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The purpose of this paper is to examine numerically the three natural convection of air induced by temperature difference between a cold outer cubic enclosure and a hot inner cylinder. Simulations have been carried out for Rayleigh numbers ranging from 103 to 107 and titled angle of the enclosure from 0° to 90°. The developed mathematical model is governed by the coupled equations of continuity, momentum and energy, and is solved by finite volume method. The effects of cylinder inclination and Rayleigh number on fluid flow and heat transfer are presented. The distribution of isocontours of temperature and isosurfaces of velocity eventually reaches a steady state in the range of Rayleigh numbers between 103 and 107 for titled inclination of 90°; however, for the remaining inclinations, Rayleigh number must be in the range 103-106 to avoid unsteady state, which is manifested by the division of the area containing the maximum local heat transfer rate into three parts for a Rayleigh number equal to 107 and an inclination of 90°. We mention that instability study is not included in the present paper, which is solely devoted to three-dimensional calculations. Results also indicate that optimal average heat transfer rate is obtained for both high Rayleigh number of 106 and high inclination of 90° for the two cases of the inner cylinder and cubical enclosure.

The manuscript deals with prediction of the three-dimensional natural convection phenomena in a cubical cavity induced by an isothermal cylinder at the center with different inclinations by simulating the flow using highly numerical methods such as finite volume method.

It is found that the local Nusselt number through active walls for titled inclination set at 90°, the symmetry of the flow is conserved and the area containing the maximum heat transfer is divided into three smaller areas situated near the upper portion of the wall, taking the maximum value. That may be due to the preparation of local occurrence of instabilities and bifurcation phenomena that appear for Ra > 107, which is not included in the present paper to save journal space. It was found also that an optimal heat transfer appears when the cylinder orientation becomes vertical (a = 90°). For this inclination, buoyancy forces act upward, corresponding to an aiding situation. In addition, heat transfer rate is increasing with Rayleigh numbers, so correlations of average Nusselt through the cubical cavity and the cylinder are established as function of two parameters (Ra, a). Comparisons of the numerical results with those obtained from all correlations show good agreements.

To the author’s knowledge, studies have thus far adressed three-dimensional cuboids enclosures induced by an inner shape which the location is changed. However, no study has examined three-dimensional natural convection between the inner isothermal cylinder and outer cooled cubical enclosure when the outer enclosure is tilted.

The purpose of this paper is to carry out a comprehensive review of some latest studies devoted to natural convection phenomenon in the enclosures because of its significant industrial applications.

Geometries of the enclosures have considerable influences on the heat transfer which will be important in energy consumption. The most useful geometries in engineering fields are treated in this literature, and their effects on the fluid flow and heat transfer are presented.

A great variety of geometries included with different physical and thermal boundary conditions, heat sources and fluid/nanofluid media are analyzed. Moreover, the results of different types of methods including experimental, analytical and numerical are obtained. Different natures of natural convection phenomenon including laminar, steady-state and transient, turbulent are covered. Overall, the present review enhances the insight of researchers into choosing the best geometry for thermal process.

A comprehensive review on the most practical geometries in the industrial application is performed.

Thermo-magnetic convective flow analysis under the impact of thermal radiation for heat and entropy generation phenomena is an active research field for understanding the efficiency of thermodynamic systems in various engineering sectors. This study aims to examine the characteristics of convective heat transport and entropy generation within an inverted T-shaped porous enclosure saturated with a hybrid nanofluid under the influence of thermal radiation and magnetic field.

The mathematical model incorporates the Darcy-Forchheimer-Brinkmann model and considers thermal radiation in the energy balance equation. The complete mathematical model has been numerically simulated through the penalty finite element approach at varying values of flow parameters, such as Rayleigh number (Ra), Hartmann number (Ha), Darcy number (Da), radiation parameter (Rd) and porosity value (e). Furthermore, the graphical results for energy variation have been monitored through the energy-flux vector, whereas the entropy generation along with its individual components, namely, entropy generation due to heat transfer, fluid friction and magnetic field, are also presented. Furthermore, the results of the Bejan number for each component are also discussed in detail. Additionally, the concept of ecological coefficient of performance (ECOP) has also been included to analyse the thermal efficiency of the model.

The graphical analysis of results indicates that higher values of Ra, Da, e and Rd enhance the convective heat transport and entropy generation phenomena more rapidly. However, increasing Ha values have a detrimental effect due to the increasing impact of magnetic forces. Furthermore, the ECOP result suggests that the rising value of Da, e and Rd at smaller Ra show a maximum thermal efficiency of the mathematical model, which further declines as the Ra increases. Conversely, the thermal efficiency of the model improves with increasing Ha value, showing an opposite trend in ECOP.

