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Solves steady, laminar, two‐dimensional, conjugate natural convection in an rectangular enclosure numerically. The enclosure consists of heated and cooled isothermal walls connected by either adiabatic or perfectly conducting end walls. The enclosure is partially filled with a finitely conducting non‐porous thermal insulation, adjacent to the heated surface. Solves the governing equations (in stream function‐vorticity form) using a finite element method. Obtains data Pr = 0.7 over a Rayleigh number range (based on the enclosure width) of 0 ≤ Ra ≤ 10⁶. The results show the effect of solid insulation thickness on the average Nusselt number for a range of enclosure aspect ratios, inclination angles and solid‐to‐fluid conductivity ratios. Aims to determine the conditions that produce the minimum overall heat transfer rate.

This study aims to elucidate the role of curved walls in the presence of identical mass of porous bed with identical heating at a wall for two heating objectives: enhancement of heat transfer to fluid saturated porous beds and reduction of entropy production for thermal and flow irreversibilities.

Two heating configurations have been proposed: Case 1: isothermal heating at bottom straight wall with cold side curved walls and Case 2: isothermal heating at left straight wall with cold horizontal curved walls. Galerkin finite element method is used to obtain the streamfunctions and heatfunctions associated with local entropy generation terms.

The flow and thermal maps show significant variation from Case 1 to Case 2 arrangements. Case 1 configuration may be the optimal strategy as it offers larger heat transfer rates at larger values of Darcy number, Da_m. However, Case 2 may be the optimal strategy as it provides moderate heat transfer rates involving savings on entropy production at larger values of Da_m. On the other hand, at lower values of Da_m (Da_m ≤ 10⁻³), Case 1 or 2 exhibits almost similar heat transfer rates, while Case 1 is preferred for savings of entropy production.

The concave wall is found to be effective to enhance heat transfer rates to promote convection, while convex wall exhibits reduction of entropy production rate. Comparison between Case 1 and Case 2 heating strategies enlightens efficient heating strategies involving concave or convex walls for various values of Da_m.

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.

Because the local Re numbers, ratio of inertia to viscous forces, are not same at different regions of the enclosures, the present study aims to deal with the influences of using the turbulent/transition models on numerical results of the natural convection and flow field within a trapezoidal enclosure.

The three-dimensional (3D) trapezoidal enclosure with different inclined side walls of 75, 90 and 105 degrees are considered, where the side walls are heated and cooled at Ra = 1.5 × 10⁹ for all cases. The turbulent models of the k-ε-RNG, k- ω-shear-stress transport (SST) and the newly developed transition/turbulent model of Re_θ-γ-transition SST are utilized to analyze the fluid flow and heat transfer characteristics within the enclosure and compared their results with validated results.

Comprehensive comparisons have been carried out for all cases in terms of flow and temperature fields, as well as turbulent quantities, such as turbulent kinetic energy and turbulent viscosity ratio. Furthermore, the velocity and thermal boundary layers have been investigated, and the approximate transition regions for laminar, transitional and turbulent regimes have been determined. Finally, the heat transfer coefficient and skin friction coefficient values have been presented and compared in terms of different turbulent models and configurations. The results show that the transition/turbulence model has better prediction for the flow and heat fields than fully turbulent models, especially for local parameters for all abovementioned governing parameters.

The originality of this work is to analyze the 3D turbulent/transitional natural convection with different turbulence/transition models in a trapezoidal enclosure.

Numerical simulations have been performed for three‐dimensional natural convection of water near its maximum‐density (cold water) inside rectangular enclosures with differential heating at the vertical (left and right) walls. The horizontal (top and bottom) walls and the lateral (front and rear) walls are taken as insulated. Computations are performed for the buoyancy‐driven convection of cold water with density inversion parameter θ_m = 0.5 in the enclosures with aspect ratio (height/width) A_y = 8 and depth ratios (depth/width) A_z = 0.5, 1, and 2. The influence of the depth ratio on the onset of oscillatory convection in a cold‐water‐filled enclosure is investigated. The presence of the lateral walls tends to suppress the onset of unsteadiness in the convective flow. The main features of the oscillatory convection flow and temperature fields as well as the instability mechanism in the three‐dimensional enclosure were similar to those found in the two‐dimensional model. However, there exists a strong three‐dimensionality in the spatial distribution of the fluctuation amplitude. With the decrease of the depth ratio, the damping effect of the lateral walls becomes increasingly pronounced, leading to a reduced heat transfer rate.

