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This numerical investigation explores the enhanced control of the 3D natural convection (NC) within a cubic cavity filled with graphene–water nanofluids, utilizing a bottom-center-located tree-shaped obstacle and a horizontal magnetic field (MF). The analysis includes the effects of the Rayleigh number (Ra), the solid volume fraction of graphene ( φ ), the Hartmann number (Ha), and the fins' length (W). The results show complex flow patterns and thermal behavior within the cavity, indicating the interactive effects of nanofluid properties, the tree-shaped obstacle, and magnetic field effects. The MHD effects reduce the convection, while the addition of graphene improves the thermal conductivity of the fluid, which enhances the heat transfer observed with increasing Rayleigh numbers. The increase in the fins' length on the heat transfer efficiency is found to be slightly negative, which is attributed to the complex interplay between the enhanced heat transfer surface area and fluid flow disruption. This study presents an original combination of non-destructive methods (magnetic field) and a destructive method (tree-shaped obstacle) for the control of the fluid flow and heat transfer characteristics in a 3D cavity filled with graphene–water nanofluids. In addition, it provides valuable information for optimizing heat transfer control strategies, with applications in electronic cooling, renewable energy systems, and advanced thermal management solutions. The application of a magnetic field was found to reduce the maximum velocity and total entropy generation by about 82% and 76%, respectively. The addition of graphene nanoparticles was found to reduce the maximum velocity by about 5.5% without the magnetic field and to increase it by 1.12% for Ha = 100. Varying the obstacles' length from W = 0.2 to W = 0.8 led to a reduction in velocity by about 23.6%. [ABSTRACT FROM AUTHOR]

This study numerically investigates the two-dimensional natural convection in a square enclosure with an isothermal diamond elliptic array at Rayleigh numbers of 104 ≤ Ra ≤ 107. Three cases are considered, i.e., case 1 where two pairs of circular heating bodies are used inside the cavity, one is placed on the vertical centerline (VC) of the cavity and the other on the horizontal centerline (HC), case 2 where one pair of horizontal elliptic heating bodies is placed on the VC of the cavity and the other on the HC and case 3 where the horizontal elliptic heating bodies are replaced by vertical elliptic heating bodies. Numerical simulation was carried out based on the mesoscopic approach (LBM). The effects of the horizontally and vertically heated arrays were investigated. We demonstrate that, only when the Rayleigh number increases to Ra = 107, the numerical solutions reach an unsteady state for all cases. The transition of the flow regime from the unsteady state to the steady state depends on the variation in the ratio of the elliptical cylinder. [ABSTRACT FROM AUTHOR]

The present work is a numerical analysis of electro-thermo convection, occurring in a square differentially heated cavity filled with a dielectric fluid. The cavity experiences the combined effects of viscous, electrical, and thermal forces. The equations modelling the physical problem are solved via the finite volume approach. The study focuses on the effect of cavity tilt on the fluid flow structure and thermal performance inside the enclosure under the action of an electric field. A parametric study was performed, where the tilt angle is getting varied between 0° and 90°, as well as the Rayleigh number (5000 ≤ Ra ≤ 250,000) and the electric field (0 ≤ T ≤ 800). Furthermore, the electric charge injection level C, the mobility M and the Prandtl Pr numbers were all adjusted to a value of 10. The obtained results demonstrate that the hydrodynamic and thermal fields are significantly impacted by the cavity inclination. In addition, regardless of the thermal Rayleigh's number, high electric field values could govern fluid movement through electric forces. Electro-convection typically demonstrates an oscillating flow due to the tilting of the cavity which gives rise to a bicellular regime occupying the entire cavity. A correlation has been established to estimate heat transfer by considering various system parameters such as cavity inclination, electrical Rayleigh number, and thermal Rayleigh number. [ABSTRACT FROM AUTHOR]

Three-dimensional investigation has been carried out to simulate buoyancy induced heat transfer and fluid flow as well as entropy creation inside C-shaped enclosure charged with based water CNT–Al2O3 (15–85%) hybrid nanofluid. Left side is isothermally heated while the vertical portions of the right wall are isothermally cooled. Effects of various parameters on the flow behavior and the produced irreversibilities, namely the cavity aspect ratio (0.1 ≤ Ar ≤ 0.4), Rayleigh number (103 ≤ Ra ≤ 106) and volumetric fraction of hybrid nanofluid (0 ≤ φ ≤ 0.06) have been examined. It was revealed that the aspect ratio is the main controlling parameter of thermal energy transfer and generated entropy. In addition, for specific Ra, adding hybrid nanoparticles leads to the increase of the average Nusselt number while the highest produced entropy is observed with higher Rayleigh number. Moreover, the maximum Bejan number occurred for a shape factor Ar = 0.1 and Ra = 104 disregarding the hybrid nanoparticles volume fraction showing the dominance of thermal irreversibility over the viscous dissipation irreversibility in such conditions. [ABSTRACT FROM AUTHOR]

