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# NUMERICAL STUDY OF LAMINAR NATURAL CONVECTION IN THE BOUNDARY LAYER AROUND A VERTICAL CYLINDER WITH OPPOSING BUOYANCIES

DOI: 10.1615/ICHMT.2008.CHT.1130
page 9

Mayouf Si Abdallah
Physics Department, University of Mentouri, Constantine 25000, Algeria ; Physics Department, Faculty of Sciences, University of M'Sila, Algeria

Belkacem Zeghmati
Laboratoire de Mathématiques et de Physique, Université de Perpignan Via Domitia, Perpignan, France

## Abstrakt

In this paper, a numerical study is presented for laminar free convection heat and mass transfer in the boundary layer along a vertical cylinder with opposing buoyancies. The surface is maintained at a constant temperature and concentration. Upon starting the process, gradients of temperature and concentration appear in the fluid adjacent to the wall of the cylinder, thus giving rise to buoyancy forces that are the cause of natural convective motion in this study. The homotopic transformation is proposed to transform the physical domain into a flat plate. The boundary layer equations and the boundary conditions are solved numerically using an implicit finite difference scheme and the Gauss-Seidel algorithm. The buoyancy ratio N, Prandtl number Pr and Schmidt number Sc are important parameters for this problem. The numerical results for Pr=Sc and Pr≠Sc, including the velocity, temperature, concentration fields and the Nusselt number as well as the Sherwood number along the surface of the cylinder are discussed for aiding and opposing buoyancies. Results show that the Nusselt (Sherwood) number increase with positive or negative values of N. Moreover, for opposing flows with Sc<Pr , the flow is completely downward, the thickness of the concentration layer is larger than that of the thermal layer . For PR<SC , the velocity are weak and the thermal layer thickness is much larger.

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