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Research Papers

Convective Heat Transfer Utilizing Magnetic Nanoparticles in the Presence of a Sloping Magnetic Field Inside a Square Enclosure

[+] Author and Article Information
Latifa M. Al-Balushi

Department of Mathematics,
College of Science,
Sultan Qaboos University,
PO Box 36,
Al-Khod, Muscat, PC 123, Oman

M. M. Rahman

Department of Mathematics,
College of Science,
Sultan Qaboos University,
PO Box 36,
Al-Khod, Muscat, PC 123, Oman
e-mail: mansurdu@yahoo.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received October 12, 2018; final manuscript received June 20, 2019; published online July 15, 2019. Assoc. Editor: Ali J. Chamkha.

J. Thermal Sci. Eng. Appl 11(4), 041013 (Jul 15, 2019) (19 pages) Paper No: TSEA-18-1512; doi: 10.1115/1.4044120 History: Received October 12, 2018; Revised June 20, 2019

Unsteady natural convection flow and heat transfer utilizing magnetic nanoparticles in the presence of a sloping magnetic field inside a square enclosure are simulated numerically following nonhomogeneous dynamic model. Four different thermal boundary conditions: constant, parabolic in space, sinusoidally in space, and time for the bottom hot wall are considered. The top wall of the enclosure is cold while the vertical walls are thermally insulated. Galerkin weighted residual finite element method is used to solve the governing nondimensional partial differential equations. For simulations, 12 types of nanofluids consisting magnetite (Fe3O4), cobalt ferrite (CoFe2O4), Mn–Zn ferrite (Mn–ZnFe2O4), and silicon dioxide (SiO2) nanoparticles along with water, engine oil, and kerosene as base fluids are used. The effects of the important model parameters such as Hartmann number, magnetic field sloping angle, and thermal Rayleigh number on the flow fields are investigated. The results show that the average Nusselt number, shear rate, as well as the nanofluid velocity decreases as the Hartmann number intensifies. Moreover, the rate of heat transfer in nanofluid exaggerates with the increase of the thermal Rayleigh number and the magnetic field sloping angle. Sinusoidally varied in space thermal boundary condition at the bottom wall provides the highest average Nusselt number and the shear rate compared to the other types of thermal boundary conditions studied here. For this case, the highest average Nusselt number is obtained for the Mn–ZnFe2O4–Ke nanofluid. On the other hand, Fe3O4–H2O nanofluid delivers the highest shear rate compared to the other premeditated nanofluids.

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Figures

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Fig. 1

Physical model and coordinates system

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Fig. 2

Grid generation of the square-shape cavity with legend of quality measure (left) and the zoom in the upper right corner of the cavity (right)

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Fig. 3

Grid test for CoFe2O4–EO nanofluid for case I when Pr=6.84, RaT=105, RaC=103, γ=30 deg, ϕ=0.1, Ha=10, dp=10 nm, n=3, and  τ=5

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Fig. 4

Comparison of the average Nusselt number (Nuave) with those of Khanafer et al. [2], Barakos et al. [49], and Fusegi et al. [50] for different (RaT) when ϕ=0

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Fig. 5

The streamlines, isotherms, and isoconcentrations for Fe3O4–H2O nanofluid for different values of the Hartmann number (Ha) for case I (θ=1) when Pr=6.84, RaT=105, RaC=103, Ha=10, ϕ=0.05, dp=10 nm, n=3, and  τ=10

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Fig. 6

The streamlines and isotherms for Fe3O4–H2O nanofluid for different values of the Hartmann number (Ha) when Pr=6.84, RaT=105, RaC=103, γ=30 deg, ϕ=0.05, dp=10 nm, n=3, and  τ=10

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Fig. 7

The streamlines, isotherms, and isoconcentrations of Fe3O4–H2O nanofluid for different values of the magnetic field inclination angle (γ) when Pr=6.84, RaT=105, RaC=103, Ha=10, ϕ=0.05, dp=10 nm, n=3, and  τ=10

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Fig. 8

The streamlines and isotherms for Fe3O4–H2O nanofluid for different values of the magnetic field inclination angle (γ) when Pr=6.84, RaT=105, RaC=103, Ha=10, ϕ=0.05, dp=10 nm, n=3, and  τ=10

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Fig. 9

The average Nusselt number versus τ for different Ha for cases I–IV when Pr=6.84, RaT=105, RaC=103, γ=30 deg, ϕ=0.05, dp=10 nm, f=π/20, and n=3: (a) case I, (b) case II, (c) case III, and (d) case IV

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Fig. 10

The average Nusselt number versus τ for different γ for cases I–IV when Pr=6.84, RaT=105, RaC=103, Ha=10, ϕ=0.05, dp=10 nm, and n=3: (a) case I, (b) case II, (c) case III, and (d) case IV

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Fig. 11

The average Nusselt number versus arc length for different values of the Hartmann number (Ha) for cases I–IV when Pr=6.84, RaT=105, RaC=103, γ=30 deg, ϕ=0.05, dp=10 nm, n=3, f=π/20, and  τ=10: (a) case I, (b) case II, (c) case III, and (d) case IV

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Fig. 12

The shear rate versus arc length for different values of the Hartmann number (Ha) for cases I–IV when Pr=6.84, RaT=105, RaC=103, γ=30 deg, ϕ=0.05, dp=10 nm, n=3, f=π/20, and  τ=10: (a) case I, (b) case II, (c) case III, and (d) case IV

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Fig. 13

The average Nusselt number versus arc length for different values of the magnetic field inclination angle (γ) for cases I–IV when Pr=6.84, Ha=10, RaC=103, γ=30 deg, ϕ=0.05, dp=10 nm, n=3, and  τ=10: (a) case I, (b) case II, (c) case III, and (d) case IV

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Fig. 14

The shear rate versus arc length varying γ for cases I–IV when Pr=6.84, Ha=10, RaC=103, γ=30 deg, ϕ=0.05, dp=10 nm, n=3, and  τ=10: (a) case I, (b) case II, (c) case III, and (d) case IV

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Fig. 15

The average Nusselt number versus arc length for different values of the local thermal Rayleigh number RaT for cases I–IV when Pr=6.84, Ha=40, RaC=103, ϕ=0.05, dp=10 nm, n=3, f=π/20, and  τ=10: (a) case I, (b) case II, (c) case III, and (d) case IV

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Fig. 16

The shear rate versus arc length for different values of the local thermal Rayleigh number RaT for cases I–IV when Pr=6.84, Ha=40, RaC=103, ϕ=0.05, dp=10 nm, f=π/20, n=3, and  τ=10: (a) case I, (b) case II, (c) case III, and (d) case IV

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