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In this paper, the free convective flow and heat transfer in a porous rectangular enclosures filled with Cu-water nanofluid is studied and analyzed. The cavity sidewalls are exposed to a constant heat flux and the horizontal walls are assumed to be adiabatic. The governing equations describing the problem are solved using a finite difference method. The main parameters of our problem are: aspect ratio, volume fraction of nanoparticles, types of media, porosity of the medium, and Rayleigh number. The results indicate that an increase in aspect ratio from 0.1 to 0.7 leads to a significant increase of Nusselt number, which then reaches a maximum value. However, the heat transfer rate progressively decreases for aspect ratios greater than 0.7. Moreover, the addition of Cu-nanoparticles weakens the heat transfer. As a result, when the porous medium has low thermal conductivity, the solid matrix porosity becomes particularly more effective in improving heat transfer. Also, a correlation was established between the average Nusselt number and the influencing parameters. Results show that the governing parameters impact the flow regime. [ABSTRACT FROM AUTHOR]

The present investigation centers around a numerical study of the impact of the presence of phototactic microorganisms on the thermo-bioconvection inside a wavy-walled horizontal porous annulus that is saturated with a Newtonian fluid. Consequently, an equation describing the movement of the microorganism cells is added to the mathematical model of natural convection. The thermal equilibrium, Oberbeck–Boussinesq approximations and Darcy law are taken into consideration. The transformed dimensionless partial differential equations with the temperature-concentration-stream function formulation are discretized applying the alternate direction implicit finite difference scheme. Results confirm that in the absence of microorganisms the Nusselt number decreases with the increase of the amplitude of wall waviness. It was also observed that the wall waviness influence the thermo-bioconvective instabilities and the flow regime structure. [ABSTRACT FROM AUTHOR]

Natural convection and heat transfer inside a porous concentric horizontal cylindrical annulus saturated by a Cu–water nanofluid was investigated in this study. The governing equations were discretized using the finite difference technique and solved using the alternating direction implicit (ADI) method. It was found that the increase in nanoparticles had a favorable effect on the enhancement of the heat transfer for low Rayleigh numbers. However, exceeding a given threshold of Rayleigh number, the addition of nanoparticles had an adverse effect on the heat transfer. Also, the study revealed the effect of porosity on Nusselt number, where the increase in volume fraction of nanoparticles in the porous medium leads to a considerable increase in the Nusselt number ratio when the porosity equals 0.5 and 0.8, an opposite behavior was observed when this latter equals 0.1. The bifurcation between the unicellular and the bicellular regimes was investigated for several nanoparticles volume fractions and a wide range of porosity. The results revealed that regardless of the porosity, the critical Rayleigh number for the transition from the unicellular to the bicellular regime increases with volume fraction of nanoparticles for the whole range of the radius ratio. Several numerical correlations were developed for the critical Rayleigh number in terms of volume fraction of nanoparticles and porosity of the medium. [ABSTRACT FROM AUTHOR]

The effect of temperature modulation on natural convection in a horizontal porous annulus is investigated in this paper. The porous medium is confined between the inner and outer cylinders of the annulus which is subjected to time-dependent temperature. It is assumed that the time-dependent modulation is periodic with frequency σ and amplitude λ. The model consists of the heat equation and the equations of motion under the Darcy law. The derived problem with the stream function-temperature formulation is solved numerically using the alternating direction implicit method. It is shown that a stabilizing effect can be gained for appropriate values of the frequency σ and the amplitude λ. [ABSTRACT FROM AUTHOR]