Fluids have played and still play a vital role in attaining an optimized output from industrial processes. However, due to technological advancement, fluids with high hydrothermal characteristics are required. In order to overcome these challenges, researchers have developed fluids with dispersed nanoparticles, which are recognized as nanofluids. Various types of nanoparticles can be added to base fluids to produce thermally enhanced liquids. Among these, the addition of multi-walled carbon nanotubes (MWCNTs) is considered the best due to the considerable enhancement of thermophysical properties and the stability of the solution. Thus, in the present investigation, an analysis of the heat transfer characteristics of an MWCNT–water nanofluid included in a star-shaped cavity equipped with a hot rectangular baffle is conducted. In addition, a uniform magnetic field is applied along the x-direction to oppose the convective flow generated by variations in density. Mathematical formulations under assumed boundary conditions and physical assumptions are established in the form of dimensionless PDEs. The finite-element-method-based software "COMSOL" is used to execute the numerical simulations. PARADISO is employed to resolve the developed non-linear system of equations. The effects of the governing parameters on the velocity and temperature fields are presented through streamlines and isotherms. The Nusselt number is evaluated to depict the impact of the addition of nanoparticles (MWCNTs) on the heat transfer enhancement. Changes in the horizontal and vertical components of velocity are also evaluated against the Rayleigh number and nanoparticle volume fraction via cutline representation. [ABSTRACT FROM AUTHOR]

Research interest in nanotechnology is growing due to its diversified engineering and medical applications. Due to the importance of bioconvection in biotechnology and various biological systems, scientists have made significant contributions in the last ten years. The present study is focusing on the investigation of the magnetohydrodynamics (MHD) bioconvective heat transfer of a Williamson nanofluid past an inclined moving plate embedded in a porous medium. The partial differential equations governing the considered configuration are established, then transformed into ordinary differential equations using suitable similarity transformations. The variables corresponding to the velocity, temperature, nanoparticle volume fraction, and density of motile micro-organisms along with their gradients, are computed using the bvp4c-MATLAB built-in numerical solver. Results showed the rising of the buoyancy ration parameter leads to an increase in the flow velocity. It has been also observed that the flow intensity becomes more important with an increase in the Weissenberg number, and the opposite occurs with an increase in the bioconvective Rayleigh number. As an effect of the Brownian motion, a random fluid particle's motion is encountered. [ABSTRACT FROM AUTHOR]

This paper emphasizes the effect of applying a rotating magnetic field on the natural convective flow of CNT/Water nanofluid inside a corrugated square cavity differentially heated through its sidewalls, while the upper and lower boundaries are supposed to be perfectly insulated. The aim of this study is to highlight the impact of a large variety of parameters, namely Hartman number, frequency of rotation, Rayleigh number, nanoparticles volume fraction, and corrugation aspect ratio on the flow behaviour and thermal transport characteristics. The governing non-linear coupled differential equations are solved by using the finite element technique. Outcomes indicated that the thermal energy exchange is improved with the Rayleigh number increment and nanoparticles loading, while it is weakened with the rising of Ha, ascribed to the Lorentz force opposition to buoyancy. Moreover, enlarging the corrugation aspect ratio causes the apparition of stagnant fluid zones and the rate of heat transfer is reduced as a result. [ABSTRACT FROM AUTHOR]

Two-dimensional numerical simulations are performed to investigate the problem of thermocapillary, and buoyancy driven convection. A hybrid MWCTN-Fe 3 O 4 -thermal oil nanofluid was used in an enclosed cavity equipped with a hot obstacle. The entire set of equations associated with the convective heat transfer phenomena in a hybrid nanofluid layer with a free surface are solved numerically using the blocked-off region method of Patankar. A parametric study varying the position, the size of the obstacle, the Marangoni number, the Rayleigh number, the volume fraction of the nanofluid has been performed. The results concern the flow profile, the temperature profile and the evolution of the Nusselt number under different conditions. It was shown that an enhancement of the convective heat transfer of more than 170% can be achieved on the cold wall just by switching the position of the obstacle from the bottom to the top. [ABSTRACT FROM AUTHOR]

In this paper a numerical investigation on the double diffusive natural convection in a finned solar still is performed using the finite volume method. The 3D vector potential-vorticity formalism is used to eliminate the gradient pressure terms and due to the complex shape of the cavity the blocked-off-region method is adopted. After getting the dimensionless governing equations, they are written in a generalised form then discretised. The effects of the buoyancy ratio, conductivity ratio and Rayleigh number of the flow structure, temperature field and heat and mass transfer are studied. The results show that the increase of conductivity ratio and Rayleigh number leads to an enhancement of the heat and mass transfer. [ABSTRACT FROM AUTHOR]

