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The purpose of this paper is to analyze numerically the nanofluid natural convection inside a square enclosure with two L-shaped heaters using lattice Boltzmann method.

An environmentally friendly nanofluid, clove-treated graphene nanoplatelet (CGNP), is used to study the enhancement of heat transfer. Six various heaters configurations are considered and effects of nanoparticle concentration (0–0.1%) and Rayleigh number (10^3–10^6) on streamlines, isothermal lines and heat transfer parameters are studied. The developed computational code has been validated using mesh sensitivity analysis and numerical data of other authors.

It is observed that in contrast to distilled water, CGNP/water nanofluid is an efficient coolant and the Nusselt number is increased as the nanoparticle concentration and Rayleigh numbers increment. The nanoparticle concentration cannot change the flow pattern inside the enclosure. However, the Rayleigh number and heaters configuration can change the flow pattern significantly. Several heaters configurations (Cases 1–4) related to the symmetry of geometrical shape and corresponding boundary conditions, illustrate the symmetry of streamlines and isotherms about the vertical line (X = 0.5). The formation of vortices inside the enclosure is affected by the raising heat plume above the heaters. Moreover, at different Rayleigh numbers, the relative magnitude of average Nu for various cases is different. At Ra = 103, the energy transport characteristic depends on the relative location of heaters and cold walls, and the order of average Nusselt number is Case 3 ˜ Case 4 ˜ Case 6 > Case 1 ˜ Case 2 ˜ Case 5. However, at Ra = 106, an influence of thermal convection mechanism on heat transfer is significant and the ranking of average Nusselt number is Case 1 ˜ Case 4 > Case 5 > Case 6 > Case 2 > Case 3.

The originality of the research lies in both the study of thermogravitational convection in a closed chamber with two L-shaped heaters, and the analysis of the influence of control parameters for an environmentally friendly nanoliquid on electronics cooling process.

This study aims at investigating the heat transfer characteristics of a nonsquare enclosure when hydrodynamic resistance is altered discontinuously along its inner surface. Particularly, it focuses on investigating how several essential factors collaboratively influence the natural convection, including the Rayleigh number (Ra), the aspect ratio (AR), the nanoparticle volume fraction (ϕ) and the locations of changing hydrodynamic resistance.

To achieve these objectives, an L-shaped enclosure of various AR is adopted, while zero local shear resistance is applied and modeled by stress-free (SF) patches of four distinct arrangements (corresponding to Cases 1–4). The nanofluid is modeled by Buongiorno’s two-phase model. The effects are explored using an in-house numerical framework based on a hybrid lattice Boltzmann-finite difference method with the total variation minimization scheme.

The results show that when Ra is sufficiently large, i.e. Ra = 10⁵, SF patches can generally enhance the heat transfer performance regardless of other factors. However, the ways of achieving those enhancements are different, which mainly depend on the arrangement of the SF patches and AR but are nearly independent of ϕ. The maximum improvement of heat transfer can be achieved in Case 3 with AR = 0.6, Ra = 10⁵ and ϕ = 0.04, where the averaged Nusselt number is enhanced by 8.89%.

This study presents a new scenario where the SF patches of various arrangements are applied to enhance the nanofluid natural convection of a nonsquared enclosure, and it reveals how the improvement is achieved and cooperatively affected by several important factors.

Nowadays, the most important challenge in mechanical engineering, power engineering and electronics is a development of effective cooling systems for heat-generating units. Taking into account this challenge, this study aims to deal with computational investigation of thermogravitational energy transport of pseudoplastic nanoliquid in an electronic chamber with a periodic thermally producing unit placed on the bottom heat-conducting wall of finite thickness under an influence of isothermal cooling from vertical side walls.

The control equations formulated using the Boussinesq approach, Ostwald–de Waele power law and single-phase nanofluid model with experimentally based correlations of Guo et al. for nanofluid dynamic viscosity and Jang and Choi for nanofluid thermal conductivity have been worked out by the in-house computational procedure using the finite difference technique. The impact of the Rayleigh number, nanoadditives concentration, frequency of the periodic heat generation from the local element and thickness of the bottom solid substrate on nanoliquid circulation and energy transport has been studied.

It has been found that a raise of the nanoadditives concentration intensifies the cooling of the heat-generating element, while a growth of the heat-generation frequency allows reducing the amplitude of the heater temperature.

Mathematical modeling of a pseudoplastic nanomaterial thermogravitational energy transport in an electronic cabinet with a periodic thermally generating unit, a heat-conducting substrate and isothermal cooling vertical surfaces to identify the possibility of intensifying heat removal from a heated surface.

This paper aims to investigate the free convection, heat transfer and entropy generation numerically and experientially. A numerical/experimental investigation is carried out to investigate the free convection hydrodynamically/thermally and entropy generation.

