Nusselt Number

#### 3.2. Sherwood Number

## 4. Entropy

## 5. Solution Methodology

## 6. Graphical Results and Review

#### 6.1. Velocity

#### 6.2. Temperature

#### 6.3. Concentration

#### 6.4. Entropy Generation Rate

## 7. Closing Points

- The theermal field and velocity for the magnetic field had opposing trends.
- A decrease in velocity was noted for the Forchheimer number and suction variable.
- The velocity versus the porosity parameter was decreased.
- Similar behavior for the concentration and temperature against suction was noticed.
- The temperatures for the Eckert and Prandtl numbers were dissimilar.
- Radiation for the entropy and temperature had a similar role.
- The concentration decayed via larger approximation of the Soret number and reaction parameter.
- A decay in concentration against the Schmidt number held.
- Entropy generation enhancement against the Brinkman number and diffusion variable was noticed.
- The entropy rate was boosted with variation in the diffusion variable.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

$u,v$ | Velocity components (ms${}^{-1}$) | $x,y$ | Cartesian coordinates (m) |

t | Time (s) | ${v}_{0}>0$ | Suction velocity (ms${}^{-1}$) |

$\rho $ | Density (kgm${}^{-3}$) | $\sigma $ | Electrical conductivity (Sm${}^{-1}$) |

T | Temperature (K) | ${c}_{p}$ | Specific heat (Jkg${}^{-1}$K${}^{-1}$) |

${k}_{p}$ | Porous medium permeability (m${}^{2}$) | ${C}_{b}$ | Drag coefficient |

${T}_{w}$ | Wall temperature (K) | $\alpha $ | Thermal diffusivity (m${}^{2}$ s${}^{-1}$) |

k | Thermal conductivity (Wm${}^{-1}$K${}^{-1}$) | ${T}_{\infty}$ | Ambient temperature (K) |

${\sigma}^{\ast}$ | Stefan–Boltzman constant (Wm${}^{-2}$K${}^{-4}$) | ${K}_{T}$ | Thermal diffusion ratio |

${C}_{s}$ | Concentration susceptibility | ${k}^{\ast}$ | Mean absorption coefficient (cm${}^{-1}$) |

C | Concentration | ${k}_{r}$ | Reaction rate (s) |

${C}_{w}$ | Wall concentration | ${D}_{B}$ | Mass diffusivity (m${}^{2}$ s${}^{-1}$) |

${L}_{1}$ | Reference length (m) | ${C}_{\infty}$ | Ambient concentration |

${u}_{w}$ | Stretching velocity (ms${}^{-1}$) | a | Stretching rate constant (s${}^{-1}$) |

$N{u}_{x}$ | Nusselt number | ${q}_{w}$ | Heat flux (Wm${}^{2}$) |

$S{h}_{x}$ | Sherwood number | ${j}_{w}$ | Mass flux |

R | Molar gas constant (kgm${}^{2}$ s${}^{-2}$K${}^{-1}$mol${}^{-1}$) | M | Magnetic variable |

$\lambda $ | Porosity variable | $Fr$ | Forchheimer number |

S | Suction parameter | Pr | Prandtl number |

$Rd$ | Radiation variable | $Du$ | Dufour number |

$Ec$ | Eckert number | $\gamma $ | Reaction variable |

$Sr$ | Soret number | Re | Reynold number |

$Sc$ | Schmidt number | ${N}_{G}$ | Entropy rate |

${\alpha}_{1}$ | Temperature ratio variable | $Br$ | Brinkman number |

${\alpha}_{2}$ | Concentration ratio variable | L | Diffusion variable |

${T}_{m}$ | Mean fluid temperature (K) | ${B}_{0}$ | Magnetic field strength |

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**Table 1.**Comparison of Nusselt numbers with [44].

Pr | Bidin and Nazar [44] | Recent Outcomes |
---|---|---|

1.0 | 0.9547 | 0.954710 |

2.0 | 1.4714 | 1.471409 |

3.0 | 1.8961 | 1.896115 |

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**MDPI and ACS Style**

Khan, S.A.; Hayat, T.
Entropy Analysis for Hydromagnetic Darcy–Forchheimer Flow Subject to Soret and Dufour Effects. *Math. Comput. Appl.* **2022**, *27*, 80.
https://doi.org/10.3390/mca27050080

**AMA Style**

Khan SA, Hayat T.
Entropy Analysis for Hydromagnetic Darcy–Forchheimer Flow Subject to Soret and Dufour Effects. *Mathematical and Computational Applications*. 2022; 27(5):80.
https://doi.org/10.3390/mca27050080

**Chicago/Turabian Style**

Khan, Sohail A., and Tasawar Hayat.
2022. "Entropy Analysis for Hydromagnetic Darcy–Forchheimer Flow Subject to Soret and Dufour Effects" *Mathematical and Computational Applications* 27, no. 5: 80.
https://doi.org/10.3390/mca27050080