Search

AbstractIn order to study the effect of porous fin parameters on the natural convection heat transfer in the side-heated cavity containing the internal heat source, the influence of the structural parameters of porous fins (length of porous fins l, installation position of porous fins s, Installation angle of porous fins θ) and the physical property parameters of porous fins (effective thermal conductivity Ke, Darcy number Da) on the natural convection heat transfer in the cavity was numerically analyzed by arranging a porous fin on the hot wall. The effect of the coupling effect of the structure parameters of porous fins was analyzed by the response surface method, and it was found that the coupling effect of the installation position and installation angle of porous fins had the most significant effect on the convective heat transfer in the cavity, the combination of the structural parameters of porous fins with the optimal convective heat transfer effect is l = 0.053 H, s = 0.373 H, and θ = 93.21°, which increases the average Nusselt number of the hot wall by 38.72% compared with no-fin structure; The effect of Darcy number and effective thermal conductivity of porous fins on the average Nusselt number of the hot wall surface is analyzed. The results of the study can guide the study of solar radiation in buildings, the internal temperature control of automobiles, and the study of the thermal performance of electronic components. [ABSTRACT FROM AUTHOR]

Phase change material (PCM) are characterized by their high latent heat and low density. Combining PCM with building walls, aircraft fuselages, and other structures can significantly enhance the thermal sink capability of these structures. In order to address the issue of low heat storage efficiency resulting from the low thermal conductivity of PCM, a novel integrated thermal protection structure (ITPS) architecture with a supportive structure based on a porous lattice has been designed. Experimental and numerical methods were employed to investigate the thermal response characteristics of the ITPS with and without PCM, the melting behavior of PCM within the porous lattice, and the effects of lattice configuration and pore size on the PCM melting rate. The current ITPS study includes evaluation of two types of lattice configurations and three different pore sizes. The results indicate that the inclusion of PCM reduces the internal panel temperature of the ITPS by approximately 15%. The melting of PCM occurs primarily at the central region of the porous lattice and gradually spreads towards the periphery until complete melting is achieved. Specifically, the Gibson–Ashby lattice configuration enhances the PCM melting rate by 43.5%, while the tetradecahedron lattice configuration yields a 53.1% improvement. Furthermore, for PCM with different pore sizes, smaller pores exhibit faster melting rates during the early and intermediate stages, whereas larger pores exhibit faster melting rates in the later stages as the proportion of liquid PCM increases. The conclusions of this study provide valuable insights for the application of PCM in the field of thermal management. [ABSTRACT FROM AUTHOR]

AbstractMetallic ligaments in open-cell metal foams have effectively improved the heat conduction of phase change materials (PCMs). However, when the gradient direction of porosity is perpendicular to the direction of heat conduction, the mechanism by which graded foam (GF) influences the phase transition of PCM remains elusive. To address this issue, this study employs the pore-scale numerical simulation and develops a numerical model to study the impact of GF on the charging of PCM-foam composites. The analysis identifies the local convection and heat conduction as the most crucial factors influencing heat transfer during phase transition. To effectively examine the role of metallic ligaments in the phase transition, simplified tetrakaidecahedron cells are adopted. The results demonstrate that the GF delays the charging of PCM. Specifically, compared to the homogeneous foam, the full melting time (FMT) of PCM in the GF increases by over 29%. Additionally, the integral-mean temperature response rate (ITRR) of PCM in the GF decreases by 20.2% to 22.1%. Within the GF, the PCM requires more time to melt completely in the tetrakaidecahedron cells with high porosity. Moreover, local convection plays a pivotal role, considerably reducing the FMTs of PCMs by over 85% and increasing the ITRRs of these structures by 588.1% to 599.0%. [ABSTRACT FROM AUTHOR]

AbstractThe influence of the local thermal nonequilibrium (LTNE) state on steady-state natural convection due to the heating and cooling of the side walls of the slender porous cavity has been addressed analytically and numerically. The porous medium is assumed to be hydrodynamically anisotropic. The Darcy model has been adopted. A closed-form solution, based on a parallel hypothesis, is reported for a slender cavity. The combined impact of media anisotropy and LTNE state on the heat transfer rate, as well as flow dynamics, have been analyzed. The help of boundary layer analysis is taken to report the boundary layer thickness and heat transfer rate of fluid flow analytically. It has been found that the maximum (minimum) heat transfer rate of the fluid phase as well as solid phase takes place at orientation angle, ϕ, equal to π/2 when permeability along the horizontal (vertical) direction is higher than the same along vertical (horizontal) direction. [ABSTRACT FROM AUTHOR]