The coupled lattice Boltzmann method is used as a numerical approach which keeps the significant advantages of standard lattice Boltzmann method with better numerical stability. On the other hand, the thermal conductivity and dynamic viscosity are measured using modern devices in the laboratory.

Some correlations based on the temperature at different nanofluid concentration are derived and used in the numerical simulations. In this regard, the results will be accurate with respect to using theoretical properties of nanofluid, and close agreements will be detected between present results and the previous numerical and experimental works. The numerical investigation is done under the effect of Rayleigh number (103 < Ra < 106), volume concentration of nanofluid (?? = 0.5, 1, 1.5, 2, 2.5 and 3%) and thermal configuration of the cavity (Cases A, B, C and D).

The originality of the present work lies in coupling of the lattice Boltzmann method with experimental observations to analyse the free convection in a cavity.

This study aims to analyze the impact of fractional derivatives on heat transfer and entropy generation during transient free convection inside various complex porous enclosures, such as triangle, L-shape and square-containing wavy surfaces. These porous enclosures are saturated with Cu-water nanofluid and subjected to the influence of a uniform magnetic field.

In the present study, Darcy’s model is used for the momentum transport equation in the porous matrix. Additionally, the Caputo time fractional derivative is introduced in the energy equation to assess the heat transfer phenomenon. Furthermore, the total entropy generation has been computed by combining the entropy generation due to fluid friction (S_ff), heat transfer (S_ht) and magnetic field (S_mf). The complete mathematical model is further simulated using the penalty finite element method, and the Caputo time derivative term is approximated using the L1 scheme. The study is conducted for various ranges of the Rayleigh number (102≤Ra≤104), Hartmann number (0≤Ha≤20) and fractional order parameter (0<α<1) with respect to time.

It has been observed that the fractional order parameter α governs the characteristics of entropy generation and heat transfer within the selected range of parameters. The Bejan number associated with heat transfer (Be_ht), fluid friction (Be_ff) and magnetic field (Be_mf) further demonstrate the dominance of flow irreversibilities. It becomes evident that the initial evolution state of streamlines, isotherms and local entropy varies according to the choice of α. Additionally, increasing Ra values from 10² to 10⁴ shows that the heat transfer rate increases by 123.8% for a square wavy enclosure, 7.4% for a triangle enclosure and 69.6% for an L-shape enclosure. Moreover, an increase in the value of Ha leads to a reduction in heat transfer rates and entropy generation. In this case, Bemf→1 shows the dominance of the magnetic field irreversibility in the total entropy generation.

Recently, fractional-order models have been widely used to express numerous physical phenomena, such as anomalous diffusion and dispersion in complex viscoelastic porous media. These models offer a more accurate representation of physical reality that classical models fail to capture; this is why they find a broad range of applications in science and engineering.

The fractional derivative model is used to illustrate the flow pattern, heat transfer and entropy-generating characteristics under the influence of a magnetic field. Furthermore, to the best of the author’s knowledge, a fractional-derivative-based mathematical model for the entropy generation phenomenon in complex porous enclosures has not been previously developed or studied.

The purpose of this study is to explore the heat transfer enhancement in copper–water nanofluid flowing in a diagonally vented rectangular enclosure with four discrete heaters mounted centrally on the sidewalls and a square-shaped embedded heated block in the influence of a static magnetic field.

Four discrete heaters are mounted centrally on each sidewall of the rectangular enclosure that embraces a heated square block. A static transverse magnetic field is acting on the vertical walls. The Navier–Stokes equations of motion and the energy equation are modified by incorporating Lorentz force and basic physical properties of nanofluid. The derived momentum and energy equations are tackled numerically using the successive over-relaxation technique associating with the Gauss–Seidel iteration technique. The effects of physical parameters connected to dynamics of flow and heat convection are explored from streamlines and isotherms graphs and discussed numerically in terms of Nusselt number.

The effect of the embedded heated square block size and its location in the enclosure, nanoparticles volume fraction and the intensity of the magnetic field on flow and heat transfer are computed. Compared with the case when no heated block is embedded in the enclosure, in free convection at Ra = 106, the average local Nusselt number on the wall-mounted heaters is attenuated by 8.25%, 11.24% and 12.75% when the enclosure embraced a heated square block of side length 10% of H, 20% of H and 30% of H, respectively. An increase in Hartmann number suppresses the heat convection.

The enhancement in the convective heat is greater when the buoyancy effect dominates the viscous effects. Placing the embedded heated block near the inlet vent, the lower temperature zone has reduced while the embedded heated block is at the central location of the enclosure, the high-temperature zone has expanded. The external magnetic field can be used as a non-invasive controlling device.

The numerically simulated results for heat convection of water-based copper nanofluid agreed qualitatively with the existing experimental results.

The models could be used in designing a target-oriented heat exchanger.

