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The purpose of this paper is to numerically study MHD natural convection and entropy generation of Al₂O₃-water alumina nanofluid inside of T-shaped baffled cavity which is subjected to a magnetic field.

Effect of various geometrical, fluid and flow factors such as aspect ratio of enclosure and baffle length, Rayleigh and Hartmann number of nanofluid have been considered in detail. The hydrodynamics and thermal indexes of nanofluid have been described using streamlines, isotherms and isentropic lines.

It is found that by enhancing Hartmann number, symmetrical streamlines gradually lose symmetry and their values decline. It is found that by enhancing Hartmann number, symmetrical streamlines gradually lose symmetry and their values decline. The interesting finding is an increase in the impact of Hartmann number on heat transfer indexes with augmenting Rayleigh number. However, with augmenting Rayleigh number and, thus, strengthening the buoyant forces, the efficacy of Hartmann number one, an index indicating the simultaneous impact of natural heat transfer to entropy generation increases. It is clearly seen that the efficacy of nanofluid on increased Nusselt number enhances with increasing aspect ratio of the enclosure. Based on the results, the Nusselt number generally enhances with the larger baffle length in the enclosure. Finally, with larger Hartmann number and lesser Nusselt one, entropy production is reduced.

The authors believe that all the results, both numerical and asymptotic, are original and have not been published elsewhere.

The purpose of this paper is to numerically examine the conjugate natural convection in an inclined enclosure with a conducting centred block. This enclosure is filled with an Ethylene Glycol‐copper nanofluid. This study utilises numerical simulations to quantify the effects of pertinent parameters such as the Rayleigh number, the solid volume fraction, the length and the thermal conductivity of the centred block and the inclination angle of the enclosure on the conjugate natural convection characteristics.

The SIMPLE algorithm is utilised to solve the governing equations with the corresponding boundary conditions. The convection‐diffusion terms are discretised by a power‐law scheme and the system is numerically modelled in FORTRAN.

The results show that the utilisation of the nanofluid enhances the thermal performance of the enclosure and that the length of the centred block affects the heat transfer rate. The results also show that the higher block thermal conductivity results in a better heat transfer that is most noticeable at low Rayleigh numbers, and that increasing the inclination angle improves the heat transfer, especially at high Rayleigh numbers.

This paper presents an original research on conjugate natural convection in nanofluid‐filled enclosures.

The purpose of this paper is to address various works on mixed convection and proposes 10 unified models (Models 1–10) based on various thermal and kinematic conditions of the boundary walls, thermal conditions and/ or kinematics of objects embedded in the cavities and kinematics of external flow field through the ventilation ports. Experimental works on mixed convection have also been addressed.

This review is based on 10 unified models on mixed convection within cavities. Models 1–5 involve mixed convection based on the movement of single or double walls subjected to various temperature boundary conditions. Model 6 elucidates mixed convection due to the movement of single or double walls of cavities containing discrete heaters at the stationary wall(s). Model 7A focuses mixed convection based on the movement of wall(s) for cavities containing stationary solid obstacles (hot or cold or adiabatic) whereas Model 7B elucidates mixed convection based on the rotation of solid cylinders (hot or conductive or adiabatic) within the cavities enclosed by stationary or moving wall(s). Model 8 is based on mixed convection due to the flow of air through ventilation ports of cavities (with or without adiabatic baffles) subjected to hot and adiabatic walls. Models 9 and 10 elucidate mixed convection due to flow of air through ventilation ports of cavities involving discrete heaters and/or solid obstacles (conductive or hot) at various locations within cavities.

Mixed convection plays an important role for various processes based on convection pattern and heat transfer rate. An important dimensionless number, Richardson number (Ri) identifies various convection regimes (forced, mixed and natural convection). Generalized models also depict the role of “aiding” and “opposing” flow and combination of both on mixed convection processes. Aiding flow (interaction of buoyancy and inertial forces in the same direction) may result in the augmentation of the heat transfer rate whereas opposing flow (interaction of buoyancy and inertial forces in the opposite directions) may result in decrease of the heat transfer rate. Works involving fluid media, porous media and nanofluids (with magnetohydrodynamics) have been highlighted. Various numerical and experimental works on mixed convection have been elucidated. Flow and thermal maps associated with the heat transfer rate for a few representative cases of unified models [Models 1–10] have been elucidated involving specific dimensionless numbers.

This review paper will provide guidelines for optimal design/operation involving mixed convection processing applications.

Water/Al₂O₃ nanofluid with volume fractions of 0, 0.3 and 0.06 was investigated inside a rectangular microchannel. Jet injection of nanofluid was used to enhance the heat transfer under a homogeneous magnetic field with the strengths of Ha = 0, 20 and 40. Both slip velocity and no-slip boundary conditions were used.

The laminar flow was studied using Reynolds numbers of 1, 10 and 50. The results showed that in creep motion state, the constricted cross section caused by fluid jet is not observable and the rise of axial velocity level is only because of the presence of additional size of the microchannel. By increasing the strength of the magnetic field and because of the rise of the Lorentz force, the motion of fluid layers on each other becomes limited.

