Conjugate natural convection in a square porous cavity filled by a nanofluid using Buongiorno's mathematical model

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Abstract

Steady-state natural convection heat transfer in a square porous enclosure having solid walls of finite thickness and conductivity filled by a nanofluid using the mathematical nanofluid model proposed by Buongiorno is presented. The nanofluid model takes into account the Brownian diffusion and thermophoresis effects. The study is formulated in terms of the vorticity-stream function procedure. The governing equations were solved by finite difference method and solution of algebraic equations was made on the basis of successive under relaxation method. Effort has been focused on the effects of seven types of influential factors such as the Rayleigh and Lewis numbers, the buoyancy-ratio parameter, the Brownian motion parameter, the thermophoresis parameter, the thermal conductivity ratio, and solid walls thickness on the fluid flow and heat transfer. Streamlines, isotherms, isoconcentrations, local Nusselt and Sherwood numbers are presented. It has been found that the local Nusselt number at the solid-porous interface (x = D) is an increasing function of Ra, Nr and a decreasing function of Nt, Le and D. An effect of Kr on Nu and Sh is non-monotonic. Ranges of key parameters for which a non-homogeneous model is more appropriate for the description of the system have been determined.

Original languageEnglish
Pages (from-to)137-145
Number of pages9
JournalInternational Journal of Heat and Mass Transfer
Volume79
DOIs
Publication statusPublished - 1 Jan 2014

Fingerprint

Natural convection
free convection
Thermophoresis
mathematical models
Mathematical models
thermophoresis
cavities
Nusselt number
Heat transfer
Brownian movement
heat transfer
Vorticity
Buoyancy
Enclosures
Finite difference method
Lewis numbers
Isotherms
Flow of fluids
Thermal conductivity
Rayleigh number

Keywords

  • Buongiorno's model
  • Conjugate natural convection
  • Nanofluid
  • Numerical study
  • Square porous cavity

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes

Cite this

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title = "Conjugate natural convection in a square porous cavity filled by a nanofluid using Buongiorno's mathematical model",
abstract = "Steady-state natural convection heat transfer in a square porous enclosure having solid walls of finite thickness and conductivity filled by a nanofluid using the mathematical nanofluid model proposed by Buongiorno is presented. The nanofluid model takes into account the Brownian diffusion and thermophoresis effects. The study is formulated in terms of the vorticity-stream function procedure. The governing equations were solved by finite difference method and solution of algebraic equations was made on the basis of successive under relaxation method. Effort has been focused on the effects of seven types of influential factors such as the Rayleigh and Lewis numbers, the buoyancy-ratio parameter, the Brownian motion parameter, the thermophoresis parameter, the thermal conductivity ratio, and solid walls thickness on the fluid flow and heat transfer. Streamlines, isotherms, isoconcentrations, local Nusselt and Sherwood numbers are presented. It has been found that the local Nusselt number at the solid-porous interface (x = D) is an increasing function of Ra, Nr and a decreasing function of Nt, Le and D. An effect of Kr on Nu and Sh is non-monotonic. Ranges of key parameters for which a non-homogeneous model is more appropriate for the description of the system have been determined.",
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author = "Sheremet, {M. A.} and I. Pop",
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T1 - Conjugate natural convection in a square porous cavity filled by a nanofluid using Buongiorno's mathematical model

AU - Sheremet, M. A.

AU - Pop, I.

PY - 2014/1/1

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N2 - Steady-state natural convection heat transfer in a square porous enclosure having solid walls of finite thickness and conductivity filled by a nanofluid using the mathematical nanofluid model proposed by Buongiorno is presented. The nanofluid model takes into account the Brownian diffusion and thermophoresis effects. The study is formulated in terms of the vorticity-stream function procedure. The governing equations were solved by finite difference method and solution of algebraic equations was made on the basis of successive under relaxation method. Effort has been focused on the effects of seven types of influential factors such as the Rayleigh and Lewis numbers, the buoyancy-ratio parameter, the Brownian motion parameter, the thermophoresis parameter, the thermal conductivity ratio, and solid walls thickness on the fluid flow and heat transfer. Streamlines, isotherms, isoconcentrations, local Nusselt and Sherwood numbers are presented. It has been found that the local Nusselt number at the solid-porous interface (x = D) is an increasing function of Ra, Nr and a decreasing function of Nt, Le and D. An effect of Kr on Nu and Sh is non-monotonic. Ranges of key parameters for which a non-homogeneous model is more appropriate for the description of the system have been determined.

AB - Steady-state natural convection heat transfer in a square porous enclosure having solid walls of finite thickness and conductivity filled by a nanofluid using the mathematical nanofluid model proposed by Buongiorno is presented. The nanofluid model takes into account the Brownian diffusion and thermophoresis effects. The study is formulated in terms of the vorticity-stream function procedure. The governing equations were solved by finite difference method and solution of algebraic equations was made on the basis of successive under relaxation method. Effort has been focused on the effects of seven types of influential factors such as the Rayleigh and Lewis numbers, the buoyancy-ratio parameter, the Brownian motion parameter, the thermophoresis parameter, the thermal conductivity ratio, and solid walls thickness on the fluid flow and heat transfer. Streamlines, isotherms, isoconcentrations, local Nusselt and Sherwood numbers are presented. It has been found that the local Nusselt number at the solid-porous interface (x = D) is an increasing function of Ra, Nr and a decreasing function of Nt, Le and D. An effect of Kr on Nu and Sh is non-monotonic. Ranges of key parameters for which a non-homogeneous model is more appropriate for the description of the system have been determined.

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KW - Nanofluid

KW - Numerical study

KW - Square porous cavity

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