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The purpose of this paper is to investigate the effects of Ha and the Nanoparticles (NP) volume fraction over the irreversibility and heat transport in Darcy–Forchheimer nanofluid saturated lid-driven porous medium.

The present paper highlights entropy generation because of mixed convection for a lid-driven porous enclosure filled through a nanoliquid and submitted to a uniform magnetic field. The analysis is achieved using Darcy–Brinkman–Forchheimer technique. The set of partial differential equations governing the considered system was numerically solved using the finite element method.

The main observations are as follows. The results indicate that the movement of horizontal wall is an important factor for the entropy generation inside the porous cavity filled through Cu–water nanoliquid. The variation of the thermal entropy generation is linear through NPs volume fraction. The total entropy generation reduces when the Darcy, Hartmann and the nanoparticle volume fraction increase. The porous media and magnetic field effects reduce the total entropy generation.

Interest in studying thermal interactions by convective flow within a saturating porous medium has many fundamental considerations and has received extensive consideration in the literature because of its usefulness in a large variety of engineering applications, such as the energy storage and solar collectors, crystal growth, food processing, nuclear reactors and cooling of electronic devices, etc.

By examining the literature, the authors found that little attention has been paid to entropy generation encountered during convection of nanofluids. Hence, this work aims to numerically study entropy generation and heat transport in a lid-driven porous enclosure filled with a nanoliquid.

The purpose of this paper is to investigate the mixed convection of a two-phase water–aluminum oxide nanofluid in a cavity under a uniform magnetic field.

The upper wall of the cavity is cold and the lower wall is warm. The effects of different values of Richardson number, Hartmann number, cavitation length and solid nanoparticles concentration on the flow and temperature field and heat transfer rate were evaluated. In this paper, the heat flux was assumed to be constant of 10 (W/m²) and the Reynolds number was assumed to be constant of 300 and the Hartmann number and the volume fraction of solid nanoparticles varied from 0 to 60 and 0 to 0.06, respectively. The Richardson number was considered to be 0.1, 1 and 5. Aspect ratios were 1, 1.5 and 2.

Comparison of the results of this paper with the results of the numerical and experimental studies of other researchers showed a good correlation. The results were presented in the form of velocity and temperature profiles, stream and isotherm lines and Nusselt numbers. The results showed that by increasing the Hartmann number, the heat transfer rate decreases. An increase from 0 to 20 in Hartmann number results in a 20 per cent decrease in Nusselt numbers, and by increasing the Hartmann number from 20 to 40, a 16 per cent decrease is observed in Nusselt number. Accordingly, it is inferred that by increasing the Hartmann number, the reduction in the Nusselt number is decreased. As the Richardson number increased, the heat transfer rate and, consequently, the Nusselt number increased. Therefore, an increase in the Richardson number results in an increase of the Nusselt number, that is, an increase in Richardson number from 0.1 to 1 and from 1 to 5 results in 37 and 47 per cent increase in Nusselt number, respectively.

Even though there have been numerous investigations conducted on convection in cavities under various configurations and boundary conditions, relatively few studies are conducted for the case of nanofluid mixed convection in square lid-driven cavity under the effect of magnetic field using two-phase model.

The purpose of this paper is to model mixed convection in a square cavity included circular cylinders motion using an incompressible smoothed particle hydrodynamics (ISPH) technique.

The problem is solved numerically by using the ISPH method.

The SPH tool shows robust performance to simulate the rigid body motion in the mixed convective flow with heat transfer, and it may apply easily to complicated problems in 2D and 3D problem without difficulties.

The application of the SPH method to mixed convective flow with heat transfer and its potential application easily to complicated 3D problems is original.

This paper aims to study the mixed convective process due to various dynamics, namely, inner rotating cylinders and upper-wavy wall movement for the first time.

The Galerkin finite element method together with the characteristic-based split scheme is applied to solve the governing system.

The main outcomes revealed that the direction of the rotation of the cylinders, radius and locations of the rotating shapes are beneficial controlling elements for the enhancement of heat transfer. Also, for all the considered cases, values of the Bejan number indicate that the fluid friction irreversibility is dominance compared to the heat transfer irreversibility. Further, average values of the heat transfer entropy, fluid friction entropy and total entropy are minimized in the case of fixed cylinders regardless of the cylinder radius.

The authors are interested in the mixed convection case due to regular boundaries and hence this simulation purposes a first attempt to examine the mixed convective flow due to irregular wavy boundaries. This study considered various dynamics, namely, inner rotating cylinders and wavy-lid driven wall which makes it more attractive to the readers. Various cases based on radius of the cylinder and direction of the rotations together with several locations of the rotating shapes are taken into account which makes the current simulation is comprehensive. Various studies presented in this field are made by commercial software and these treatments need special conditions (having limitation) but the current solution methodology is based on a finite element method home-code. Various important impacts, are, also, examined, namely, inclined geometry, inclined magnetic field, thermal radiation and heat generation/absorption. The entropy of the current complex system is analyzed based on the second law of thermodynamics.

The main purpose of this work is to arrive at a three-dimensional (3D) numerical solution on mixed convection in a cubic cavity with a longitudinally located triangular fin in different sides.

The 3D governing equations are solved via finite volume technique by writing a code in FORTRAN platform. The governing parameters are chosen as Richardson number, 0.01 ≤ Ri ≤ 10 and thermal conductivity ratio 0.01 ≤ Rc ≤ 100 for fixed parameters of Pr = 0.7 and Re = 100. Two cases are considered for a lid-driven wall from left to right (V+) and right to left (V−).

It is observed that entropy generation due to heat transfer becomes dominant onto entropy generation because of fluid friction. The most important parameter is the direction of the moving lid, and lower values are obtained when the lid moves from right to left.

The main originality of this work is to arrive at a solution of a 3D problem of mixed convection and entropy generation for lid-driven cavity with conductive triangular fin attachments.

This study aims to numerically analyse the impact of an inclined magnetic field and Joule heating on the conjugate heat transfer because of the mixed convection of an Al₂O₃–water nanofluid in a thick wall enclosure.

A horizontal temperature gradient together with the shear-driven Flow creates the mixed convection inside the enclosure. The nonhomogeneous model, in which the nanoparticles have a slip velocity because of thermophoresis and Brownian diffusion, is adopted in the present study. The thermal performance is evaluated by determining the entropy generation, which includes the contribution because of magnetic field. A control volume method over a staggered grid arrangement is adopted to compute the governing equations.

The Lorentz force created by the applied magnetic field has an adverse effect on the flow and thermal field, and consequently, the heat transfer and entropy generation attenuate because of the presence of magnetic force. The Joule heating enhances the fluid temperature but attenuates the heat transfer. The impact of the magnetic field diminishes as the angle of inclination of the magnetic field is increased, and it manifests as the volume fraction of nanoparticles is increased. Addition of nanoparticles enhances both the heat transfer and entropy generation compared to the clear fluid with enhancement in entropy generation higher than the rate by which the heat transfer augments. The average Bejan number and mixing-cup temperature are evaluated to analyse the thermodynamic characteristics of the nanofluid.

This literature survey suggests that the impact of an inclined magnetic field and Joule heating on conjugate heat transfer based on a two-phase model has not been addressed before. The impact of the relative slip velocity of nanoparticles diminishes as the magnetic field becomes stronger.