The paper includes a comparative study for three locations of the embedded heated square. The optimal results for the centrally located heated block are also performed for three different sizes of the embedded block. The numerically simulated results are compared with the published numerical and experimental studies.

The purpose of this paper is to investigate numerically thermal convection heat transfer in closed square and cubical cavities with local energy sources of various geometric shapes.

The analyzed regions are square and cubical cavities with two isothermally cold opposite vertical walls, whereas other walls are adiabatic. A local energy element of rectangular, trapezoidal or triangular shape is placed on the lower surface of the cabinet. The lattice Boltzmann technique has been used as the main method for the problem solution in two-dimensional (2D) and three-dimensional (3D) formulations, whereas the finite difference technique with non-primitive parameters such as stream function and vorticity has been also used.

The velocity and temperature fields for a huge range of Rayleigh number 104–106, as well as for various geometry shapes of the heater have been studied. A comparative analysis of the results obtained on the basis of two numerical techniques for 2D and 3D formulations has been performed. The dependences of the energy transfer strength in the region on the shape of energy source and Rayleigh number have been established. It has been revealed that the triangular shape of the energy source corresponds to the maximum values of the velocity vector and temperature within the cavity, and the rectangular shape corresponds to the minimum values of these mentioned variables. With the growth of the Rayleigh number, the difference in the values of these mentioned variables for rectangular and triangular shapes of heaters also increases.

The originality of this work is to scrutinize the lattice Boltzmann method and finite difference method for the problem of natural convection in 2D and 3D closed chambers with a local heated element.

The purpose of this study is to investigate the impact of varying baffle height and spacing distance on heat transfer and cooling performance of electronic components in a baffled horizontal channel, using a Cu-H₂O nanofluid under mixed convection and laminar flow.

The mathematical model is two-dimensional and comprises a system of four governing equations, such as the conservation of continuity, momentum and energy. To obtain numerical solutions for these equations, the finite volume method was used for discretization. A validation process was performed by comparing this study’s results with those of previously published studies. The comparison revealed a close agreement. The numerical study was performed for a wide range of key parameters: The baffle height (0 ≤ h ≤ 0.7), the spacing distance between baffle and blocks (0.25 ≤ w ≤ 3), the Grashof and Reynolds numbers are kept equal to 10⁴ and 75, respectively, the channel aspect ratio is L/H = 10, and the volume fraction of Cu nanoparticles is fixed at φ = 5%.

The results of the study reveal a significant improvement in heat transfer in terms of total Nusselt number of the top and bottom hot components, which exhibited an improvement of 16.89% and 17.23% when the baffle height increases from h = 0 to h = 0.7. Additionally, the study found that reducing the distance between the baffle and the electronic components up to a certain limit can improve the heat transfer rate. Therefore, the optimal height of the baffle was found to be no lower than 0.6, and the recommended distance between the heaters and the baffle was 0.5.

This study provides valuable insights into the optimization of the design of baffled channels for improved heat transfer performance. The findings of study can be used to improve heat exchangers and cooling systems in various applications. The use of Cu-H₂O nanofluid under mixed convection and laminar flow conditions in channel with baffle and electronic components is also unique, making this study an original contribution to the field.

This study/paper aims to deal with thermal convection and entropy production of a ferrofluid in an enclosure having an isothermally warmed solid body placed inside. It should be noted that this research deals with a development of passive cooling system for the electronic devices.

The domain of interest is a square chamber of size L including a rectangular solid block of sizes l₁ and l₂. Thermal convection of ferrofluid (water–Fe₃O₄ nanosuspension) is analyzed within this enclosure. The solid body is considered to be isothermal with temperature T_h and also its area is L²/9. The vertical borders are cold with temperature T_c and the horizontal boundaries are adiabatic. The flow driven by temperature gradient in the cavity is two-dimensional. The governing equations, formulated in dimensionless primitive variables with corresponding initial and boundary conditions, are worked out by using the finite volume technique with the semi-implicit method for pressure-linked equations algorithm on a uniformly staggered mesh. The influence of nanoparticles volume fraction, aspect ratio of the solid block and an irreversibility ratio on energy transport and flow patterns are examined for the Rayleigh number Ra = 10⁷.

The results show that the nanoparticles concentration augments the thermal transmission and the entropy production increases also, while the augmentation of temperature difference results in a diminution of entropy production. Finally, lower aspect ratio has the significant impact on heat transfer, isotherms, streamlines and entropy.

An efficient numerical technique has been developed to solve this problem. The originality of this work is to analyze convective energy transport and entropy generation in a chamber with internal block. To the best of the authors’ knowledge, the effects of irreversibility ratio are scrutinized for the first time. The results would benefit scientists and engineers to become familiar with the analysis of convective heat transfer and entropy production in enclosures with internal isothermal blocks, and the way to predict the heat transfer rate in advanced technical systems, in industrial sectors including transportation, power generation, chemical sectors, electronics, etc.