# Buoyancy Convection in a Square Cavity with Parallel Heaters Under Magnetic Field

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## Abstract

Buoyancy-driven convection in a square cavity induced by heated thin plates with arbitrary length is studied numerically. The hydrodynamics and thermal behavior of the flow are examined numerically using the two-phase mixture model and the finite volume method. Comparisons with previously published numerical works on natural convection in a cavity show excellent agreements between the results. For a given Rayleigh number and Hartman number, the effects of hot fins on the hydrodynamics and thermal parameters are presented and discussed. The steady-state results are depicted in terms of streamline and isotherm plots. It is found that the resulting convection pattern is stronger for the isothermal boundary condition. A better overall heat transfer can be achieved by placing horizontal heaters in symmetric configuration.

## Keywords

Natural convection Nanofluid Heater CFD## List of symbols

*B*_{0}Magnetic flux density

*C*_{p}Specific heat (J/kg K)

*g*Gravitational acceleration (m/s

^{2})*h*Heat transfer coefficient (W/m

^{2}K)*H*Enclosure height (m)

*Ha*Hartman number

*L*_{h}Dimensionless partition height

*k*Thermal conductivity (W/m K)

*Nu*Nusselt number

*p*Pressure (N/m

^{2})*P*Dimensionless pressure

*Pr*Prandtl number

*q*Heat flux per unit area (W/m

^{2})*Ra*Rayleigh number

*T*Temperature (K)

*u*,*v*Velocity components (m/s)

*U*,*V*Dimensionless velocity components

*x*,*y*Cartesian coordinates (m)

*X*,*Y*Dimensionless Cartesian coordinates

## Greek symbols

*α*Thermal diffusivity (m

^{2}/s)*β*Thermal expansion coefficient (K

^{−1})*θ*Dimensionless temperature

*μ*Dynamic viscosity (kg/m s)

*ν*Kinematic viscosity (m

^{2}/s)*ρ*Density (kg/m

^{3})*σ*Electrical conductivity

*φ*Volume fraction of the nanoparticles

*ψ*Stream function

## Subscripts

*c*Cold (lower value)

*f*Fluid

*h*Hot (higher value)

*m*Average

*nf*Nanofluid

*p*Particle

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