Unsteady natural convection within a differentially heated enclosure of sinusoidal corrugated side walls

Abstract

a b s t r a c tNumerically investigation of natural convection within a differentially heated modified square enclosure with sinusoidally corrugated side walls has been performed for different values of Rayleigh number. The fluid inside the enclosure considered is air and is quiescent, initially. The top and bottom surfaces are flat and considered as adiabatic. Results reveal three main stages: an initial stage, a transitory or oscillatory stage and a steady stage for the development of natural convection flow inside the corrugated cavity. The numerical scheme is based on the finite element method adapted to triangular non-uniform mesh element by a non-linear parametric solution algorithm. Investigation has been performed for the Rayleigh number, Ra ranging from 10 5 to 10 8 with variation of corrugation amplitude and frequency. Constant physical properties for the fluid medium have been assumed except for the density where Boussinesq's approximation has been considered. Results have been presented in terms of the isotherms, streamlines, temperature plots, average Nusselt numbers, traveling waves and thermal boundary layer thickness plots, temperature and velocity profiles. The effects of sudden differential heating and its consequent transient behavior on fluid flow and heat transfer characteristics have been observed for the range of governing parameters. The present results show that the transient phenomena are greatly influenced by the variation of the Rayleigh number with corrugation amplitude and frequency.

MHD Free Convection and Entropy Generation in a Corrugated Cavity Filled with a Porous Medium Saturated with Nanofluids

“…Hydro-thermal performance in a corrugated channel with nanofluid was numerically examined in [ 24 ]. As was shown by Hasan et al [ 25 ], the corrugation amplitude and frequency have a significant impact on the heat transfer rate in natural convection for a deferentially-heated cavity. Hussain et al [ 26 ] numerically examined the natural convection in a tilted sinusoidal corrugated cavity with magnetic field effects.…”

Magnetohydrodynamics Mixed Convection in a Lid-Driven Cavity Having a Corrugated Bottom Wall and Filled With a Non-Newtonian Power-Law Fluid Under the Influence of an Inclined Magnetic Field

“…The effect of a corrugated side wall on the natural convection of a differentially heated cavity was investigated in Ref. [16] by using the finite element method. Their results showed that the heat transfer is greatly influenced by the variation corrugation amplitude and frequency.…”

Conduction and convection heat transfer characteristics of water-based au nanofluids in a square cavity with differentially heated side walls subjected to constant temperatures

“…compact heat exchangers [8] and cooling systems [9,10], selective laser melting process [11]). Although quite some various different configurations of the enclosure problem are possible [12][13][14][15][16][17][18], one of the most studied cases involves the two-dimensional square enclosure with differentially heated isothermal vertical walls and adiabatic horizontal walls [19,20]. When the vertical walls are insulated to ensure adiabatic conditions and the lower horizontal wall held at the higher temperature then one has the Rayleigh-Bénard configuration [21,22].…”