Numerical Study of Natural Convection in a Two-Dimensional Enclosure with a Sinusoidal Boundary Thermal Condition Utilizing Nanofluid

摘要

Nanofluids are considered to offer important advantages over conventional heat transfer fluids. A model is developed to analyze the behavior of nanofluids taking into account the solid fraction χ. The Navier-Stokes equations are solved numerically with Alternating Direct Implicit method (ADI method) for various Grashof numbers 104 and 105;we have an excellent agreement between our numerical code and previously published works. Copper-Water nanofluid is used with Pr = 6.2 and solid volume fraction χ is varied as 0%;5%;10%;15% and 20%. The problem considered is a two-dimensional heat transfer in a square cavity. The vertical walls are differentially heated, the left is maintained at hot con- dition (sinusoidal) when the right one is cold. The horizontal walls are assumed to be insulated, non conducting and impermeable to mass transfer. The nanofluid in the enclosure is Newtonian, incompressible and laminar. The nanopar- ticles are assumed to have a uniform shape and size. Moreover, it is assumed that both the fluid phase and nanoparticles are in thermal equilibrium state and they flow at the same velocity. The thermophysical properties of the nanofluid are assumed to be constant except for the density variation in the buoyancy force, which is based on the Boussinesq approximation. Different correlations are proposed for predicting heat transfer for uniform and sinusoidal boundary thermal conditions.