# Effect of Magnetic Baffles and Magnetic Nanofluid on Thermo-Hydraulic Characteristics of Dimple Mini Channel for Thermal Energy Applications

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

_{3}O

_{4}magnetic nanofluid is used as a working fluid. The Reynolds number (Re) is varied from 150 to 210 and the magnetic field intensities range from 1200 G to 2000 G. Finite-volume based commercial computational fluid dynamics (CFD) solver ANSYS-Fluent 18.1 was used for the numerical simulations. A laminar viscous model is used with pressure-velocity coupling along with second-order upwind discretization and QUICK scheme for discretizing the momentum and energy equations. The results show that there is an increase of 3.53%, 10.77%, and 25.39% in the Nusselt numbers when the magnetic fields of 1200 G, 1500 G and 2000 G, respectively, are applied at x = 15 mm, as compared to the flow without a magnetic field when the pitch = 10 mm. These values change to 1.51%, 6.14% and 18.47% for a pitch = 5 mm and 0.85%, 4.33%, and 15.25% for a pitch = 2.5 mm, when compared to the flow without a magnetic field in the respective geometries. When the two sources are placed at x = 7.5 mm and 15 mm, there is an increase of 4.52%, 13.93%, and 33.08% in the Nusselt numbers when magnetic fields of 1200 G, 1500 G, and 2000 G are applied when the pitch = 10 mm. The increment changed to 1.82%, 8.16%, and 22.31% for a pitch = 5 mm and 1.01%, 5.96%, and 21.38% for a pitch = 2.5 mm. This clearly shows that the two sources at the front have a higher increment in the Nusselt numbers compared to one source, due to higher turbulence. In addition, there is a decrease in the pressure drop of 10.82%, 16.778%, and 26.75% when magnetic fields of 1200 G, 1500 G, and 2000 G, respectively, are applied at x = 15 mm, as compared to flow without magnetic field when the pitch = 10 mm. These values change to 2.46%, 4.98%, and 8.54% for a pitch = 5 mm and 1.62%, 3.52%, and 4.78% for a pitch = 2.5 mm, when compared to flow without magnetic field in the respective geometries. When two sources are placed at x = 7.5 mm and 15 mm, there is an decrease of 19.02%, 31.3%, and 50.34% in the pressure drop when the magnetic fields of 1200 G, 1500 G and 2000 G are applied when the pitch = 10 mm. These values change to 4.18%, 9.52%, and 16.52% for a pitch = 5 mm and 3.08%, 6.88%, and 14.88% for a pitch = 2.5 mm. Hence, with the increase in the magnetic field, there is a decrease in pressure drop for both the cases and the pitches. This trend is valid only at lower magnetic field strength, because the decrease in the pressure drop dominates over the increase in pressure drop due to turbulence.

## 1. Introduction

_{3}O

_{4}), spinel-type ferrites, and so on [13,14,15,16,17].

_{2}O

_{4}(M = Fe and Co) nanofluid under the influence of a magnetic field and compared the results when no magnetic field was applied. It was found that the thermal conductivity increases with the increase in the magnetic field intensity as well as the nanoparticle concentration. Qi et al. [19] investigated the thermal and flow performance of the magnetic nanofluid under the influence of magnetic field for cooling application for different (i) mass concentrations of nanoparticles, (ii) magnetic field intensities, and (iii) angles of magnetic field. It was found that the increase in the magnetic field intensity and the angle of the surface temperature of the CPU decreased significantly. Mousavi et al. [20] carried out a numerical investigation for a sinusoidal tube in a circular tube heat exchanger under the influence of a magnetic field and validated their results with the experimental investigation. Zhang and Zhang [21] experimentally revealed the heat transfer and pressure drop in a heat exchanger tube under the influence of a magnetic nanofluid and a magnetic field. It was found that the said configuration was good for a low Re application, while at a higher Res, the system did not perform well. Sundar et al. [22] investigated the heat transmission properties of Fe

_{3}O

_{4}magnetic nanofluids in a circular tube without the use of an external magnetic field and reported a 36% enhancement in the heat transfer coefficient. Yu et al. [23] studied the thermal conductivity of kerosene-based Fe

_{3}O

_{4}nanofluids and Oleic acid and discovered a 34.0% increase for a 1% volume fraction nanofluid. Wen and Ding [24] conducted research with Al