Because of the limitation of sudden changes of fluid in jet injection areas, the magnetic force compresses the fluid to the bottom wall, and this behavior limits the vertical velocity gradients. In the absence of a magnetic field and under the influence of the velocity boundary layer, the fluid motion has more variations. In creeping velocities of fluid, the presence or absence of the magnetic field does not have an essential effect on Nusselt number enhancement.

In lower velocities of fluid, the effect of the jet is not significant, and the thermal boundary layer affects the entire temperature field. In this case, for Hartmann numbers of 40 and 0, changing the Nusselt number on the heated wall is similar.

The purpose of this paper is to make a numerical study of natural convection of water‐based nanofluids in a square cavity when a discrete heat source is embedded on the bottom wall, applying a “nanofluid‐oriented” model for the calculation of the effective thermal conductivity (Xu‐Yu‐Zou‐Xu's model) and the effective dynamic viscosity (Jang‐Lee‐Hwang‐Choi's model). Another motivation is the numerical solution of the equations of the flow with a meshless method.

A meshless point collocation method with moving least squares (MLS) approximation is used. A test validation study of the numerical method takes place for pure water flow, as well for water/Al₂O₃ nanofluids. The influence of pertinent parameters such as Rayleigh number (Ra), the non‐uniform nanoparticle size keeping the mean nanoparticle diameter fixed, the volume fraction of nanoparticles and the location of heat source on the cooling performance are studied.

The presence of a discrete heat source, as well as the various thermal boundary conditions affects the characteristics of the nanofluid flow and heat transfer. When the ratio of minimum to maximum nanoparticle diameter is increased, the local Nusselt number is increased and the heat source temperature is decreased. The increase of solid volume fraction of nanoparticles causes the heat source maximum temperature to decrease and the Nusselt Number to increase.

The present study constitutes an original contribution to the nanofluid flow and heat transfer characteristics when a discrete heat source is presence. “Nanofluid‐oriented” models are used for the calculation of the effective thermal conductivity and dynamic viscosity.

The purpose of this study is to indicate the effect of mounting heat generating porous matrix in a close cavity on the Brownian term of CuO-water nanofluid and its impact on improving the Nusselt number.

Because of the presence of heat source in porous matrix, couple of energy equations is solved for porous matrix and nanofluid separately. Thermal conductivity and viscosity of nanofluid were assumed to be consisting of a static component and a Brownian component that were functions of volume fraction of the nanofluid and temperature. To explain the effect of the Brownian term on the flow and heat fields, different parameters such as heat conduction ratio, interstitial heat transfer coefficient, Rayleigh number, concentration of nanoparticles and porous material porosity were investigated and compared to those of the non-Brownian solution.

The Brownian term caused the cooling of porous matrix because of rising thermal conductivity. Mounting the porous material into cavity changes the temperature distribution and increases Brownian term effect and heat transfer functionality of the nanofluid. Besides, the effect of the Brownian term was seen to be greatest at low Rayleigh number, low-porosity and small thermal conductivity of the porous matrix. It is noteworthy that because of decrement of thermal conduction in high porosities, the impact of Brownian term drops severely making it possible to obtain reliable results even in the case of neglecting Brownian term in these porosities.

The effect of mounting the porous matrix with internal heat generation was investigated on the improvement of variable properties of nanofluid.

The purpose of this paper is to study natural convection heat transfer and fluid flow in a square cavity filled with CuO-water nanofluid.

The entire length of the bottom wall of the cavity is covered by two pairs of heat source-sink, whereas the other walls are insulated. The governing equations of fluid flow are discretized using a finite volume method with a collocated grid arrangement. The coupling between velocity and pressure is solved using the SIMPLEC and the Rhie and Chow interpolation is used to avoid the checker-board solutions for the pressure.

The numerical results are reported for the effect of Rayleigh number, solid volume fraction and both presence and absence of thermophoresis and Brownian motion effects. The numerical results show an improvement in heat transfer rate for the whole range of Rayleigh numbers when Brownian and thermophoresis effects are considered. Furthermore, an increase in the Rayleigh number and nanoparticle volume fraction in both cases – when Brownian and thermophoresis effects are neglected or considered – has an excellent influence on heat transfer of nanofluids.

The area of nanofluids is very original.

The purpose of this study is to numerically investigate the effect of jet impingement, magnetic field and nanoparticle shape (sphericity) on the hydrodynamic/heat transfer characteristics of nanofluids over stationary and vibrating plates.

A two-dimensional finite volume method-based homogeneous heat transfer model has been developed, validated and used in the present investigation. Three different shapes of non-spherical carbon nanoparticles namely nanotubes, nanorods and nanosheets are used in the analysis. Sphericity-based effective thermal conductivity of nanofluids with Brownian motion of nanoparticles is considered in the investigation. Moreover, the ranges of various comprehensive parameters used in the study are Re = 500 to 900, St = 0.0694 to 0.2083 and Ha = 0 to 80.