A numerical study was performed to analyze the impact of the combination of several factors on heat transfer rate, flow behavior, and entropy generation in a hybrid nanofluid occupying a porous trapezoid enclosure containing a rotating inner tube. The governing equations were discretized and solved using the Finite Element Method using Comsol multiphysics. The effects of the Darcy and Hartman number, nanoparticle volume fraction (from 0 to 6%), the utilization of various zigzag patterns of the hot wall, and the rotation speed of the inner tube (Ω = 100. 250 and 500) are illustrated and discussed in this work. The outputs reveal that flow intensity has an inverse relationship with Hartman number and a direct relationship with the Darcy number and the velocity of the inner tube, especially at high numbers of undulations of the zigzag hot wall (N = 4); also, intensification of heat transfer occurs with increasing nanoparticle volume fraction, Darcy number and velocity of the inner tube. In addition, entropy generation is strongly affected by the mentioned factors, where increasing the nanoparticle concentration augments the thermal entropy generation and reduces the friction entropy generation; furthermore, the same influence can be obtained by increasing the Hartman number or decreasing the Darcy number. However, the lowest entropy generation was found for the case of Ø = 0, Ha = 0 and Da = 0.01. [ABSTRACT FROM AUTHOR]

This study deals with the effect of the power law index on the convective heat transfer of hybrid nanofluids in a square cavity divided into three layers. The effect of a solid fluid layer is also given attention. A two-dimensional system of partial differential equations is discretized by using the generalized finite element method (FEM). A FEM having cubic polynomials (P3) is employed to approximate the temperature and velocity components, whereas the pressure is approached using quadratic finite element functions. The discretized set of equations have been solved using Newton's method. The numerical code which is used in this study has been validated by comparing with experimental findings. Mathematical simulations are performed for different sets of parameters, including the Rayleigh number (between 10 3 and 10 6 ), the power law index (between 0.6 to 1.8 ), Darcy number (between 10 − 6 to 10 − 2 ), undulation (between 1 and 5) and the thermal conductivity ratio (between 0.1 and 10). The results infer that a remarkable penetration of streamlines is figured out towards the porous hybrid layer as the power law index is increased. The average N u increases with increasing R a , and the maximum value is noted at R a = 10 6 . There is no much alteration observed for isotherms at the solid layer by increasing D a . The average N u decreases by increasing the undulations. The rate of heat transfer is enhanced at the heated boundary and solid fluid interface of the cavity by raising the ratio of thermal conductivity. [ABSTRACT FROM AUTHOR]

This study deals with the influence of a wavy interface separating two layers filled with power law fluid and porous media, respectively. The governing equations are solved using the Finite Element Method (FEM) and the numerical model is validated by comparing with experimental findings. The parameters governing the studied configuration are varied as: Rayleigh number (103 ≤ Ra ≤ 106), power law index (0.6 ≤ n ≤ 1.4), Darcy number (10−2 ≤ Da ≤ 10−6), buoyancy ratio (0.1 ≤ N ≤ 10) and Lewis number (1 ≤ Le ≤ 10). It is inferred that the temperature gradient increases by augmenting the Rayleigh number, as the flow is observed from the vertical to horizontal direction in both layers. Constant enhancement in the heat and mass transfer is also observed by enriching the buoyancy effect. Moreover, the average Nusselt and Sherwood numbers decline by increasing the width of the porous layer. [ABSTRACT FROM AUTHOR]

The current research presents a numerical investigation of the mixed convection inside a horizontal rectangular duct combined with an open trapezoidal cavity. The region in the bottom wall of the cavity is heated by using two discrete heat sources. The cold airflow enters the duct horizontally at a fixed velocity and a constant temperature. All the other walls of the duct and the cavity are adiabatic. Throughout this study, four various cases were investigated depending on the driven walls. The effects of the Richardson number and Reynolds number ratio are studied under various cases related to the lid-driven sidewalls. The results are presented in terms of the flow and thermal fields and the average Nusselt number. The yielded data show that the average Nusselt number rises as the Richardson number and Reynolds number ratio increases. Furthermore, the Reynolds number ratio and the movement of the cavity sidewall(s) have a significant effect on the velocity and temperature contours. By the end of the study, it is shown that the maximum rates of heat transfer are related to Case 1 where the left sidewall moves downward and heater 2, which is placed near the left sidewall. [ABSTRACT FROM AUTHOR]

• The heat and mass transfer in a solar still embedded with PCM is studied. • The Finite volume method is used to solve the governing equations. • An external water stream is used to enhance the heat and mass transfer. • The effects of the buoyancy ratio and the Rayleigh number have been investigated. The increase demand of water for irrigation and human activities leads to a global development of alternative methods to produce distillate water especially from sea. In this context, the use of solar distiller instead of the classic distillation process is a good solution to preserve environment and reduce the use of fuel. This study explores the advantages of the classic solar still by studying the effect of the PCM-RT42. Hence, a detailed investigation of the heat and mass transfer of a single slope solar still incorporation PCM-RT42 as heat storage system will be presented. The governing equations are solved numerically with employing the finite volume method. The next scopes of parameters are utilized in the computations: dimensionless time (τ = 4.2×10–3, 25.2×10–3, and 50.4×10–3), Rayleigh number (104 ≤ Ra ≤ 106), buoyancy ratio (1 ≤ N ≤ 5). Mixture Prandtl number (Pr m), Schmidt number (Sc) and Lewis number (Le) are presumed as fixed to 0.705, 0.613 and 0.869, respectively. The results show the good effect of the PCM-RT42 on the transfer of heat and mass compared to the initial time for low Ra. However, for Ra=105 and 106, a reduction in the efficiency of condensation and the performance of the solar distiller is observed. [Display omitted] [ABSTRACT FROM AUTHOR]