The stability of two‐dimensional natural convection of water near its density maximum (cold water) inside a vertical rectangular enclosure with an aspect ratio of eight is investigated via a series of direct numerical simulations. The simulations aim to clarify, under the influence of density inversion, the physical nature of the instability mechanism responsible for the laminar buoyancy‐driven flow transition from a steady state to an oscillatory state in the enclosure filled with cold water. Two values of the density inversion parameter, _m= 0.4 and 0.5, where the density inversion of cold water may exert strong influence on the flow, are considered in the present study. The results show that the transition from steady state to periodically oscillatory convection arises in the cold‐water‐filled enclosure through a Hopf bifurcation. The oscillatory convection in the water‐filled enclosure for both values of _m is found to feature an oscillatory multicellular structure within the contra‐rotating bicellular flow regions. A traveling wave motion accordingly results along the maximum density contour, which demarcates the contra‐rotating bicellular flows in the enclosure. For both cases the nature of transition into unsteadiness is found to be buoyancy‐driven. The critical Rayleigh number for the bifurcation at _m = 0.4 is found to be markedly higher than that at _m = 0.5.

In the present paper the analysis of heat transfer and free convective motion have been carried out numerically for dome shaped enclosures. The solution method is based on the finite element technique with the frontal solver and is used to examine the flow parameters and the heat transfer characteristics inside dome shaped enclosures of various offsets. In formulating the solution a general conic equation is considered to represent the dome of circular, elliptical, parabolic and hyperbolic shapes. The numerical results indicate that the circular and elliptical shapes of dome give higher heat transfer rate and offset of the dome effects convective heat transfer quite significantly. However, beyond 0.3 top dome offset, the change in overall heat transfer rate is not significant. In addition, the convective phenomenon influenced by a dome shaped cover results in establishing a secondary core region even at a moderate Rayleigh number when compared with an equivalent rectangular enclosure. A good comparison between the present numerical predictions and the previous published data is achieved.

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.

The objective of present research is to characterize the unsteady thermal behavior of a square enclosure filled with water-Al₂O₃ nanofluids in the presence of oriented magnetic fields. The purpose this paper is to study the effect of pertinent parameters on the transient natural convection in the enclosure.

In this research, an in-house implicit finite volume code based on the SIMPLE algorithm is utilized for numerical calculations. To ensure the accuracy of results, comparisons are also made with previous works in literature. In this study, a constant strength magnetic field is concerned and for Rayleigh numbers of Ra=103, 104 and 105 the effect of magnetic field orientation with respect to the case of zero inclination on the thermal performance of cavity is investigated at Hartmann number range of Ha=15-90. In the present work, the nano-particle volume fractions range from φ=0-0.06.

Results show that when Rayleigh number is Ra=103, the inclination angle, solid particles and Hartmann number has no effect on the transient behavior. It is shown that during the time advancement to steady condition, the heat transfer rate relative to zero inclination angle, may reach to a maximum value. This relative maximum heat transfer increases as the inclination angle increases and decreases as the solid volume fraction increases. The effect of increase in Hartmann number is to decrease this maximum value at Rayleigh number of Ra=104 and at Rayleigh number of Ra=105, depending on the Hartmann number, this value may increase or decrease. It is also found that an increase in Hartmann number leads to delay the appearance of the relative maximum value of heat transfer. Results show that this maximum value is of more significance at zero solid volume fraction when inclination angle is 90 degrees and Hartmann number is Ha=60.

Limited works could be found in the literature regarding the idea of using nanofluids as the working fluid in an enclosure in the presence of magnetic field. In these works, the steady state thermal behavior of enclosures subjected to fixed magnetic fields is concerned. In the present work, the unsteady thermal behavior is concerned and the effect of magnetic field orientation angles on transient heat transfer performance of the enclosure at different Rayleigh and Hartmann numbers and solid volume fractions is explored.

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.