Such complex porous enclosures have practical applications in engineering and science, including areas like solar power collectors, heat exchangers and electronic equipment. Furthermore, the present study of entropy generation would play a vital role in optimizing system performance, improving energy efficiency and promoting sustainable engineering practices during the natural convection process.

To the best of the authors’ knowledge, this study is the first ever attempted detailed investigation of heat transfer and entropy generation phenomena flow parameter ranges in an inverted T-shaped porous enclosure under a uniform magnetic field and thermal radiation.

A numerical simulation has been carried out to investigate the buoyancy induced flow and heat transfer characteristics inside a wavy walled enclosure. The enclosure consists of two parallel wavy and two straight walls. The top and the bottom walls are wavy and kept isothermal. Two straight‐vertical sidewalls are considered adiabatic. Governing equations are discretized using the control volume based finite‐volume method with collocated variable arrangement. Simulation was carried out for a range of surface waviness ratios, λ=0.00‐0.25; aspect ratios, A=0.25‐0.5; and Rayleigh numbers Ra=10⁰‐10⁷ for a fluid having Prandtl number equal to 1.0. Results are presented in the form of local and global Nusselt number distributions, streamlines, and isothermal lines for different values of surface waviness and aspect ratios. For a special case of λ=0 and A=1.0, the average Nusselt number distribution is compared with available reference. The results suggest that natural convection heat transfer is changed considerably when surface waviness changes and also depends on the aspect ratio of the domain. In addition to the heat transfer results, the heat transfer irreversibility in terms of Bejan number (Be) was measured. For a set of selected values of the parameters (λ, A, and Ra), a contour of the Bejan number is presented at the end of this paper.

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.

This paper aims to numerically investigate the heat transfer and entropy generation characteristics of water-based hybrid nanofluid in natural convection flow inside a concentric horizontal annulus.

The hybrid nanofluid is prepared by suspending tetramethylammonium hydroxide-coated Fe₃O₄ (magnetite) nanoparticles and gum arabic (GA)-coated carbon nanotubes (CNTs) in water. The effects of nanoparticle volume concentration and Rayleigh number on the streamlines, isotherms, average Nusselt number and the thermal, frictional and total entropy generation rates are investigated comprehensively.

Results show the advantageous effect of hybrid nanofluid on the average Nusselt number. Furthermore, the study of entropy generation shows the increment of both frictional and thermal entropy generation rates by increasing Fe₃O₄ and CNT concentrations at various Rayleigh numbers. Increasing Rayleigh number from 103 to 105, at Fe₃O₄ concentration of 0.9 per cent and CNT concentration of 1.35 per cent, increases the average Nusselt number, thermal entropy generation rate and frictional entropy generation rate by 224.95, 224.65 and 155.25 per cent, respectively. Moreover, increasing the Fe₃O₄ concentration from 0.5 to 0.9 per cent, at Rayleigh number of 105 and CNT concentration of 1.35 per cent, intensifies the average Nusselt number, thermal entropy generation rate and frictional entropy generation rate by 18.36, 22.78 and 72.7 per cent, respectively.

To the best knowledge of the authors, there are not any archival publications considering the detailed behaviour of the natural convective heat transfer and entropy generation of hybrid nanofluid in a concentric annulus.

This paper aims to numerically investigate the natural convection heat transfer of multi-wall carbon nanotubes (MWCNTs)-water nanofluid in U-shaped enclosure equipped with a hot obstacle by using the lattice Boltzmann method.

The combination of the three topics (U-shaped enclosure, different positions of the hot obstacle and MWCNTs-water nanofluid) is innovative in the present study. In total, 15 different positions of the hot obstacle have been arranged, and the effects of pertinent parameters such as Rayleigh numbers, the solid volume fraction of the MWCNTs nanoparticles on the flow field, temperature distribution and the rate of heat transfer inside the enclosure are also investigated.

It is found that the average Nusselt number increased by raising the Rayleigh number, and so did the nanoparticle solid volume fraction regardless the position of the hot obstacle. Moreover, enclosures where the hot obstacle is located at the bottom region proved to provide a better rate of heat transfer at high Rayleigh number (106). It is concluded that at a low Ra number (103-105), the higher heat transfer rate and Nu number will be obtained when the hot obstacle is located in the left or right channel.