The electro-thermo-convection in a square cavity with incorporated hot solid body is numerically investigated. The finite volume method associated with Patankar's "blocked-off-regions" technique is applied. A potential difference is applied between the hot obstacle and the horizontal walls in order to eliminate the so-called dead zone created at the bottom of the cavity. The flow movement is induced not only by thermal buoyancy forces but also by the electric Coulomb force. Calculations are made for several injection levels (1 ≤ C ≤ 10), various obstacle shape factors (1 ≤ l/w ≤ 9), different number of electric Rayleigh (0 ≤ T ≤ 800), multiple thermal Rayleigh numbers (2000 ≤ Ra≤ 30,000) and 03 obstacle positions. The results show that according to the intensity of the applied electrical forces, two types of regimes are identified: a thermally dominated regime characterized by a low heat exchange at the bottom of the obstacle and conversely an electrically dominated regime with an excellent heat exchange over the entire cavity. It has been demonstrated that it is possible to improve the heat transfer up to: 43% by changing the shape factor of the obstacle; 82% by varying the injection level and 532% by applying electrical forces. [ABSTRACT FROM AUTHOR]

The laminar two-dimensional mixed convection in a trapezoidal enclosure with a rotating inner circular cylinder and a sinusoidal bottom wall is studied numerically. The fluid inside the enclosure is a CuO–water nanofluid layer in the top space of it, while the bottom space includes a CuO–water nanofluid saturated with a porous medium. Both the right and left sidewalls are assumed adiabatic, while the bottom and the top walls of the enclosure are maintained, respectively, at the hot and cold temperatures. The dimensionless governing equations are expressed for velocity and temperature formulation and modeled by using COMSOL code based on the Galerkin finite element method. Parametric studies on the effects of various significant parameters such as Rayleigh number, Darcy number, the inner cylinder radius, the porous layer thickness, the angular rotational velocity, the solid volume fraction and the number of undulations on the flow and thermal fields together with the heat transfer rate have been performed. The highest value of the stream function for (Ra = 103 and Ra = 105) is seen at (R = 0.2 and S = 0.2). The same thing is observed, when the bottom wall is considered wavy. For (Ra = 103 and N = 0) and (0.5 ≤ S ≤ 0.8), it can be seen that as the inner cylinder radius increases from (R = 0.1) to (R = 0.3), the stream function values increase continuously. It is found that the average Nusselt number increases as the Rayleigh and Darcy numbers, the solid volume fraction, inner cylinder radius and the angular rotational velocity of the cylinder increase, while it decreases as the porous layer thickness and the number of undulations increase. Comparisons with previously published numerical works are performed, and good agreements between the results are observed. [ABSTRACT FROM AUTHOR]

Numerical simulation of the natural convection and entropy generation in an airfilled cubical cavity with active lateral walls is performed in this work. Both the lateral front and right sidewalls are maintained at an isothermal cold temperature. While an isothermal hot temperature is applied for both the lateral back and left sidewalls. The upper and lower walls are kept adiabatic. Entropy generation rates due to the fluid friction and the heat transfer are simulated by using the Second law of thermodynamics. Results are illustrated for Rayleigh numbers varied from (103 ≤ Ra ≤ 106). It was shown that the increase in the Rayleigh number leads to increase the average Nusselt number and to decrease the Bejan number. Also, it was found that both, Sth, and Stot, increase slightly with the increase in Rayleigh number until they reach (Ra = 105) and then begin to jump after this value. After (Ra = 105), the increase in both, Stot, and Sfr, is greater than Sth. Moreover, it was observed that iso-surfaces of Stot are similar to Sth at (103 ≤ Ra ≤ 105), while they are similar to Sfr at high Rayleigh number. [ABSTRACT FROM AUTHOR]

Three-dimensional numerical simulation on natural convection inside the T-shaped cavity, filled with water-based hybrid nanofluid of CNT–aluminum oxide is performed by vorticity–vector potential formalism. The variables considered are size of enclosure (0.1 < L < 0.9), volumetric percentage of nanoparticles (0 < φ < 4%), fraction of CNT composites (0 < fr < 1), and Rayleigh number (103 < Ra < 106). The heat transfer is increased with the increase in size, volumetric percentage of nanoparticles, fraction of CNT composites, and Rayleigh number. [ABSTRACT FROM AUTHOR]

In this paper, the effect electric field on the flow induced by the combined buoyancy and thermocapillary forces is carried out. Calculations are performed for a strong unipolar injection (C = 10) and different values of Marangoni number (−10000 ≤ Ma ≤ 10000), thermal Rayleigh number (5000 ≤ Ra ≤ 50,000) and electric Rayleigh number (0 ≤ T ≤ 800). The Prandtl number (Pr) and the mobility parameter (M) are fixed at 116.6 and 49, respectively. These values correspond to the Silicone oil used as working liquid several practical applications. The full set of coupled equations: Navier–Stokes, Electro-hydrodynamic (EHD) and heat transfer equations are directly solved using stream function-vorticity formalism. Obtained results show that the electric forces can control the thermocapillary instabilities. According to the intensity and the direction of the applied electric forces, it is demonstrated that these instabilities can be accentuated, attenuated, or even completely eliminated. [ABSTRACT FROM AUTHOR]