_{2}O

_{3}nanofluid and discovered that the convective heat transfer enhancement increases with Re and volume concentration in the laminar flow area. Using alternating magnetic fields, Goharkhan et al. [25] investigated the thermal hydraulic performance of magnetic nanofluids. The convective heat transfer coefficient is directly related to the Re and volume percentage of the magnetic nanofluids, according to the findings. The impact of a constant magnetic field on the laminar convective heat transfer and the pressure drop of magnetite nanofluid in a vertical tube was investigated by Azizian et al. [26], and found a significant increase in the local heat transfer coefficient, despite just a 7.5% pressure reduction. The heat transfer coefficient can be lowered when a uniform magnetic field perpendicular to the flow is supplied, according to Li and Xuan [27]. Other important investigations comprise the work of Safaei et al., Alrashed et al., Togun et al., and Safaei et al. [28,29,30,31].

## 2. Computational Methodology

#### 2.1. Geometry and Grid Generation

_{3}O

_{4}/water ferrofluid was considered as the coolant and fluid flown into the channel at a uniform inlet velocity and temperature. A rectangular grid, as shown in Figure 1b, was chosen for the flow domain, having 80 computational nodes in vertical direction and 320 nodes in the horizontal direction, with bias of factor 4 near the hot wall to effectively capture the velocity and thermal gradient. The magnets were placed at two different locations x = 7.5 mm and 15.0 mm, and the magnetic force acted in an upwards direction, as shown in Figure 1, and three different dimple pitches were also studied (2.5 mm, 5.0 mm, and 10.0 mm).

#### 2.2. Governing Equations

- Continuity equation:

- Momentum equations:

- Energy equation:

#### 2.3. Boundary Conditions

#### 2.4. Thermo-Hydraulic Parameters

#### 2.5. CFD Solver Settings

## 3. Grid Independence Test and Validation

## 4. Results and Discussion

#### 4.1. Variation of Nusselt Number with Re

#### 4.2. Variation of Nusselt Number along the Length of the Channel

#### 4.3. Variation of the Pressure Drop across the Channel with Re

#### 4.4. Comparison

## 5. Conclusions

- The magnetic field is used to create a virtual baffle along with artificial roughness (dimple turbulator) which helps to create turbulence and flow mixing regions, hence increasing the heat transfer;
- The height of the ‘baffle’ is to be varied by varying the magnetic field. Higher Nusselt numbers were obtained when the magnet was placed more downstream as compared to upstream;
- The pressure drop due to the virtual baffle is less than the physical baffle, because of the absence of a horizontal backwards force in the case of the magnetic field;
- There is an increase of 3.53%, 10.77%, and 25.39% in the Nusselt numbers when the magnetic fields of 1200 G, 1500 G, and 2000 G, respectively, are applied at x = 15 mm, as compared to the flow without a magnetic field when the pitch = 10 mm;
- When two sources are placed at x = 7.5 mm and 15 mm, there is an increase of 4.52%, 13.93%, and 33.08% in the Nusselt numbers when the magnetic fields of 1200 G, 1500 G and 2000 G are applied and when the pitch = 10 mm.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Symbols | |

