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Nusselt-Rayleigh-Fourier type correlations are proposed to quantify the temporal evolution of convective heat transfer occurring within air-filled hemispherical enclosures whose disk, initially at ambient temperature, is suddenly maintained at a higher temperature. The temperature difference imposed between this hot wall and the isothermal cold dome involves Rayleigh number varying between 104 and 2.55×1012. Depending on the application, the disk can be inclined with respect to the horizontal plane by an angle varying between 0° (horizontal disk) and 90° (vertical disk) in steps of 15°. The paper aims to discuss these issues.

The results are obtained by means of a numerical approach based on the finite volume method. The proposed correlations linked to the steady state Nusselt-Rayleigh internships recently published, concerning the same inclination angle and Rayleigh ranges.

The statistical analysis of a large number of calculations leads to reliable results covering laminar, transitional and turbulent natural convection heat transfer zones.

The proposed relationships can be applied in several engineering fields such as nuclear technology, solar energy, security and safety electronics, building, domotics or aeronautics.

The new relationships proposed in this paper provide important information on the evolution of convective heat transfer during the transient regime.

The purpose of this study is to quantify the free convective heat transfer around a vertical cylindrical electronic component equipped with vertical fins representing an antenna, contained in a closed cavity maintained isothermal. Its cooling is provided via a water-based copper nanofluid whose volume fraction varies between 0% and 10%. Its effective viscosity and thermal conductivity are determined with the Brinkman and Maxwell models.

The governing equation system has been solved by means of the volume control method based on the SIMPLE algorithm.

A Nusselt-Rayleigh correlation valid in the 3.32 × 10⁵ – 6.74 × 10⁷ Rayleigh number range is proposed. It allows the thermal sizing of the considered system used in high power electronics to ensure their correct operation in the worst conditions.

The proposed correlations are original and unpublished.

The main purpose of this work is to quantify the convective heat transfer occurring between two inclined and concentric hemispheres.

The inner one is an electronic assembly generating a constant heat flux during operation. The outer hemisphere is maintained isothermal at cold temperature. The interstitial space is air-filled. The base of the equipment can be inclined with respect to the horizontal plane by an angle ranging from 0° (horizontal position with dome faced upwards) to 180° (horizontal position with dome faced downwards).

Nusselt–Rayleigh correlations are proposed for several configurations obtained by varying the generated power and the base inclination. The large resulting Rayleigh number ranging between 2.4 × 10⁵ and 1.7 × 10⁷ allows using these new and original correlations in various engineering fields, such as electronics in the present work. The calculations are realized by means of a 3D numerical approach based on the finite volume method.

The geometry and the thermal boundary conditions considered in the present survey are suitable for applications in many engineering areas.

Natural convection with heat transfer in porous media has been subject of extensive study in engineering due to its numerous applications. A case of particular interest is the Bénard-type flow.The paper aims to discuss this issue.

Based on the network simulation method in order to solve this problem, a numerical model is proposed.

Nusselt-Rayleigh correlation is determined for a broad range of Rayleigh, the dimensionless number that influences the solution, above and below the threshold which separates the conduction and convection pure mechanisms.

Based on the network simulation method.

This study aims to carry out the analysis of Rayleigh-Bénard convection within enclosures with curved isothermal walls, with the special implication on the heat flow visualization via the heatline approach.

The Galerkin finite element method has been used to obtain the numerical solutions in terms of the streamlines (ψ ), heatlines (Π), isotherms (θ), local and average Nusselt number ( Nut¯) for various Rayleigh numbers (10³ ≤ Ra ≥ 10⁵), Prandtl numbers (Pr = 0.015 and 7.2) and wall curvatures (concavity/convexity).

The presence of the larger fluid velocity within the curved cavities resulted in the larger heat transfer rates and thermal mixing compared to the square cavity. Case 3 (high concavity) exhibits the largest Nut¯ at the low Ra for all Pr. At the high Ra, Nut¯ is the largest for Case 3 (high concavity) at Pr = 0.015, whereas at Pr = 7.2, Nut¯ is the largest for Case 1 (high concavity and convexity).

The results may be useful for the material processing applications.

The study of Rayleigh-Bénard convection in cavities with the curved isothermal walls is not carried out till date. The heatline approach is used for the heat flow visualization during Rayleigh-Benard convection within the curved walled enclosures for the first time. Also, the existence of the enhanced fluid and heat circulation cells within the curved walled cavities during Rayleigh-Benard heating is illustrated for the first time.