Three-dimensional natural convection in an inclined solar collector equipped with partitions has been investigated numerically. The presence of partitions improves the performances of the collector by increasing the heat transfer near the absorber. A parametric study was done for various partitions length and Rayleigh numbers, while Prandtl number and inclination angle were fixed at 0.71 and 45°, respectively. Results are reported in terms of isosurfaces of temperature, isotherms, particles trajectories, velocity vector projection, average Nusselt number along the absorber plate and entropies generation contours. [ABSTRACT FROM AUTHOR]

The effect of inclination angle on three dimensional (3D) natural convection in an inclined rectangular cavity similar to a solar collector equipped with partitions has been investigated numerically. Governing equations were established using the 3D velocity vector-vorticity formalism and discretized via the finite volume method (FVM). A parametric study has been performed for various inclination angles (from 0° to 90°), different partitions length (from 0.2 to 0.8). and a range of Rayleigh numbers varied from 103 to 10s while, Prandtl number was fixed at Pr = 0.71. Results are reported in terms of iso-surfaces of temperature, isotherms, particles trajectories, vector velocity projection, average Nusselt number and the entropies generation contours and graphs. Results showed the 3D character of the flow is more pronounced for higher Rayleigh numbers and lower partition lengths. For all inclinations and partition lengths, heat transfer and entropy generation are enhanced by increasing Rayleigh number [ABSTRACT FROM AUTHOR]

A numerical study of the 3-D double-diffusive natural convection in an inclined solar distiller was established. The flow is considered laminar and caused by the interaction of thermal energy and the chemical species diffusions. The governing equations of the problem, are formulated using vector potential-vorticity formalism in its 3-D form, then solved by the finite volumes method. The Rayleigh number is fixed at Ra = 105 and effects of the buoyancy ratio and inclination are studied for opposed temperature and concentration gradients. The main purpose of the study is to find the optimum inclination angle of the distiller which promotes the maximum mass and heat transfer. [ABSTRACT FROM AUTHOR]

A computational analysis has been performed in this work to solve three-dimensional magnetohydrodynamic natural convection in an open cubical enclosure filled with CNT-water nanofluid. The cavity is heated from left vertical wall and an inclined plate is attached inside the cavity with finite length. The study is solved for different governing parameters as Rayleigh number (10 3 ≤ Ra ≤ 10 5 ), nanoparticle volume fraction (0% ≤ φ ≤ 5%), Hartmann number (0 ≤ Ha ≤ 100) and inclination angle of the fin (0° ≤ θ ≤ 360°). It is observed that all of these parameters can be used as passive control element for heat and fluid flow and the maximum heat transfer is formed when θ = 180° but minimal value of average Nusselt number is changed according to nanoparticle addition into base fluid. [ABSTRACT FROM AUTHOR]

Three-dimensional computational analysis of entropy generation due to natural convection in partially open enclosure has been performed in this work by using finite volume method. A written computer code was developed to solve governing equations of this three-dimensional problem. The study has been performed for different governing parameters such as opening ratio 0. 25 ≤ h ≤ 0.75, center of opening 0.25 ≤ d ≤ 0.75 and Rayleigh number 10 3 ≤ Ra ≤ 10 5 . It is observed that edge of openings is the most effective parameter on entropy generation and after comparing many cases, both the highest heat transfer and entropy generation were observed for the fully opened cavity. [ABSTRACT FROM AUTHOR]

Convective heat transfer and entropy generation in a 3D closed cavity, equipped with adiabatic-driven baffle and filled with CNT (carbon nanotube)-water nanofluid, are numerically investigated for a range of Rayleigh numbers from 103 to 105. This research is conducted for three configurations; fixed baffle (V = 0), rotating baffle clockwise (V+) and rotating baffle counterclockwise (V-) and a range of CNT concentrations from 0 to 15%. Governing equations are formulated using potential vector vorticity formulation in its three-dimensional form, then solved by the finite volume method. The effects of motion direction of the inserted driven baffle and CNT concentration on heat transfer and entropy generation are studied. It was observed that for low Rayleigh numbers, the motion of the driven baffle enhances heat transfer regardless of its direction and the CNT concentration effect is negligible. However, with an increasing Rayleigh number, adding driven baffle increases the heat transfer only when it moves in the direction of the decreasing temperature gradient; elsewhere, convective heat transfer cannot be enhanced due to flow blockage at the corners of the baffle. [ABSTRACT FROM AUTHOR]