B | Magnetic field intensity (Gauss) |

C_{p} | Specific heat (J/kg/K) |

D | Hydraulic diameter (m) |

F_{k} | Magnetic body force (N) |

H | Channel height (m), magnetic field intensity |

h | Heat transfer coefficient (W/m^{2} K) |

k | Boltzmann constant |

K | Thermal conductivity (W/m^{−1} K^{−1}) |

L | 2D channel length (m) |

M | Magnetization (A m^{−1}) |

Nu | Nusselt number |

P | Pressure drop (Pa) |

q | Heat flux (W/m^{2}) |

Re | Reynolds number |

T | Temperature (K) |

u | Horizontal velocity (m/s) |

v | Vertical velocity (m/s) |

V | Velocity (m/s) |

x, y | Directions |

Greek Symbols | |

ϕ | Volume fraction |

χ_{m} | Magnetic susceptibility |

χ_{o} | Differential magnetic Susceptibility (0.06) |

ρ | Density (kg/m^{3}) |

μ | Dynamic viscosity (N s/m^{2}) |

μ_{0} | Permeability of free space (4π × 10^{−7} N/A^{2}) |

β | Fraction of the liquid volume (k^{−1}) |

τ | Wall shear stress (Pa) |

δ | Thickness (m) |

Subscripts | |

b | Bulk |

f | Fluid |

nf | Nanofluid |

np | Nanoparticle |

in | Inlet |

w | Wall |

## References

- Bhattacharyya, S.; Vishwakarma, D.K.; Srinivasan, A.; Soni, M.K.; Goel, V.; Sharifpur, M.; Ahmadi, M.H.; Issakhov, A.; Meyer, J. Thermal performance enhancement in heat exchangers using active and passive techniques: A detailed review. J. Therm. Anal. Calorim.
**2022**, 147, 9229–9281. [Google Scholar] [CrossRef] - Bhattacharyya, S.; Vishwakarma, D.K.; Chakraborty, S.; Roy, R.; Issakhov, A.; Sharifpur, M. Turbulent flow heat transfer through a circular tube with novel hybrid grooved tape inserts: Thermohydraulic analysis and prediction by applying machine learning model. Sustainability
**2021**, 13, 3068. [Google Scholar] [CrossRef] - Bhattacharyya, S.; Vishwakarma, D.K.; Goel, V.; Chamoli, S.; Issakhov, A.; Meyer, J.P. Thermodynamics and heat transfer study of a circular tube embedded with novel perforated angular-cut alternate segmental baffles. J. Therm. Anal. Calorim.
**2021**, 145, 1445–1465. [Google Scholar] [CrossRef] - Bhattacharyya, S.; Vishwakarma, D.K.; Soni, M.K. Heat transfer and pressure drop in transitional flow: A short review. In Proceedings of the 3rd International Conference on Advances in Mechanical Engineering and its Interdisciplinary Areas (ICAMEI 2021), Kolaghat, India, 5–7 January 2021; Volume 1080, p. 012050. [Google Scholar] [CrossRef]
- Bhattacharyya, S.; Vishwakarma, D.K.; Roy, S.; Biswas, R.; Ardekani, M.M. Applications of heat transfer enhancement techniques: A state-of-the-art review. In Inverse Heat Conduction Heat Exchange; IntechOpen: London, UK, 2020. [Google Scholar] [CrossRef]
- Bhattacharyya, S.; Vishwakarma, D.K.; Roy, S.; Dey, K.; Benim, A.C.; Bennacer, R.; Paul, A.R.; Huan, Z. Computational investigation on heat transfer augmentation of a circular tube with novel hybrid ribs. E3S Web Conf.
**2021**, 321, 04012. [Google Scholar] [CrossRef] - Kumar, A.; Dey, K.; Bhattacharyya, S.; Paul, A.R.; Benim, A.C.; Vishwakarma, D.K.; Huan, Z. Augmented thermal performance in a non-uniform heat flux circular tube with twisted tape insert using hybrid nanofluid. E3S Web Conf.
**2021**, 321, 04009. [Google Scholar] [CrossRef] - Souayeh, B.; Bhattacharyya, S.; Hdhiri, N.; Alam, M.W. Heat and fluid flow analysis and ann-based prediction of a novel spring corrugated tape. Sustainability
**2021**, 13, 3023. [Google Scholar] [CrossRef] - Ibrahim, M.; Saeed, T.; Bani, F.R.; Sedeh, S.N.; Chu, Y.M.; Toghraie, D. Two-phase analysis of heat transfer and entropy generation of water-based magnetite nanofluid flow in a circular microtube with twisted porous blocks under a uniform magnetic field. Powder Technol.