In the literature, no trace of studying the natural convection of nanofluids in U-shaped enclosures with heating obstacles was found. Also, MWCNTs were less used as nanoparticles. As the natural convection of nanofluids in thermal engineering applications would expand the existing knowledge, the current researchers conducted a numerical study of the natural convection of Maxwell nanofluid with MWCNTs in U-shaped enclosure equipped with a hot obstacle by using lattice Boltzmann method.

The purpose of this study is to address magnetohydrodynamic (MHD) bioconvection caused by the swimming of oxytactic microorganisms in a linearly heated square cavity filled with porous media and Cu–water nanofluid. The effects of different multiphysical aspects are demonstrated using local distributions as well as global quantities for fluid flow, temperature, oxygen concentration and microorganisms population.

The coupled transport equations are converted into the nondimensional partial differential equations, which are solved numerically using a finite volume-based computing code. The flow of Cu–water nanofluid through the pores of porous media is formulated following the Brinkman–Forchheimer–Darcy model. The swimming of oxytactic microorganisms is handled following a continuum model.

The analysis of transport phenomena of bioconvection is performed in a linearly heated porous enclosure containing Cu–water nanofluid and oxytactic microorganisms under the influence of magnetic fields. The application of such a system could have potential impacts in diverse fields of engineering and science. The results show that the flow and temperature distribution along with the isoconcentrations of oxygen and microorganisms is markedly affected by the involved governing parameters.

Similar study of bioconvection could be extended further considering thermal radiation, chemical attraction, gravity and light.

The outcomes of this investigation could be used in diverse fields of multiphysical applications, such as in food industries, chemical processing equipment, fuel cell technology and enhanced oil recovery.

The insight of the linear heating profile reveals a special attribute of simultaneous heating and cooling zones along the heated side. With such an interesting feature, the MHD bioconvection of oxytactic microorganisms in nanofluid-filled porous substance is not reported so far.

The purpose of this study is to numerically analyze the mixed convection and entropy generation in an annulus with a rotating heated inner cylinder for single-wall carbon nanotube (SWCNT)–water nanofluid flow using local thermal nonequilibrium (LTNE) model. An examination of the system behavior is presented considering the heat-generating solid phase inside the porous layer partly filled at the inner surface of the outer cylinder.

The discretized governing equations for nanofluid and porous layer by means of the finite volume method are solved by using the SIMPLE algorithm.

It is found that the buoyancy force and rotational effect have an important impact on the change of the strength of streamlines and isotherms for nanofluid flow. The minimum average Nusselt number on the inner cylinder is obtained at Ra$_E$ = 10$^4$, and the minimum total entropy generation is found at Re = 400 for given parameters. The entropy generation minimization is determined in case of different nanoparticle volume fractions. It is observed that at the same external Rayleigh numbers, the LTNE condition obtained with internal heat generation is very different from that without heat generation.

To the best of the authors’ knowledge, there is no previous paper presenting mixed convection and entropy generation of SWCNT–water nanofluid in a porous annulus under LTNE condition. The addition of nanoparticles to based fluid leads to a decrease in the value of minimum total entropy generation. Thus, using nanofluid has a significant role in the thermal design and optimization of heat transfer applications.

This paper aims to perform the lattice Boltzmann simulation of natural convection heat transfer in cavities included with active hot and cold walls at the side walls and internal hot and cold obstacles.

The cavity is filled with double wall carbon nanotubes (DWCNTs)-water nanofluid. Different approaches such as local and total entropy generation, local and average Nusselt number and heatline visualization are used to analyze the natural convection heat transfer. The cavity is filled with DWCNTs-water nanofluid and the thermal conductivity and dynamic viscosity are measured experimentally at different solid volume fractions of 0.01 per cent, 0.02 per cent, 0.05 per cent, 0.1 per cent, 0.2 per cent and 0.5 per cent and at a temperature range of 300 to 340 (K).

Two sets of correlations for these parameters based on temperature and solid volume fraction are developed and used in the numerical simulations. The influences of different governing parameters such as Rayleigh number, solid volume fraction and different arrangements of active walls on the fluid flow, heat transfer and entropy generation are presented, comprehensively. It is found that the different arrangements of active walls have pronounced influence on the flow structure and heat transfer performance. Furthermore, the Nusselt number has direct relationship with Rayleigh number and solid volume fraction. On the other hand, the total entropy generation has direct and reverse relationship with Rayleigh number and solid volume fraction, respectively.

The originality of this work is to analyze the two-dimensional natural convection using lattice Boltzmann method and different approaches such as entropy generation and heatline visualization.