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Purpose: The purpose of this paper is to investigate the effects of gravitational modulation on natural convection in a square inclined porous cavity filled by a fluid containing copper nanoparticles. Design/methodology/approach: The present study uses a system of equations that couple hydrodynamics to heat transfer, representing the governing equations of fluid flow in a square domain. The Boussinesq–Darcy flow with Cu-water nanofluid is considered. The dimensionless partial differential equations are solved numerically using finite difference method based on alternating direction implicit scheme. The cavity is differentially heated by constant heat flux, while the top and bottom walls are insulated. The authors examined the effects of gravity amplitude (λ), vibration frequency (σ), tilt angle (α) and Rayleigh number (Ra) on flow and temperature. Findings: The numerical simulations, in the form of streamlines, isotherms, Nusselt number and maximum stream function for different values of amplitude, frequency, tilt angle and Rayleigh number, have revealed an oscillatory behavior in the development of flow and temperature under gravity modulation. An increase of amplitude from 0.5 to 1 intensifies the flow stream (from |ψmax| = 21.415 to |ψmax| = 25.262) and improves heat transfer (from Nu¯ = 17.592 to Nu¯ = 20.421). Low-frequency vibration below 50 has a significant impact on the flow and thermal distributions. However, once this threshold is exceeded, the flow weakens, leading to a gradual decrease in heat transfer rate. The inclination angle is an effective parameter for controlling the flow and temperature characteristics. Thus, transitioning the tilt angle from 30° to 60° can increase the flow velocity (from 22.283 to 23.288) while reducing the Nusselt number (from 16.603 to 13.874). Therefore, by manipulating the combination of vibration and inclination, it is founded that for a fixed frequency value of σ = 100 and for increased amplitude (from 0.5 to 1), the flow intensity at inclination of 60° is boosted, and an increase of the heat transfer rate at inclination of 30° is also observed. Convective thermal instabilities may arise depending on the different key factors. Originality/value: To the best of the authors' knowledge, this study is original in its examination of the combined effects of modulated gravity and cavity inclination on free convection in nanofluid porous media. It highlights the crucial roles of these two important factors in influencing flow and heat transfer properties. [ABSTRACT FROM AUTHOR]

In this paper, we study the influence of the presence of phototactic microorganisms on thermal bioconvection in horizontal porous annulus. To this end, an additional equation describing the concentration of the microorganism cells will be added to the classical ones of heat and hydrodynamics. The Boussinesq and Darcy approximations will be under consideration due to the incompressibility of the fluid in the porous medium. The derived problem with the stream function will be descritized numerically using the alternate direction implicit finite difference method and solved via Thomas algorithm. Numerical simulations have shown that the presence of the microorganisms enhances the heat transfer and has a destabilizing effect on the natural convection. [ABSTRACT FROM AUTHOR]