# Heat Transfer Study of the Ferrofluid Flow in a Vertical Annular Cylindrical Duct under the Influence of a Transverse Magnetic Field

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## Abstract

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## 1. Introduction

_{3}O

_{4}–water ferrofluids [27,28]. However, the range of applications is not restricted to engineering; there have been reports on the use of blood as ferrofluid [29,30].

## 2. Mathematical Model

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

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**Figure 2.**Contour plots of the axial velocity ${\tilde{v}}_{\zeta}$ for various values of $\xi $ and $\mathrm{Gr}$ for $\varphi =0.1$.

**Figure 3.**Contour plots of the streamlines $\psi $ of transverse velocities ${\tilde{v}}_{r},{\tilde{v}}_{\theta}$ for various values of $\xi $ and $\mathrm{Gr}$ for $\varphi =0.1$.

**Figure 4.**Contour plots of the temperature $\tilde{T}$ for various values of $\xi $ and $\mathrm{Gr}$ for $\varphi =0.1$.

**Figure 5.**Effect of $\varphi $ and $\xi $ values on the average Nusselt number of the inner and outer cylinder for $\mathrm{Gr}={10}^{3}$.

**Figure 6.**Effect of $\mathrm{Gr}$, $\varphi $ and $\xi $ values on the axial pressure gradient ${\tilde{P}}_{c,\zeta}$.

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**MDPI and ACS Style**

Bakalis, P.A.; Papadopoulos, P.K.; Vafeas, P.
Heat Transfer Study of the Ferrofluid Flow in a Vertical Annular Cylindrical Duct under the Influence of a Transverse Magnetic Field. *Fluids* **2021**, *6*, 120.
https://doi.org/10.3390/fluids6030120

**AMA Style**

Bakalis PA, Papadopoulos PK, Vafeas P.
Heat Transfer Study of the Ferrofluid Flow in a Vertical Annular Cylindrical Duct under the Influence of a Transverse Magnetic Field. *Fluids*. 2021; 6(3):120.
https://doi.org/10.3390/fluids6030120

**Chicago/Turabian Style**

Bakalis, Panteleimon A., Polycarpos K. Papadopoulos, and Panayiotis Vafeas.
2021. "Heat Transfer Study of the Ferrofluid Flow in a Vertical Annular Cylindrical Duct under the Influence of a Transverse Magnetic Field" *Fluids* 6, no. 3: 120.
https://doi.org/10.3390/fluids6030120