AbstractNumerical analysis is performed to deduce the effect of aspect ratio (AR) and inclination of a rough-walled cavity on heat transfer, fluid flow, and entropy generation due to natural convection for Rayleigh number (Ra = 105). The cavity is filled with Al2O3-water nanofluid of 0.05 solid volume fraction. The natural convection process is caused by the temperature difference between the left hot wall and the right cold wall of the cavity. The walls are subjected to slip boundary conditions and the slip velocity is characterized by the Knudsen number (Kn = 0.5). The profile of the rough surface is generated by Weierstrass-Mandelbrot (W-M) function. Numerical simulations have been performed using Finite Element based software COMSOL Multiphysics 6.0. The AR is varied in the range of 0.5 to 4, and the inclination of the cavity is kept at 0°, 30°, and 60°. The numerical results are exhibited in terms of isotherms, streamlines, entropy generation due to heat transfer, and fluid friction irreversibilities. It is observed that the slip velocity on the walls has a strong influence on the fluid flow. Entropy generation due to fluid friction is found to increase with the rise in AR up to 2 and then it starts declining. The entropy generation due to fluid friction irreversibility at the center of the cavity is minimal, so the Bejan number is close to unity. Cavity with an inclination of 30° gives the maximum Nusselt number at any value of AR. Notably, the total entropy generation is observed to reach its maximum at α = 60° and minimum at α = 30°, offering comprehensive insights into the interplay of geometric and flow parameters within the cavity. [ABSTRACT FROM AUTHOR]

In this research, the effect of different models of thermal conductivity and dynamic viscosity has been investigated by considering the effect of Brownian motion of nanoparticles on the flow field and heat transfer of nanofluids. This study was performed numerically in a square cavity with water/aluminum-oxide nanofluid in three modes of natural, mixed and forced convection by changing the independent variable such as nanoparticle volume fraction, Rayleigh number, Richardson number, and Reynolds number. The governing equations with certain boundary conditions are solved using the finite volume method. Also, according to the obtained numerical results, Nusselt number has been investigated for different conditions with and without considering Brownian motion. The results showed that for all the studied models, in all three modes of natural, mixed and forced convection, the average Nusselt number when the effect of Brownian motion is considered, is more than the case that the effect of this motion is not considered. In all cases, the Koo & Kleinstreuer and Li & Kleinstreuer models show approximately the same values for the maximum mean Nusselt number. The similar results are obtained employing the Wajjha & Das and Xiao et al. models. For mixed convection, the highest and lowest increases of Nusselt number, considering Brownian motion are 17.68% and 14.84%, respectively. While referred values for forced convection are 30.46% and 17.94 %, respectively. [ABSTRACT FROM AUTHOR]

This study aims to look into the temperature distribution on a vertical flat plate with a variable temperature boundary condition. As a novelty, the variable temperature is considered on the wall, and coupled momentum and energy equation are solved. Moreover, a novel variable change transforms the infinite boundary condition into the finite one. The partial differential governing equations were introduced and transformed into ordinary differential equations form using the similarity solution. The obtained equations were numerically solved and validated using previous research. The results showed that for a constant variable temperature index (n), increasing the Prandtl number (Pr) from 0.1 to 2 reduces the dimensionless maximum velocity by less than half and the skin friction coefficient by about 32%. In this case, the dimensionless temperature approaches zero faster; as a result, the thermal boundary layer thickness declines, and the Nusselt number (Nu) rises. Furthermore, for a constant Pr, when n increases from 0 to 1.5, the dimensionless maximum velocity and the skin friction decrease by about 38% and 23%, respectively. Since the dimensionless temperature continues to descending trend, Nu still rises in this case. [ABSTRACT FROM AUTHOR]

Thermally-driven natural convection is theoretically explored in the present work within a porous layer with respect to the Darcy's law. The usual non circulating basic cellular flow between two infinitely long horizontal Darcy porous plates leads to generalized basic state considering the isothermal boundary conditions leading to the Hadley flow configuration. Such a motion is governed by a circulatory flow together with a temperature both varying along the horizontal axis. Hence, besides the buoyancy Rayleigh parameter, yet another parameter appears dominating the evolution of basic cellular circulation and thermal progress. Instability onset of this basic state is targeted based on the linear stability analysis of small normal modes. The resulting 3D instability system of equations is treated numerically and the stationary modes leading to convective neutral stability are determined. The found eigenvalues are also justified to be those deviating from the well-known no-flow Darcy porous solution through an asymptotic perturbation method in the special circumstances. The bounds of neutral stability curves in regard to the longitudinal, oblique and transverse modes are thoroughly investigated and it is shown that longitudinal modes are always the most unstable ones, while the transverse and oblique modes having finite encapsulated zone of instability can undergo a complete stability after a threshold value of horizontal temperature gradient parameter. [ABSTRACT FROM AUTHOR]