**2021**, 384, 522–541. [Google Scholar] [CrossRef] - Lee, A.; Jeon, Y.; Chinnasamy, V.; Cho, H. Investigation of forced convective heat transfer with magnetic field effect on water/ethylene glycol-cobalt zinc ferrite nanofluid. Int. Commun. Heat Mass Transf.
**2021**, 128, 105647. [Google Scholar] [CrossRef] - Mehryan, S.A.M.; Izadi, M.; Namazian, Z.; Chamkha, A.J. Natural convection of multi-walled carbon nanotube–Fe
_{3}O_{4}/water magnetic hybrid nanofluid flowing in porous medium considering the impacts of magnetic field-dependent viscosity. J. Therm. Anal. Calorim.**2019**, 138, 1541–1555. [Google Scholar] [CrossRef] - Niknejadi, M.; Afrand, M.; Karimipour, A.; Shahsavar, A.; Isfahani, A.H.M. An experimental study on the cooling efficiency of magnetite–water nanofluid in a twisted tube exposed to a rotating magnetic field. J. Therm. Anal. Calorim.
**2021**, 146, 1893–1909. [Google Scholar] [CrossRef] - Rawa, M.J.H.; Abu-Hamdeh, N.H.; Golmohammadzadeh, A.; Goldanlou, A.S. An investigation on effects of blade angle and magnetic field on flow and heat transfer of non-Newtonian nanofluids: A numerical simulation. Int. Commun. Heat Mass Transf.
**2021**, 120, 105074. [Google Scholar] [CrossRef] - Alghamdi, M.; Wakif, A.; Thumma, T.; Khan, U.; Baleanu, D.; Rasool, G. Significance of variability in magnetic field strength and heat source on the radiative-convective motion of sodium alginate-based nanofluid within a Darcy-Brinkman porous structure bounded vertically by an irregular slender surface. Case Stud. Therm. Eng.
**2021**, 28, 101428. [Google Scholar] [CrossRef] - Biswas, N.; Mondal, M.K.; Mandal, D.K.; Manna, N.K.; Subba, R.; Gorla, R.; Chamkha, A.J. A narrative loom of hybrid nanofluid-filled wavy walled tilted porous enclosure imposing a partially active magnetic field. Int. J. Mech. Sci.
**2021**, 271, 107028. [Google Scholar] [CrossRef] - Bezaatpour, M.; Goharkhah, M. A magnetic vortex generator for simultaneous heat transfer enhancement and pressure drop reduction in a mini channel. Heat Transf. Asian Res.
**2020**, 49, 1192–1213. [Google Scholar] [CrossRef] - Bezaatpour, M.; Goharkhah, M. Effect of magnetic field on the hydrodynamic and heat transfer of magnetite ferrofluid flow in a porous fin heat sink. J. Magn. Magn. Mater.
**2019**, 476, 506–515. [Google Scholar] [CrossRef] - Karimi, A.; Afghahi, S.S.S.; Shariatmadar, H.; Ashjaee, M. Experimental investigation on thermal conductivity of MFe
_{2}O_{4}(M = Fe and Co) magnetic nanofluids under influence of magnetic field. Thermochim. Acta**2014**, 598, 59–67. [Google Scholar] [CrossRef] - Qi, C.; Tang, J.; Fan, F.; Yan, Y. Effects of magnetic field on thermo-hydraulic behaviors of magnetic nanofluids in CPU cooling system. Appl. Therm. Eng.
**2020**, 179, 115717. [Google Scholar] [CrossRef] - Mousavi, S.V.; Sheikholeslami, M.; Goriji Bandpy, M.; Gerdroodbary, M.B. The Influence of magnetic field on heat transfer of magnetic nanofluid in a sinusoidal double pipe heat exchanger. Chem. Eng. Res. Des.
**2016**, 113, 112–124. [Google Scholar] [CrossRef] - Zhang, X.; Zhang, Y. Experimental study on enhanced heat transfer and flow performance of magnetic nanofluids under alternating magnetic field. Int. J. Therm. Sci.
**2021**, 164, 106897. [Google Scholar] [CrossRef] - Sundar, L.S.; Naik, M.T.; Sharma, K.V.; Singh, M.K.; Reddy, T.C.S. Experimental investigation of forced convection heat transfer and friction factor in a tube with Fe3O4 magnetic nanofluid. Exp. Therm. Fluid Sci.
