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Magnetohydrodynamic natural convection and entropy generation analyses inside a nanofluid-filled incinerator-shaped porous cavity with wavy heater block

  • M. Hashemi-TilehnoeeEmail author
  • A. S. Dogonchi
  • Seyyed Masoud Seyyedi
  • Ali J. Chamkha
  • D. D. Ganji
Article
  • 40 Downloads

Abstract

The aim of the current study is natural convection analysis conjugated with entropy generation analysis in an incinerator shaped permeable enclosure loaded with Al2O3–H2O nanofluid subjected to the magnetic field with a rectangular wavy heater block positioned on the bottom of the cavity wall. The bottom and top horizontal walls are adiabatic; the inclined and vertical walls are thought to be cooled. Firstly, the governing expressions and standard kε turbulence model are rewritten from dimensional form to non-dimensional form using dimensionless parameters such as vorticity and stream function. In the next step, the equation of entropy generation is written in dimensionless form. Then, the system of non-dimensional governing equations is solved by the finite volume method (FVM) conjugated with a non-dimensionalization scheme using ANSYS Fluent. Fine grids (wall y+ < 2) with inflated layers have been used for the higher Rayleigh number. The effects of the Rayleigh number in the laminar region (Ra = 103, 104, and 105) and turbulent region (Ra = 108, 0.5 × 109, and 109), Darcy number (Da = 0.01 and 100), Hartmann number (Ha = 0 and 40), and the nanoparticles (\( \phi = 2{{\% }} \)) on the entropy generation number and natural convection are investigated. The validation results were in good agreement with those of the literature. The results demonstrate that for the laminar region, the Nusselt number and entropy generation number increase as the Rayleigh number and the Darcy number grow, whereas both of them abate as Hartmann number increases. In the turbulent region, the average Nusselt number decreases by ascending the Darcy number. Also, for turbulent region (Ra = 109), convection flow strength decreases 6.28% when Hartmann number increases from 0 to 40, whereas the entropy generation number increases 31.5% at Da = 0.01.

Keywords

Turbulent natural convection Nanofluid Entropy generation Porous media MHD ANSYS fluent 

List of symbols

B0

Magnetic field strength

B

Magnetic field (T)

Be

Bejan number

Cp

Specific heat capacity (J kg−1 K−1)

E

Dimensionless dissipation rate of turbulent kinetic energy

g

Gravitational acceleration (m s−2)

Ha

Hartmann number

k

Dimensional turbulent kinetic energy (m2 s−2)

\(\tilde{k}\)

Thermal conductivity (W m−1 K−1)

K

Dimensionless turbulent kinetic energy

KP

Permeability of the medium (m2)

L

Length of the cavity (m)

m

Shape factor of nanoparticles

N

Entropy generation number

Nu

Nusselt number

p

Pressure (N m−2)

Pr

Prandtl number (–)

Ra

Rayleigh number

\(\dot{S}_{\text{gen}}\)

Rate of entropy generation per unit volume (J s−1 K−1 m−3)

T

Temperature (K)

u, v

Dimensional x and y components of velocity (m s−1)

x, y

Dimensional coordinates (m)

X, Y

Dimensionless coordinates

Greek letters

α

Thermal diffusivity (m2 s−1)

β

Thermal expansion coefficient (K−1)

ɛ

Turbulent dissipation of kinetic energy (m2 s−3)

\({{\Theta}}\)

Dimensionless temperature (–)

λ

Inclination angle (°)

μ

Dynamic viscosity (N s m−2)

ν

Kinematic viscosity (m2 s−1)

ρ

Density (kg m−3)

σ

Electrical conductivity (Ω m−1)

\(\sigma_{\text{k}}\)

\({k} - {\varepsilon}\) Turbulent model parameters

φ

Cavity inclination angle (°)

ΔT

Temperature difference

ϕ

Volume fraction

\({{\Phi}}\)

Irreversibility distribution ratio

ψ

Dimensional stream function (m2 s−1)

\({{\Psi }}\)

Dimensionless stream function

ω

Dimensional vorticity (s−1)

\({{\Omega }}\)

Dimensionless vorticity

Subscripts

ave

Average

FF

Fluid friction

gen

Generation

h

Hot

HT

Heat transfer

MF

Magnetic field

nf

Nanofluid

PM

Porous medium

s

Solid

t

Turbulent

Notes

Acknowledgements

This work has been supported by a research contract of the Islamic Azad University, Aliabad Katoul Branch, Iran.

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2020

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Aliabad Katoul BranchIslamic Azad UniversityAliabad KatoulIran
  2. 2.Mechanical Engineering Department, Prince Sultan Endowment for Energy and EnvironmentPrince Mohammad Bin Fahd UniversityAl-KhobarSaudi Arabia
  3. 3.RAK Research and Innovation CenterAmerican University of Ras Al KhaimahRas al-KhaimahUnited Arab Emirates
  4. 4.Department of Mechanical EngineeringBabol University of TechnologyBabolIran

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