A computational study has been performed to see the effects of electro-thermo-convection induced via a strong unipolar injection between two concentric or eccentric cylinders using the finite volume method. The parameters are taken in the range of radius ratio 0.1 ≤ Г ≤ 0.9, injection strength in the range of 1 ≤ C ≤ 20, mobility number changes in the range 4 ≤ M ≤ 150, electric Rayleigh number in the range of 100 ≤ T ≤ 800, and Rayleigh number changes in the range of 5000 ≤ Ra ≤ 25000. It is observed that the most important effective parameter is radius ratio, which affects both heat and fluid flow. Moreover, electrical Rayleigh numbers suppress the thermo-convection and in any case higher transfer is observed due to electric charge injection. [ABSTRACT FROM PUBLISHER]

In this study, heat transfer, flow structure and produced entropy due to natural convection in a threedimensional cavity heated via heat sinks are investigated numerically. One wall of the cavity is heated via pinfins and opposite wall is maintend at lower temperature. Remaining bouandaries are considered as adiabatic. Finite volume method is used to solve governing equations. Three geometrical cases are tested according to number and location of the fins. Other governing parameters are Rayleigh number and fin length. Number and length of the fins were found to be the most effective parameters on both heat transfer and entropy generation. [ABSTRACT FROM AUTHOR]

A three dimensional computational solution has been obtained to investigate the natural convection and entropy generation of nanofluid-filled open cavities with an adiabatic diamond shaped obstacle. In the model, the finite volume technique was used to solve the governing equations. Based on the configuration, the cavity is heated from the left vertical wall and the diamond shape was chosen as adiabatic. Effects of nanoparticle volume fraction, Rayleigh number (103ὄ Ra ὄ 106) and width of diamond shape were studied as governing parameters. It was found that the geometry of the partition is a control parameter for heat and fluid flow inside the open enclosure. [ABSTRACT FROM AUTHOR]

Effects of Rayleigh number, solid volume fraction and entropy generation on the natural convection heat transfer and fluid flow inside a three-dimensional cubical enclosure filled with water-AlO nanofluid have been investigated numerically using the control volume finite difference method. The enclosure left sidewall is maintained at isothermal hot temperature, while the right one is maintained at isothermal cold temperature. The other enclosure walls are considered adiabatic. The second law of thermodynamics is applied to predict the nature of irreversibility in terms of entropy generation rate. Numerical computations are carried out for Rayleigh numbers from $${(10^{3} \leq {\rm Ra} \leq 10^{6})}$$ , solid volume fraction from $${(0\% \leq \varphi\, \leq 20\%)}$$ , while the Prandtl number of water is considered constant as (Pr = 6.2). Streamlines, isothermal lines, counters of local and total entropy generation and the variation of Bejan number, local and average Nusselt numbers are presented and discussed in detail. The results explain that the average Nusselt number increases when the solid volume fraction of nanoparticles and the Rayleigh number increase. Also, the Bejan and average Nusselt numbers have a reverse behavior to each other for the same range of Rayleigh number and solid volume fraction. In addition, the results show that the entropy generation rate due to heat transfer, friction and the total entropy generation increase as the solid volume fraction increases, while it increases highly when the Rayleigh number increases especially near the hot left sidewall. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a numerical study of a double diffusive convection in a cubic cavity filled with a binary mixture. The vertical walls are given different temperatures and concentrations. The potential-vorticity formulation in three-dimensional configuration using the finite volume method is utilized in this study. The results are given for Rayleigh number Ra=105, Prandtl number Pr=10 and Lewis number Le=10, characterizing the case of aqueous solutions. The influence of the magnetic field on the structure of the three-dimensional flow, the distribution of temperature and concentration and the different characteristics of heat and mass transfer of the thermal and solutal dominated region are presented. [Copyright &y& Elsevier]

Abstract: Numerical results of double-diffusive natural convection are presented in a three-dimensional solar distiller. The flow is considered laminar and caused by the interaction of the thermal energy and the chemical species diffusions. Equations of concentration, energy and momentum are formulated using vector potential-vorticity formulations in its three-dimensional form, then solved by the finite volume method. The Rayleigh number is fixed at Ra =105 and the effects of the buoyancy ratio are studied for opposed temperature and concentration gradients, with a particular interest to the three-dimensional aspects and entropy generation. [Copyright &y& Elsevier]

In this article we studied the effect of radiative transfer and the aspect ratio on the 3-D natural convection. Prandtl and Rayleigh numbers are fixed at 13.6 and 105, respectively. Equations of natural convection are expressed according the vorticity-stream function formulation. This equations and radiative transfer equation are descritized by volume control method and the FTn finite volume method, respectively. Obtained simulation show that the principal flow structure is considerably modified when the radiation-conduction parameter was varied. However, the peripheral spiraling motion is qualitatively insensitive to these parameters. [ABSTRACT FROM AUTHOR]