**2012**, 37, 65–71. [Google Scholar] [CrossRef] - Yu, W.; Xie, H.; Chen, L.; Li, Y. Enhancement of thermal conductivity of kerosene-based Fe3O4 nanofluids prepared via phase-transfer method. Colloids Surf. A Physicochem. Eng. Asp.
**2010**, 355, 109–113. [Google Scholar] [CrossRef] - Wen, D.; Ding, Y. Experimental investigation into convective heat transfer of nanofluids at the entrance region under laminar flow conditions. Int. J. Heat Mass Transf.
**2004**, 47, 5181–5188. [Google Scholar] [CrossRef] - Goharkhah, M.; Ashjaee, M.; Shahabadi, M. Experimental investigation on convective heat transfer and hydrodynamic characteristics of magnetite nanofluid under the influence of an alternating magnetic field. Int. J. Therm. Sci.
**2016**, 99, 113–124. [Google Scholar] [CrossRef] - Azizian, R.; Doroodchi, E.; McKrell, T.; Buongiorno, J.; Hu, L.W.; Moghtaderi, B. Effect of magnetic field on laminar convective heat transfer of magnetite nanofluids. Int. J. Heat Mass Transf.
**2014**, 68, 94–109. [Google Scholar] [CrossRef] - Li, Q.; Xuan, Y. Experimental investigation on heat transfer characteristics of magnetic fluid flow around a fine wire under the influence of an external magnetic field. Exp. Therm. Fluid Sci.
**2009**, 33, 591–596. [Google Scholar] [CrossRef] - Safaei, M.R.; Abdelghany Elkotb, M.; Alsharif, A.M.; Mansir, I.B.; Alamri, S.; Tirth, V.; Goodarzi, M. An innovative design of a high strength and low weight sudden micro expansion by considering a nanofluid: Electronic cooling application. Case Stud. Therm. Eng.
**2021**, 28, 101637. [Google Scholar] [CrossRef] - Alrashed, A.A.A.A.; Akbari, O.A.; Heydari, A.; Toghraie, D.; Zarringhalam, M.; Shabani, G.A.S.; Seifi, A.R.; Goodarzi, M. The numerical modeling of water/FMWCNT nanofluid flow and heat transfer in a backward-facing contracting channel. Phys. B Condens. Matter
**2018**, 537, 176–183. [Google Scholar] [CrossRef] - Togun, H.; Safaei, M.R.; Sadri, R.; Kazi, S.N.; Badarudin, A.; Hooman, K.; Sadeghinezhad, E. Numerical simulation of laminar to turbulent nanofluid flow and heat transfer over a backward-facing step. Appl. Math. Comput.
**2014**, 239, 153–170. [Google Scholar] [CrossRef] - Safaei, M.R.; Togun, H.; Vafai, K.; Kazi, S.N.; Badarudin, A. Investigation of heat transfer enhancement in a forward-facing contracting channel using FMWCNT nanofluids. Numer. Heat Transf. Part A Appl.
**2014**, 66, 1321–1340. [Google Scholar] [CrossRef] - Bhattacharyya, S.; Chattopadhyay, H.; Haldar, A. Design of twisted tape turbulator at different entrance angle for heat transfer enhancement in a solar heater. Beni-Suef Univ. J. Basic Appl. Sci.
**2018**, 7, 118–126. [Google Scholar] [CrossRef] - Bhattacharyya, S.; Chattopadhyay, H.; Biswas, R.; Ewim, D.R.E.; Huan, Z. Influence of inlet turbulence intensity on transport phenomenon of modified diamond cylinder: A numerical study. Arab. J. Sci. Eng.
**2020**, 45, 1051–1058. [Google Scholar] [CrossRef] - Jin, D.; Quan, S.; Zuo, J.; Xu, S. Numerical investigation of heat transfer enhancement in a solar air heater roughened by multiple V-shaped ribs. Renew. Energy
**2019**, 134, 78–88. [Google Scholar] [CrossRef] - Mohammed, H.A.; Abbas, A.K.; Sheriff, J.M. Influence of geometrical parameters and forced convective heat transfer in transversely corrugated circular tubes. Int. Commun. Heat Mass Transf.
