Magnetic field effect on the unsteady natural convection in a wavy-walled cavity filled with a nanofluid: Buongiorno's mathematical model

Mikhail A. Sheremet, Ioan Pop, Natalia C. Roşca

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86 Citations (Scopus)

Abstract

A numerical investigation is performed on the unsteady natural convection of water based nanofluid within a wavy-walled cavity under the influence of a uniform inclined magnetic field using the mathematical nanofluid model proposed by Buongiorno. The left vertical wavy and right vertical flat walls of the cavity are kept at constant but different temperatures whereas the top and bottom horizontal walls are adiabatic. All boundaries are assumed to be impermeable to the base fluid and nanoparticles. The mathematical model formulated in dimensionless stream function, vorticity and temperature variables is solved using implicit finite difference schemes of the second order. The governing parameters are the Hartmann number, undulation number, wavy contraction ratio, inclination angle of the magnetic field relative to the gravity vector and dimensionless time. The effects of these parameters on the average Nusselt number along the hot wavy wall, as well as on the streamlines, isotherms and isoconcentrations are analyzed.

Original languageEnglish
Pages (from-to)211-222
Number of pages12
JournalJournal of the Taiwan Institute of Chemical Engineers
Volume61
DOIs
Publication statusPublished - 1 Apr 2016

Fingerprint

Magnetic field effects
Natural convection
Mathematical models
Magnetic fields
Nusselt number
Vorticity
Isotherms
Gravitation
Nanoparticles
Temperature
Fluids
Water

Keywords

  • Magnetic field
  • Nanofluid
  • Numerical results
  • Unsteady natural convection
  • Wavy-walled cavity

ASJC Scopus subject areas

  • Chemistry(all)
  • Chemical Engineering(all)

Cite this

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title = "Magnetic field effect on the unsteady natural convection in a wavy-walled cavity filled with a nanofluid: Buongiorno's mathematical model",
abstract = "A numerical investigation is performed on the unsteady natural convection of water based nanofluid within a wavy-walled cavity under the influence of a uniform inclined magnetic field using the mathematical nanofluid model proposed by Buongiorno. The left vertical wavy and right vertical flat walls of the cavity are kept at constant but different temperatures whereas the top and bottom horizontal walls are adiabatic. All boundaries are assumed to be impermeable to the base fluid and nanoparticles. The mathematical model formulated in dimensionless stream function, vorticity and temperature variables is solved using implicit finite difference schemes of the second order. The governing parameters are the Hartmann number, undulation number, wavy contraction ratio, inclination angle of the magnetic field relative to the gravity vector and dimensionless time. The effects of these parameters on the average Nusselt number along the hot wavy wall, as well as on the streamlines, isotherms and isoconcentrations are analyzed.",
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T1 - Magnetic field effect on the unsteady natural convection in a wavy-walled cavity filled with a nanofluid

T2 - Buongiorno's mathematical model

AU - Sheremet, Mikhail A.

AU - Pop, Ioan

AU - Roşca, Natalia C.

PY - 2016/4/1

Y1 - 2016/4/1

N2 - A numerical investigation is performed on the unsteady natural convection of water based nanofluid within a wavy-walled cavity under the influence of a uniform inclined magnetic field using the mathematical nanofluid model proposed by Buongiorno. The left vertical wavy and right vertical flat walls of the cavity are kept at constant but different temperatures whereas the top and bottom horizontal walls are adiabatic. All boundaries are assumed to be impermeable to the base fluid and nanoparticles. The mathematical model formulated in dimensionless stream function, vorticity and temperature variables is solved using implicit finite difference schemes of the second order. The governing parameters are the Hartmann number, undulation number, wavy contraction ratio, inclination angle of the magnetic field relative to the gravity vector and dimensionless time. The effects of these parameters on the average Nusselt number along the hot wavy wall, as well as on the streamlines, isotherms and isoconcentrations are analyzed.

AB - A numerical investigation is performed on the unsteady natural convection of water based nanofluid within a wavy-walled cavity under the influence of a uniform inclined magnetic field using the mathematical nanofluid model proposed by Buongiorno. The left vertical wavy and right vertical flat walls of the cavity are kept at constant but different temperatures whereas the top and bottom horizontal walls are adiabatic. All boundaries are assumed to be impermeable to the base fluid and nanoparticles. The mathematical model formulated in dimensionless stream function, vorticity and temperature variables is solved using implicit finite difference schemes of the second order. The governing parameters are the Hartmann number, undulation number, wavy contraction ratio, inclination angle of the magnetic field relative to the gravity vector and dimensionless time. The effects of these parameters on the average Nusselt number along the hot wavy wall, as well as on the streamlines, isotherms and isoconcentrations are analyzed.

KW - Magnetic field

KW - Nanofluid

KW - Numerical results

KW - Unsteady natural convection

KW - Wavy-walled cavity

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