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 (Fe_{3}O_{4}), cobalt ferrite (CoFe_{2}O_{4}), Mn–Zn ferrite (Mn–ZnFe_{2}O_{4}), and silicon dioxide (SiO_{2}) 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–ZnFe_{2}O_{4}–Ke nanofluid. On the other hand, Fe_{3}O_{4}–H_{2}O nanofluid delivers the highest shear rate compared to the other premeditated nanofluids.

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Department of Mathematics,

College of Science,

Sultan Qaboos University,

PO Box 36,

Al-Khod, Muscat, PC 123, Oman
Department of Mathematics,

College of Science,

Sultan Qaboos University,

PO Box 36,

Al-Khod, Muscat, PC 123, Oman

e-mail: [email protected]

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August 2019

Research-Article

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

Latifa M. Al-Balushi,

Latifa M. Al-Balushi

Department of Mathematics,

College of Science,

Sultan Qaboos University,

PO Box 36,

Al-Khod, Muscat, PC 123, Oman

College of Science,

Sultan Qaboos University,

PO Box 36,

Al-Khod, Muscat, PC 123, Oman

Search for other works by this author on:

M. M. Rahman

M. M. Rahman

Department of Mathematics,

College of Science,

Sultan Qaboos University,

PO Box 36,

Al-Khod, Muscat, PC 123, Oman

e-mail: [email protected]

College of Science,

Sultan Qaboos University,

PO Box 36,

Al-Khod, Muscat, PC 123, Oman

e-mail: [email protected]

1Corresponding author.

Search for other works by this author on:

Latifa M. Al-Balushi

College of Science,

Sultan Qaboos University,

PO Box 36,

Al-Khod, Muscat, PC 123, Oman

M. M. Rahman

College of Science,

Sultan Qaboos University,

PO Box 36,

Al-Khod, Muscat, PC 123, Oman

e-mail: [email protected]

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*. Aug 2019, 11(4): 041013 (19 pages)

**Published Online:**July 15, 2019

Article history

Received:

October 12, 2018

Revised:

June 20, 2019

Citation

Al-Balushi, L. M., and Rahman, M. M. (July 15, 2019). "Convective Heat Transfer Utilizing Magnetic Nanoparticles in the Presence of a Sloping Magnetic Field Inside a Square Enclosure." ASME. *J. Thermal Sci. Eng. Appl*. August 2019; 11(4): 041013. https://doi.org/10.1115/1.4044120

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