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Journal of Porous Media
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ISSN Druckformat: 1091-028X
ISSN Online: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v18.i6.50
pages 613-628

NATURAL CONVECTION ABOVE A HORIZONTAL PLATE IN A NANOFLUID-SATURATED POROUS MEDIUM WITH OR WITHOUT A MAGNETIC FIELD

Kaustav Pradhan
Indian Institute of Technology Kharagpur
Abhijit Guha
Mechanical Engineering Department, Indian Institute of Technology Kharagpur, Kharagpur, Pin 721302, India

ABSTRAKT

A generalized similarity theory is developed for natural convection over a horizontal plate in a nanofluid-saturated porous medium in the presence of a vertical magnetic field. The paper highlights three important aspects: role of the wall boundary condition of the nanoparticles, the magnetic field, and the porous medium. Two different boundary conditions are imposed on the nanoparticle volume fraction, one where the nanoparticle volume fraction at the wall is actively controlled and another where the nanoparticle flux is set equal to zero at the surface. It is shown that a similarity theory can be formulated for the case of a uniform magnetic field when natural convection takes place in a Darcian porous medium (which is in contrast to magnetohydrodynamic natural convection in a normal fluid for which similarity solutions exist only for a specific power law variation of the magnetic field along the plate). It is observed that the applied magnetic field reduces the velocity in the boundary layer. Consequently, the temperature of the nanofluid and the nanoparticle volume fraction near the plate is greater than that in the absence of a magnetic field. The Nusselt number and Sherwood number for a nanofluid are found to decrease with an increase in the value of the magnetic parameter. The effect of the nanofluid parameters Nr, Nb, and Nt on the velocity, temperature and nanoparticle volume fraction within the boundary layer is also investigated. The effect of the nanofluid parameters on the Nusselt and Sherwood numbers is complicated and is illustrated through tables. It is shown that the wall boundary condition of the nanoparticles has a profound effect on the computed values of Nusselt and Sherwood numbers.


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