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

- 51 Downloads

## 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

## References

- Arab Solghar A, Davoudian M (2014) Buoyancy-driven heat transfer analysis in a square cavity with a mounted variable length partition in the presence of magnetic field. Eur J Comput Mech 23(1-2):61–77CrossRefGoogle Scholar
- Arefmanesh A, Najafi M, Musavi S (2013) Buoyancy-driven fluid flow and heat transfer in a square cavity with a wavy baffle—meshless numerical analysis. Eng Anal Bound Elem 37(2):366–382MathSciNetCrossRefGoogle Scholar
- Bajorek S, Lloyd J (1982) Experimental investigation of natural convection in partitioned enclosures. J Heat Transf 104(3):527–532CrossRefGoogle Scholar
- Barakos G, Mitsoulis E, Assimacopoulos D (1994) Natural convection flow in a square cavity revisited: laminar and turbulent models with wall functions. Int J Numer Meth Fluids 18(7):695–719CrossRefGoogle Scholar
- Bilgen E (2005) Natural convection in cavities with a thin fin on the hot wall. Int J Heat Mass Transf 48(17):3493–3505CrossRefGoogle Scholar
- Brinkman H (2004) The viscosity of concentrated suspensions and solutions. J Chem Phys 20(4):571CrossRefGoogle Scholar
- Dagtekin I, Oztop H (2001) Natural convection heat transfer by heated partitions within enclosure. Int Commun Heat Mass Transf 28(6):823–834CrossRefGoogle Scholar
- Davoudian M, Arab Solghar A (2014) Natural convection heat transfer in a square cavity containing a nanofluid with a baffle under a magnetic field. Heat Transf Res 45(8):725–748CrossRefGoogle Scholar
- de Vahl Davis G (1983) Natural convection of air in a square cavity: a bench mark numerical solution. Int J Numer Meth Fluids 3(3):249–264CrossRefGoogle Scholar
- Garnett JM (1904) Colours in metal glasses and in metallic films (abstract). In: Proceedings of the Royal Society of London, pp. 443–445CrossRefGoogle Scholar
- Garoosi F, Bagheri G, Talebi F (2013) Numerical simulation of natural convection of nanofluids in a square cavity with several pairs of heaters and coolers (HACs) inside. Int J Heat Mass Transf 67:362–376CrossRefGoogle Scholar
- Ghasemi B, Aminossadati S, Raisi A (2011) Magnetic field effect on natural convection in a nanofluid-filled square enclosure. Int J Therm Sci 50(9):1748–1756CrossRefGoogle Scholar
- Khanafer K, Vafai K, Lightstone M (2003) Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. Int J Heat Mass Transf 46(19):3639–3653CrossRefGoogle Scholar
- Mahmoodi M (2011) Numerical simulation of free convection of nanofluid in a square cavity with an inside heater. Int J Therm Sci 50(11):2161–2175CrossRefGoogle Scholar
- Markatos NC, Pericleous K (1984) Laminar and turbulent natural convection in an enclosed cavity. Int J Heat Mass Transf 27(5):755–772CrossRefGoogle Scholar
- Oztop H, Dagtekin I, Bahloul A (2004) Comparison of position of a heated thin plate located in a cavity for natural convection. Int Commun Heat Mass Transf 31(1):121–132CrossRefGoogle Scholar
- Shi X, Khodadadi J (2003) Laminar natural convection heat transfer in a differentially heated square cavity due to a thin fin on the hot wall. J Heat Transf 125(4):624–634CrossRefGoogle Scholar
- Teamah MA (2008) Numerical simulation of double diffusive natural convection in rectangular enclosure in the presences of magnetic field and heat source. Int J Therm Sci 47(3):237–248CrossRefGoogle Scholar