The effect of inclination on laminar natural convection in a square cavity is studied numerically for inclination angles ranging from 40° to 160°, Rayleigh numbers between 10³ and 10⁶ and Prandtl numbers from 0.02 to 4,000. Contours of stream functions and temperature are presented in order to provide a new insight and a better understanding of the flow and heat transfer characteristics in a square cavity. Finds computed local and mean Nusselt numbers at the hot wall in satisfactory agreement with experimental and other numerical results. Finds the mean heat flux at the hot wall as well as the distribution of the local heat flux along the heated wall are found to depend on the inclination angle, the Rayleigh number and the Prandtl number. Such a dependence is significant for angles greater than 90°, while for smaller angles the effect of the inclination angle on the Nusselt‐Rayleigh correlation is weaker.

The purpose of this paper is to carry out an in-depth analysis of heat dissipation performance by natural convection phenomenon inside light-emitting diode (LED) lamps containing hot pin-fins because of its significant industrial applications.

The problem is assimilated to heat transfer inside air-filled rectangular cavity with various governing parameters appraised in ranges interesting engineering application and scientific research. The lattice Boltzmann method is used to predict the dynamic and thermal behaviors. Effects of monitoring parameters such as Rayleigh number Ra (10³-10⁶), fin length (0-0.25) and its position, pin-fins number (1-8), the tilting-angle (0-180°) and cavity aspect ratio Ar (0.25-4) are carried out.

The rising behaviors of the dynamic and thermal structures and heat transfer rate (Nu), the heatlines distribution and the irreversibility rate are appraised. It was found that the flow is constantly two contra-rotating symmetric cells. The heat transfer is almost doubled by increasing Ra. A lack of cooling performance was identified between Ar = 0.5 and 0.75. The inclination 45° is the most appropriate cooling case. At constant Ra, the maximum stream-function and the global entropy generation remain almost unchanged by increasing the pin number from 1 to 8 and the entropy generation is of thermal origin for low Ra, so that the fluid friction irreversibility becomes dominant for Ra larger than 10⁵.

Improvements may include three-dimensional complex geometries, accounting for thermal radiation, high unit power and turbulence modelling. Such factors effects will be conducted in the future.

The cooling performance/heat dissipation in LED lamps is a key manufacturing factors, which determines the lifetime of the electronic components. The best design and installation give the opportunity to increase further the product shelf-life.

Both cooling performance, irreversibility rate and enclosure configuration (aspect ratio and inclination) are taken into account. This cooling scheme will give a superior operating mode of the hot components in an era where energy harvesting, storage and consumption is met with considerable attention in the worldwide.

The purpose of this paper is to examine numerically the natural convection heat transfer in a cubical cavity induced by a thermally active plate. Effects of the plate size and its orientation with respect to the gravity vector on the convective heat transfer and the flow structures inside the cavity are studied and highlighted.

The numerical code is based on the finite volume method with semi-implicit method for pressure-linked equation algorithm. The convective and diffusive terms in momentum equations are handled by adopting the power law scheme. Finally, the discretized sets of algebraic equations are solved by the line-by-line tri-diagonal matrix algorithm.

The results show that plate orientation and size plays a significant role on heat transfer. Also, the heat transfer rate is an increasing function of Rayleigh number for both orientations of the heated plate. Depending on the thermal management of the plate and its application (as in electronics), the heat transfer rate is maximized or minimized by selecting appropriate parameters.

The flow is assumed to be 3D, time-dependent, laminar and incompressible with negligible viscous dissipation and radiation. The fluid properties are assumed to be constant, except for the density in the buoyancy term that follows the Boussinesq approximation.

The present work will give some additional knowledge in designing sealed cavities encountered in some engineering applications as in aeronautics, automobile, metallurgy or electronics.

This paper is aimed to study natural convection in enclosures with curved (concave and convex) side walls for porous media via the heatline-based heat flow visualization approach.

The numerical scheme involving the Galerkin finite element method is used to solve the governing equations for several Prandtl numbers (Pr_m) and Darcy numbers (Da_m) at Rayleigh number, Ra_m = 10⁶, involving various wall curvatures. Finite element method is advantageous for curved domain, as the biquadratic basis functions can be used for adaptive automated mesh generation.

Smooth end-to-end heatlines are seen at the low Da_m involving all the cases. At the high Da_m, the intense heatline cells are seen for the Cases 1-2 (concave) and Cases 1-3 (convex). Overall, the Case 1 (concave) offers the largest average Nusselt number ( Nur¯) at the low Da_m for all Pr_m. At the high Da_m, Nur¯ for the Case 1 (concave) is the largest involving the low Pr_m, whereas Nur¯ is the largest for Case 1 (convex) involving the high Pr_m.

Thermal management for flow systems involving curved surfaces which are encountered in various practical applications may be complicated. The results of the current work may be useful for the material processing, thermal storage and solar heating applications

The heatline approach accompanied by energy flux vectors is used for the first time for the efficient heat flow visualization during natural convection involving porous media in the curved walled enclosures involving various wall curvatures.

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.