The hydrodynamic/heat transfer performance of jet impingement in the case of vibrating plate is 298 per cent higher than that of stationary plate at Re = 500. However, for the case of vibrating plate, a reduction in the heat transfer performance of 23.35 per cent is observed by increasing the jet Reynolds number from 500 to 900. In the case of vibrating plate, the saturation point for Strouhal number is found to be 0.0833 at Re = 900 and Ha = 0. Further decrement in St beyond this limit leads to a drastic reduction in the performance. Moreover, no recirculation in the flow is observed near the stagnation point for jet impingement over vibrating plate. It is also observed that the effect of magnetic field enhances the performance of jet impingement over a stationary plate by 36.18 per cent at Ha = 80 and Re = 900. Whereas, opposite trend is observed for the case of vibrating plate. Furthermore, at Re = 500, the percentage enhancement in the Nuavg values of 3 Vol.% carbon nanofluid with nanosheets, nanorods and nanotubes are found to be 47.53, 26.86 and 26.85 per cent when compared with the value obtained for pure water.

The present results will be useful in choosing nanosheets-based nanofluid as the efficient heat transfer medium in cooling of high power electronic devices. Moreover, the obtained saturation point in the Strouhal number of the vibrating plate will help in cooling of turbine blades, as well as paper and textile drying. Moreover, the developed homogeneous heat transfer model can also be used to study different micro-convection phenomena in nanofluids by considering them as source terms in the momentum equation.

Impingement of jet over two different plate types such as stationary and vibrating is completely analyzed with the use of a validated in-house FVM code. A complete investigation on the influence of external magnetic field on the performance of plate type configuration is evaluated. The three fundamental shapes of carbon nanoparticles are also evaluated to obtain sphericity based hydrodynamic/heat transfer performance of jet impingement.

The purpose of this study is to investigate the influence of enclosure shape on magnetohydrodynamic (MHD) nanofluidic flow, heat transfer and irreversibility in square, trapezoidal and triangular thermal systems under fluid volume constraints, with the aim of optimizing thermal behavior in diverse applications.

The study uses numerical simulations based on a finite element-based technique to analyze the effects of the Rayleigh number (Ra), Hartmann number (Ha), magnetic field orientation (γ) and nanoparticle concentration (ζ) on heat transfer characteristics and thermodynamic entropy production.

The key findings reveal that the geometrical design significantly influences fluid velocity, heat transfer and irreversibility. Trapezoidal thermal systems outperform square systems, while triangular systems achieve optimal enhancement. Nanoparticle concentration enhances heat transfer and flow strength at higher Rayleigh numbers. The magnetic field intensity has a significant impact on fluid flow and heat transport in natural convection, with higher Hartmann numbers resulting in reduced flow strength and heat transfer. The study also highlights the influence of various parameters on thermodynamic entropy production.

Further research can explore additional geometries, parameters and boundary conditions to expand the understanding of enclosure shape effects on MHD nanofluidic flow and heat transfer. Experimental validation can complement the numerical simulations presented in this study.

This study provides valuable insights into the impact of enclosure shape on heat transfer performance in MHD nanofluid flow systems. The findings contribute to the optimization of thermal behavior in applications such as electronics cooling and energy systems. The comparison of different enclosure shapes and the analysis of thermodynamic entropy production add novelty to the study.

This paper aims to numerically investigate the magnetohydrodynamic (MHD) convection heat transfer of nanofluid inside a differentially heated enclosure with various fin morphologies.

The fluid flow within the cavity was governed by N-S equations while it within porous medium was solved by the non-Darcy model, called the Darcy–Forchheimer model based on representative element-averaging method. Empirical correlations from experimental data are used to evaluate the effective thermal conductivity and dynamic viscosity. Relevant governing parameters, including thermal Rayleigh number (10⁵-10⁷), Hartmann number (0-50), Darcy number (10⁻⁶-10⁻¹), thermal conductivity ratio of porous matrix (1-10³), nanoparticles volume fraction (0-0.04) and topology designs of porous fins, are sensitively varied to identify their effects and roles on the fluid flow and heat transfer. Particularly, heatlines are used to investigate the mechanism of heat transport.

Numerical results demonstrate that the predictions of average Nusselt number are augmented by using more porous fins with high permeability, and this effect becomes opposite in tiny Darcy numbers. Particularly, for high Darcy and Rayleigh numbers, the shortest fins could achieve the best performance of heat transfer. In addition, the prediction of average Nusselt number reduces with an increase in Hartmann numbers. An optimal nanoparticles concentration also exists to maximize heat transfer enhancement. Finally, numerical correlations for the average Nusselt number were proposed as functions of these governing parameters.

Present work could benefit the thermal design of electronic cooling and thermal carriers in nanofluid engineering.

Present work could benefit the thermal design of electronic cooling and thermal carriers in nanofluid engineering. In addition, optimum thermal removals could enhance the lifetime of electronics, therefore reducing the cost of energy and materials.

To the best knowledge of authors, there are not any studies considering the synergetic effects of porous fins on MHD convection of nanofluids. Present work could benefit the thermal design of electronic cooling and thermal carriers in nanofluid engineering.