**2013**, 44, 116–126. [Google Scholar] [CrossRef] - Effatpanah, S.K.; Ahmadi, M.H.; Aungkulanon, P.; Maleki, A.; Sadeghzadeh, M.; Sharifpur, M.; Chen, L. Comparative analysis of five widely-used multi-criteria decision-making methods to evaluate clean energy technologies: A case study. Sustainability
**2022**, 14, 1403. [Google Scholar] [CrossRef] - Ahmadi, M.H.; Kumar, R.; Assad, M.E.H.; Ngo, P.T.T. Applications of Machine Learning Methods in Modeling Various Types of Heat Pipes: A Review. J. Therm. Anal. Calorim.
**2021**, 146, 2333–2341. [Google Scholar] [CrossRef] - Jagtap, H.P.; Bewoor, A.K.; Kumar, R.; Ahmadi, M.H.; El Haj Assad, M.; Sharifpur, M. RAM Analysis and availability optimization of thermal power plant water circulation system using PSO. Energy Rep.
**2021**, 7, 1133–1153. [Google Scholar] [CrossRef] - Sabbagh, O.; Fanaei, M.A.; Arjomand, A.; Hossein Ahmadi, M. Multi-objective optimization assessment of a new integrated scheme for co-production of natural gas liquids and liquefied natural gas. Sustain. Energy Technol. Assess.
**2021**, 47, 101493. [Google Scholar] [CrossRef] - Zolghadri, A.; Maddah, H.; Ahmadi, M.H.; Sharifpur, M. Predicting parameters of heat transfer in a shell and tube heat exchanger using aluminum oxide nanofluid with artificial neural network (Ann) and self-organizing map (Som). Sustainability
**2021**, 13, 8824. [Google Scholar] [CrossRef] - Lohakare, P.; Bewoor, A.; Kumar, R.; Said, N.M.; Sharifpur, M. Benchmark using multi criteria decision making (MCDM) technique to optimally select piston material. Eng. Anal. Bound. Elem.
**2022**, 142, 52–60. [Google Scholar] [CrossRef] - Kumar, R.; Nadda, R.; Kumar, S.; Razak, A.; Sharifpur, M.; Aybar, H.S.; Ahamed Saleel, C.; Afzal, A. Influence of artificial roughness parametric variation on thermal performance of solar thermal collector: An experimental study, response surface analysis and ANN modelling. Sustain. Energy Technol. Assess.
**2022**, 52, 102047. [Google Scholar] [CrossRef] - Sharma, J.; Soni, S.; Paliwal, P.; Saboor, S.; Chaurasiya, P.K.; Sharifpur, M.; Khalilpoor, N.; Afzal, A. A novel long term solar photovoltaic power forecasting approach using LSTM with Nadam optimizer: A case study of India. Energy Sci. Eng.
**2022**, 10, 2909–2929. [Google Scholar] [CrossRef] - Melaibari, A.A.; Khetib, Y.; Alanazi, A.K.; Sajadi, S.M.; Sharifpur, M.; Cheraghian, G. Applying artificial neural network and response surface method to forecast the rheological behavior of hybrid nano-antifreeze containing graphene oxide and copper oxide nanomaterials. Sustainability
**2021**, 13, 11505. [Google Scholar] [CrossRef] - KAbu-Nab, A.; Selima, E.S.; Morad, A.M. Theoretical investigation of a single vapor bubble during Al
_{2}O_{3}/H_{2}O nanofluids in power-law fluid affected by a variable surface tension. Phys. Scr.**2021**, 96, 035222. [Google Scholar] [CrossRef] - Morad, A.M.; Selima, E.S.; Abu-Nab, A.K. Thermophysical bubble dynamics in N-dimensional Al
_{2}O_{3}/H_{2}O nanofluid between two-phase turbulent flow. Case Stud. Therm. Eng.**2021**, 28, 101527. [Google Scholar] [CrossRef] - Bhattacharyya, S.; Abraham, J.P.; Cheng, L.; Gorman, J. Introductory chapter: A brief history of and introduction to computational fluid dynamics. In Computational Fluid Dynamics; IntechOpen: London, UK, 2021. [Google Scholar] [CrossRef]
- Ashjaee, M.; Goharkhah, M.; Khadem, L.A.; Ahmadi, R. Effect of magnetic field on the forced convection heat transfer and pressure drop of a magnetic nanofluid in a miniature heat sink. Heat Mass Transf.
**2015**, 51, 953–964. [Google Scholar] [CrossRef]