• EHD convective MWCNT-oil nanofluid flow in a heated dielectric enclosure was numerically analyzed. • The governing equations were solved using in-house developed code with FVM. • The increase of thermal/electric Ra number and nanoparticle concentration enhanced the heat transfer. • It is found that high thermal and electric Ra numbers made the flow and heat transfer time dependent. • It is concluded that the inclusion of an electric field with nanoparticles addition leads to 43% thermal enhancement. A computational research was performed to analyze the electrohydrodynamic (EHD) convective heat transfer in a differentially heated dielectric-MWCNT nanofluid layer. The study was conducted on a square enclosure subjected to a temperature gradient between these two vertical walls as well as a potential difference between these horizontal walls. The enclosure was filled with MWCNT oil-based nanofluid; the MWCNT nanoparticles were dispersed in a perfectly insulating thermal oil with a volume fraction of hardly exceeded 0.4%. The governing equations were derived with the assumption of homogeneous nanofluid and were solved with employing finite volume method. Based on the obtained results, it was found that the increase of Rayleigh number, electric Rayleigh number and nanoparticle concentration enhanced the heat transfer. For high thermal and electric Rayleigh number values, the flow and heat transfer became time dependent and accordingly a frequency study was also performed. It was found that the inclusion of an electric field with the addition of nanoparticles led to a significant heat transfer enhancement of about 43%. [ABSTRACT FROM AUTHOR]

A numerical study on natural convection in a cubical cavity with partial top and bottom openings is performed in this paper. One of the vertical walls of the cavity has higher temperature than that of the opposite one; the remaining walls are insulated perfectly. Three-dimensional simulations of governing equations have been performed using a finite volume technique. The results are presented for different parameters such as opening length and Rayleigh number. It is observed that heat transfer rate and fluid flow can be controlled via opening ratio size and Rayleigh number. [ABSTRACT FROM AUTHOR]

Highlights • The heat and mass transfer inside a 3D solar distiller is studied. • The 3D vector-potential-vorticity formalism is used to develop the governing equation. • Complex flow structure and temperature and concentration fields occurs. • Entropy generation is evaluated. Abstract Three-dimensional computational analysis was performed to investigate the double diffusive natural convection inside a cubical solar distiller heated by a square-shaped column. Governing equations were developed using the 3D vector potential-vorticity and solved using the finite volume method. Different governing parameters, i.e., Rayleigh number 103 ≤ Ra ≤ 105, buoyancies ratio −10 ≤ N ≤ 10, geometrical parameter 0.1 ≤ L h ≤ 0.7 for Le = 0.85 and Pr = 0.7 corresponding to humid air, were tested. It was found that both heat and mass transfer are strongly affected by the change of buoyancy ratio, geometrical parameter and Rayleigh number. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

In this study, the combined impact of carbon nanotube volume fractions and the electric field on the enhancement of dielectric oil heat transfer is investigated. The geometry studied is an annular layer filled with the dielectric oil and bounded by two eccentric or concentric cylinders. A temperature gradient and an electrical potential difference are applied between the two cylindrical walls. The goal is to analyse the flow behaviour and the heat transfer improvement using a double enhancement technique by combining an active (electric field) and passive (nanoparticles) approach. An in-house numerical simulation code using the finite volume method was developed to solve the set of coupled equations describing the conservation laws of the electro-thermo-hydrodynamic flow associated with the oil. A parametric study, outlining the influence of different relevant variables has been performed. The parameters investigated are the thermal Rayleigh number (2000 ≤ T ≤ 100 000), the electrical Rayleigh number (100 ≤ T ≤ 600), the radius ratio (0.1 ≤ Γ ≤ 0.9), the eccentricity (0 % ≤ e ≤ 90%), the nanotubes volume fraction (0 % ≤ Φ ≤ 0.5%)and the injection level (1 ≤ C ≤ 10) respectively. The effect of these variables on the heat transfer intensification is examined in detail. According to the adopted configuration, heat transfer intensifications between 3% and 77% have been recorded essentially when an electric field was applied. Also, the addition of a 0.5% volume fraction of carbon nanotubes provides a heat transfer improvement of around 27%. Furthermore, for a first time a multiparameter correlation has been developed. This correlation can be useful to better understand the impact of various physical parameters on the heat transfer in annular spaces and also to predict exact values of the Nusselt number. [ABSTRACT FROM AUTHOR]

The natural convection flow of water between two coaxial cylinders where the inner cylinder generates a constant heat source is numerically studied. The outer cylinder is cold while the top and bottom walls are thermally insulated. For a laminar flow and an inclination angle equal 0°, 45°, 90° the results are determined in the form of contours of the isotherms and streamlines, average Nusselt number in the annular space. The results show that the average Nusselt number is growing with increasing Rayleigh numbers. The best heat transfer is obtained for the inclination angle 90°. [ABSTRACT FROM AUTHOR]

A numerical investigation of magneto-hydrodynamic mixed convection in a square lid-driven cavity filled with gyrotactic micro-organisms is examined. Different magnetic field inclinations are considered and the left wall of the lid-driven cavity is moving up with a constant speed in the vertical direction. The left and right vertical walls of the cavity are assumed to be adiabatic. The top horizontal wall of the cavity is assumed to be kept at features of the solution. Lower temperature, while the bottom horizontal wall is kept in a higher temperature. The developed equations of the mathematical model are put in their dimensionless forms and then solved numerically subject to appropriate boundary conditions by the control finite volume method. Comparisons with previously published works are presented and found to be in excellent agreement. The problem was studied by varying the Richardson number (Ri=0.01-2.0), Rayleigh number (Ra=102 -105), magnetic field inclination angle ( Φ = 0o-350o), Hartman number (Ha=0-50), and bio-convection Rayleigh number (Rb=10-40). A parametric study is performed and a set of graphical results is presented and discussed to demonstrate interesting. [ABSTRACT FROM AUTHOR]

