Effects of two-phase nanofluid model on MHD mixed convection in a lid-driven cavity in the presence of conductive inner block and corner heater

A. I. Alsabery, M. A. Ismael, A. J. Chamkha, Ishak Hashim

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9 Citations (Scopus)

Abstract

This paper investigates a steady mixed convection in a lid-driven square cavity subjected to an inclined magnetic field and heated by corner heater with an inserted square solid block. Water–Al(Formula presented.)O(Formula presented.) nanofluid fills the cavity based on Buongiorno’s two-phase model. A corner heater is configured in the left lower corner of the cavity by maintaining 40% of the bottom and vertical walls at constant hot temperature. The top horizontal wall is moving and maintained at a constant low temperature. The remainder walls are thermally insulated. The governing equations are solved numerically using the finite element method. The governing parameters are the nanoparticles volume fraction ((Formula presented.)), Reynolds number ((Formula presented.)), Richardson number ((Formula presented.)), Hartmann number ((Formula presented.)) and the size of the inner solid ((Formula presented.)). The other parameters: the Prandtl number, Lewis number, Schmidt number, ratio of Brownian to thermophoretic diffusivity and the normalized temperature parameter, are fixed at (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.) and (Formula presented.), respectively. The inclination of the magnetic field is fixed at (Formula presented.). Results show that at low Reynolds number, the increase in nanoparticles loading more the 2% becomes useless. It is also found that a big size of the solid block can augment heat transfer in the case of high values of both the Reynolds and Richardson numbers.

Original languageEnglish
Pages (from-to)1-22
Number of pages22
JournalJournal of Thermal Analysis and Calorimetry
DOIs
Publication statusAccepted/In press - 28 May 2018

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Mixed convection
Magnetohydrodynamics
heaters
convection
cavities
Reynolds number
Magnetic fields
Nanoparticles
Prandtl number
Volume fraction
Heat transfer
Finite element method
Temperature
Richardson number
Hartmann number
Schmidt number
Lewis numbers
nanoparticles
low Reynolds number
magnetic fields

Keywords

  • Brownian
  • Buongiorno’s model
  • Corner heater
  • Lid-driven cavity
  • Magnetic field
  • Thermophoresis

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Physical and Theoretical Chemistry

Cite this

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title = "Effects of two-phase nanofluid model on MHD mixed convection in a lid-driven cavity in the presence of conductive inner block and corner heater",
abstract = "This paper investigates a steady mixed convection in a lid-driven square cavity subjected to an inclined magnetic field and heated by corner heater with an inserted square solid block. Water–Al(Formula presented.)O(Formula presented.) nanofluid fills the cavity based on Buongiorno’s two-phase model. A corner heater is configured in the left lower corner of the cavity by maintaining 40{\%} of the bottom and vertical walls at constant hot temperature. The top horizontal wall is moving and maintained at a constant low temperature. The remainder walls are thermally insulated. The governing equations are solved numerically using the finite element method. The governing parameters are the nanoparticles volume fraction ((Formula presented.)), Reynolds number ((Formula presented.)), Richardson number ((Formula presented.)), Hartmann number ((Formula presented.)) and the size of the inner solid ((Formula presented.)). The other parameters: the Prandtl number, Lewis number, Schmidt number, ratio of Brownian to thermophoretic diffusivity and the normalized temperature parameter, are fixed at (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.) and (Formula presented.), respectively. The inclination of the magnetic field is fixed at (Formula presented.). Results show that at low Reynolds number, the increase in nanoparticles loading more the 2{\%} becomes useless. It is also found that a big size of the solid block can augment heat transfer in the case of high values of both the Reynolds and Richardson numbers.",
keywords = "Brownian, Buongiorno’s model, Corner heater, Lid-driven cavity, Magnetic field, Thermophoresis",
author = "Alsabery, {A. I.} and Ismael, {M. A.} and Chamkha, {A. J.} and Ishak Hashim",
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T1 - Effects of two-phase nanofluid model on MHD mixed convection in a lid-driven cavity in the presence of conductive inner block and corner heater

AU - Alsabery, A. I.

AU - Ismael, M. A.

AU - Chamkha, A. J.

AU - Hashim, Ishak

PY - 2018/5/28

Y1 - 2018/5/28

N2 - This paper investigates a steady mixed convection in a lid-driven square cavity subjected to an inclined magnetic field and heated by corner heater with an inserted square solid block. Water–Al(Formula presented.)O(Formula presented.) nanofluid fills the cavity based on Buongiorno’s two-phase model. A corner heater is configured in the left lower corner of the cavity by maintaining 40% of the bottom and vertical walls at constant hot temperature. The top horizontal wall is moving and maintained at a constant low temperature. The remainder walls are thermally insulated. The governing equations are solved numerically using the finite element method. The governing parameters are the nanoparticles volume fraction ((Formula presented.)), Reynolds number ((Formula presented.)), Richardson number ((Formula presented.)), Hartmann number ((Formula presented.)) and the size of the inner solid ((Formula presented.)). The other parameters: the Prandtl number, Lewis number, Schmidt number, ratio of Brownian to thermophoretic diffusivity and the normalized temperature parameter, are fixed at (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.) and (Formula presented.), respectively. The inclination of the magnetic field is fixed at (Formula presented.). Results show that at low Reynolds number, the increase in nanoparticles loading more the 2% becomes useless. It is also found that a big size of the solid block can augment heat transfer in the case of high values of both the Reynolds and Richardson numbers.

AB - This paper investigates a steady mixed convection in a lid-driven square cavity subjected to an inclined magnetic field and heated by corner heater with an inserted square solid block. Water–Al(Formula presented.)O(Formula presented.) nanofluid fills the cavity based on Buongiorno’s two-phase model. A corner heater is configured in the left lower corner of the cavity by maintaining 40% of the bottom and vertical walls at constant hot temperature. The top horizontal wall is moving and maintained at a constant low temperature. The remainder walls are thermally insulated. The governing equations are solved numerically using the finite element method. The governing parameters are the nanoparticles volume fraction ((Formula presented.)), Reynolds number ((Formula presented.)), Richardson number ((Formula presented.)), Hartmann number ((Formula presented.)) and the size of the inner solid ((Formula presented.)). The other parameters: the Prandtl number, Lewis number, Schmidt number, ratio of Brownian to thermophoretic diffusivity and the normalized temperature parameter, are fixed at (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.) and (Formula presented.), respectively. The inclination of the magnetic field is fixed at (Formula presented.). Results show that at low Reynolds number, the increase in nanoparticles loading more the 2% becomes useless. It is also found that a big size of the solid block can augment heat transfer in the case of high values of both the Reynolds and Richardson numbers.

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