**Figure 3.**(

**a**) Variation of Nusselt Number with Re for one source at x = 15 mm and pitch = 2.5 mm; (

**b**) Variation of Nusselt Number with Re for one source at x = 15 mm and pitch = 5 mm; (

**c**) Variation of Nusselt Number with Re for one source at x = 15 mm and pitch = 10 mm; (

**d**) Variation of Nusselt Number with Re for two sources at x = 7.5 mm and 15 mm and pitch = 2.5 mm; (

**e**) Variation of Nusselt Number with Re for two sources at x = 7.5 mm and 15 mm and pitch = 5 mm; and (

**f**) Variation of Nusselt Number with Re for two sources at x = 7.5 mm and 15 mm and pitch = 10 mm.

**Figure 4.**(

**a**) Velocity contours at one source at x = 15 mm and pitch = 2.5 mm and Re 190; (

**b**) Velocity contours at two sources at x = 7.5 mm and 15 mm and pitch = 2.5 mm and Re 190; (

**c**) Velocity contours at one source at x = 15 mm and pitch = 5 mm and Re 190; (

**d**) Velocity contours at one source at x = 7.5 mm and 15 mm and pitch = 5 mm and Re 190; (

**e**) Velocity contours at one source at x = 15 mm and pitch = 10 mm and Re 190; and (

**f**) Velocity contours at two sources at x = 15 mm and pitch = 10 mm and Re 190.

**Figure 5.**(

**a**) Variation of Nusselt number along the length of the channel for pitch = 2.5 mm and B = 2000 G; (

**b**) Variation of Nusselt number along the length of the channel for pitch = 5 mm and B = 2000 G; (

**c**) Variation of Nusselt number along the length of the channel for pitch = 10 mm and B = 2000 G; (

**d**) Variation of Nusselt number along the length of the channel for one source at x = 15 mm and B = 2000 G; and (

**e**) Variation of Nusselt number along the length of the channel for two sources at x = 7.5 mm and 15 mm and B = 2000 G.

**Figure 6.**(

**a**) Variation of Pressure Drop for one source at x = 15 mm and pitch = 2.5 mm; (

**b**) Variation of Pressure Drop for one source at x = 15 mm and pitch = 5 mm; (

**c**) Variation of Pressure Drop for one source at x = 15 mm and pitch = 10 mm; (

**d**) Variation of Pressure Drop for two sources at x = 7.5 mm and 15 mm and pitch = 2.5 mm; (

**e**) Variation of Pressure Drop for two sources at x = 7.5 mm and 15 mm and pitch = 5 mm; and (

**f**) Variation of Pressure Drop for two source at x = 7.5 mm and 15 mm and pitch = 10 mm.

**Figure 7.**(

**a**) Comparison of Nusselt number for different pitches at G = 2000 and one source at x = 15 mm; (

**b**) Comparison of Nusselt number for different pitches at G = 2000 and two sources at x = 7.5 mm and 15 mm; (

**c**) Comparison of Pressure Drop for different pitches at G = 2000 and one source at x = 15 mm; (

**d**) Comparison of Nusselt number for different pitches at G = 2000 and two sources at x = 7.5 mm and 15 mm; (

**e**) Comparison of Nusselt number between one source at x = 15 mm and two sources at x = 7.5 mm and 15 mm at G = 2000; and (

**f**) Comparison of Pressure Drop for different pitches at G = 2000 and two sources at x = 7.5 mm and 15 mm.

Property | Value |
---|---|

Diameter | 20 nm |

Density | $4950\mathrm{kg}/{\mathrm{m}}^{3}$ |

Thermal Conductivity | 7 W/m·K |

Specific Heat | 640 J/Kg·K |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Souayeh, B.; Bhattacharyya, S.; Hdhiri, N.; Hammami, F.; Yasin, E.; Raju, S.S.K.; Alam, M.W.; Alsheddi, T.; Al Nuwairan, M.
Effect of Magnetic Baffles and Magnetic Nanofluid on Thermo-Hydraulic Characteristics of Dimple Mini Channel for Thermal Energy Applications. *Sustainability* **2022**, *14*, 10419.
https://doi.org/10.3390/su141610419

**AMA Style**

Souayeh B, Bhattacharyya S, Hdhiri N, Hammami F, Yasin E, Raju SSK, Alam MW, Alsheddi T, Al Nuwairan M.
Effect of Magnetic Baffles and Magnetic Nanofluid on Thermo-Hydraulic Characteristics of Dimple Mini Channel for Thermal Energy Applications. *Sustainability*. 2022; 14(16):10419.
https://doi.org/10.3390/su141610419

**Chicago/Turabian Style**

Souayeh, Basma, Suvanjan Bhattacharyya, Najib Hdhiri, Fayçal Hammami, Essam Yasin, S. Suresh Kumar Raju, Mir Waqas Alam, Tarfa Alsheddi, and Muneerah Al Nuwairan.
2022. "Effect of Magnetic Baffles and Magnetic Nanofluid on Thermo-Hydraulic Characteristics of Dimple Mini Channel for Thermal Energy Applications" *Sustainability* 14, no. 16: 10419.
https://doi.org/10.3390/su141610419