This paper presents a numerical study of natural convection and entropy generation in a cubic cavity fitted by a baffle plate. Three-dimensional analysis has been done by solving governing equations with a written computational code in FORTRAN based on FVM. The study was performed for two configurations related to the position of the baffle. The first one was carried for a baffle plate attached to the upper wall of the cavity although the second case was reserved for a baffle attached to the down face. The results are given for Rayleigh number (Ra=105), Prandtl number (Pr = 7.1) and baffle length (d = 0.5). The influences of baffle position on flow structure, temperature distribution, and heat transfer and entropy generation are presented. [ABSTRACT FROM AUTHOR]

Three-dimensional natural convection in a cuboid enclosure filled with DWCNTs-water nanofluid is studied. The heat transfer performance due to convective flow of nanofluid inside the enclosure at different temperature differences between side hot and cold walls (ΔT = 20 °C, 30 °C, 40 °C and 50 °C) is analyzed experimentally and numerically. A setup has been manufactured to test the natural convection phenomenon within the enclosure. Moreover, in this work, the utilized nanofluid is prepared, the thermo-physical properties, thermal conductivity and dynamic viscosity, of the nanofluid are measured experimentally by means of modern measuring devices. The DWCNTs-water nanofluid is obtained in different solid volume fraction of 0.01%, 0.02%, 0.05%, 0.1%, 0.2%, and 0.5%, and thermo-physical properties have been measured in all solid volume fraction and temperature range of 300 to 340. The 3D computational study utilizing finite volume approach is performed with similar boundary condition with experimental setup and experimental properties of nanofluid to validate the experimental data. Height, length and depth of the enclosure are equal to 100 mm. the left and right side walls have constant and uniform hot and cold temperature respectively, and the other walls are insulated. The constant temperature of side walls is obtained by water channel supplied by circulating water bathes. The temperature of side walls is measured by nine LM-35 temperature sensors, and the temperature of nanofluid is measured by means of PT100 thermocouples inserting from watertight circular slots from back of enclosure. The numerical and experimental results are compared and a good consistency is observed. The temperature distribution between side walls at the mid-height of the enclosure, average heat transfer coefficient and average Nusselt number are presented for different Rayleigh numbers and solid volume fractions. [ABSTRACT FROM AUTHOR]

The natural convection heat transfer analysis is performed by different approaches such as heatline visualization, total and local entropy generation, average ad local Nusselt number using lattice Boltzmann numerical method in nanofluid-filled cavity with partially heated and cooled walls included by internal heaters. The cavity is filled with DWCNTs-water nanofluid which its thermal conductivity and dynamic viscosity are measured experimentally at different solid volume fractions of 0.01%, 0.02%, 0.05%, 0.1%, 0.2%, and 0.5% and a temperature range of 300–340 (K). Two sets of correlations for theses parameters based on temperature are developed and used in the numerical simulations. The side walls of cavity are cooled uniformly, two partially hot and cold surfaces at the bottom and top walls are located, respectively. The internal heaters are heated uniformly as well. The influences of different governing parameters such different arrangements of internal heaters, different concentrations of nanofluid and Rayleigh numbers on the fluid flow, temperature filed, average and local Nusselt number, total and local entropy generation and heatlines are presented. The results show that the arrangements of the internal heaters have pronounced effects on the fluid flow, heat transfer performance and entropy generation. 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. [ABSTRACT FROM AUTHOR]

Numerical results of laminar double-diffusive natural convection in a trapezoidal shape solar distiller occupied with an air-vapor mixture are carried out. In the present paper, the distiller is subjected to cooling fluid with a cold free stream temperature from the upper wall that kept at low concentration. The lower distiller wall kept with hot temperature and high concentration. The finite volume method based on SIMPLE algorithm is employed to solve the governing equations. Outcomes are performed with a scope of Rayleigh number (104 ≤ Ra ≤ 106), free stream Reynolds number (102 ≤ Re ∞ ≤ 105), buoyancy ratio (N = 1, 2,5 and 10) and varying cooling fluid (air or water). The Prandtl (Pr), Schmidt (Sc) and Lewis (Le) numbers are fixed at 0.7, 0.62 and 0.89, respectively. The results revealed a considerable enhancement on the mass and heat transfer rates with increasing of Ra, N and Re ∞. The effect of Re ∞ is more pronounced with Ra = 106. On the other hand, more vortices formed in the cavity as Ra and N augments and the maximum vortices number obtained when N = 5. Regarding the local Nusselt (Nu L) and Sherwood (Sh L) numbers, improvements are found both on the upper and lower cavity walls as Ra and N rise. The impact of N on Nu L and Sh L turns out significant with the higher value (N = 10). Image, graphical abstract [ABSTRACT FROM AUTHOR]