• A ROM methodology is proposed to solve convective-dominant conjugate heat transfer flows. • Numerical validation of the methodology is done exhaustively with benchmark solutions. • A mesh-based hyper-ROM approach is used to assess fast numerical approximations. • The use of ROM in all the unknown fields or only in the velocity and pressure is compared. • Speed-up of three hundred times is obtained through the use of ROM methodologies. This article presents a full and reduced-order methodology based on the finite element method that allows the characterization of convective-dominant conjugate heat transfer flows. Reduced-order modeling (ROM) allows the description of several degrees of freedom problems, referred to as full-order modeling (FOM), through a reduced-order surrogate representation based on a Petrov-Galerkin projection onto a reduced subspace. The FOM and ROM problems are stabilized through the Variational Multi-Scale (VMS) method, which ensures stability in dominant convective problems and allows equal interpolation spaces for the pressure, velocity, and temperature. The proposed methodology is validated solving natural heat convection in a differentially heated square cavity, considering air as the working fluid and Rayleigh numbers in the interval 10 4 ≤ Ra ≤ 10 8. In this problem, the benefit of using a ROM approximation for the three unknown fields, i.e., velocity, pressure, and temperature, is compared against ROM approximation only in the velocity and pressure fields and a FOM type approximation for temperature. The benefit of using mesh-based hyperreduction and its computational performance and precision are also analyzed. Subsequently, the method simulates a conjugate heat transfer problem that includes natural heat convection, allowing the inclusion of different rheologies between the working fluids. The results verify the precision and speed up of the calculations by more than three hundred times with respect to the time necessary to solve a full-order formulation, emerging it as a great potential tool in the resolution of thermally coupled flows. [ABSTRACT FROM AUTHOR]

In power applications, convection plays a dominant position in the transport of strength for the proper design to attain higher warmth transfer quotes. Where in the fluid movement is genuinely induced via density gradients. This has a look at what is involved with transient convection in an isosceles-superimposed triangular enclo sure. The walls were angled at θ = 45°. Critical Rayleigh numbers have been obtained: Ra = 106, especially for the fluid crushed between the two triangles where we can visualize the critical convection transaction between the air and water. The consequences in the quantitative dimension of average Nusselt quantity change and qualitative visualization of streamline and isotherms are examined. The air and water streamlines and the temperature fields had been obtained for the Rayleigh numbers 10³ ≤ Ra ≤ 108. Furthermore, the water fluid's natural convection case has the best heat transfer performance at the water fluid, whereas the dilatant fluid exhibits the lowest heat transfer performance. Heat transfer from the bottom to the top can be significantly improved by the triangle shape at first in a smooth and harmonious manner, and then it turns into a more complex and disorderly shape when the water reaches high temperatures. [ABSTRACT FROM AUTHOR]

It was found that the injection of bubbles into liquid can effectively improve heat transfer efficiency, so it is important for industrial applications to investigate the effect of bubble injection on heat transfer. The effect of bubble injection on natural convective heat transfer in steady laminar flows in a vertical channel is investigated using the volume of fluid (VOF) method, and the effects of bubble diameter, Eötvös number (Eo), bubble arrangement, and bubble distance from a hot wall on the heat transfer between the hot wall and liquid are studied, respectively. The results show that bubble injection can effectively improve the heat transfer between the hot wall and liquid; an increase in bubble diameter and Eo can improve the enhancement effect of heat transfer and can expand the enhancement area of heat transfer; the closer to the hot wall a bubble is, the better the enhancement of heat transfer is; and the spacing and arrangement of bubbles also have important effects on the heat transfer between the hot wall and liquid. The comparison shows that the enhancement of heat transfer is the best for the vertical arrangement of double bubbles, which increases the local heat transfer coefficient by 3.2 times. The enhancement of heat transfer generated by bubble injection is related to the degree of disturbance of the local liquid phase caused by bubble injection. The more strongly the local liquid is disturbed, the thinner the local temperature boundary layer becomes, and the better the enhancement of heat transfer is. [ABSTRACT FROM AUTHOR]

The aim of this study is to better understand the behavior of the nanofluid in a specific configuration, aiding in the creation of new models and designs for heat transfer systems, by investigating the MHD natural convection in an annular partially porous metal space between two vertical concentric cylinders, which is saturated by (Cu–water) nanofluid. The inside cylinder undergoes a regular heat flux, whereas the outer cylinder maintains a uniform temperature. The upper and lower walls are impermeable and insulated. In the upward direction, an exterior magnetic field with constant intensity is used. The nonlinear coupled conservation equations with specified boundary conditions in the vorticity-stream function form are solved using the finites differences method in conjunction with the successive over relaxation method. The numerical results obtained are presented to show the impact of a variety of control parameters depicted in Darcy number 10 - 5 ≤ Da ≤ 10 - 1 , Rayleigh number 10 4 ≤ Ra ≤ 10 6 , Hartmann number 0 ≤ Ha ≤ 100 , heater size, the porous layer thickness 0.25 ≤ Xp ≤ 0.75 , and nanoparticle concentration 0.01 ≤ ϕ ≤ 0.05 . From this study, the increase in the Ra number from 10 4 to 10 6 causes a thermal energy transmission improvement of 50%. Furthermore, a rise in the Da number from Da = 10 - 5 to Da = 10 - 1 enhances the thermal energy transport by approximately 30 % , while it reduces by 4.8% when we increase the Hartmann number from 0 to 100. Also, the rise in nanoparticle concentration leads to an enhancement of the average Nusselt number, while the heat transfer rate is reduced by extending the heater size. The numerical results also show a significant improvement in the thermal energy transport in active walls by using an optimum thickness layer of stainless steel porous medium, according to the Da number. Furthermore, this study demonstrates that there is a critical value of porosity for a given nanoparticle concentration and porous layer thickness for better heat transfer enhancement. [ABSTRACT FROM AUTHOR]

AbstractThis article presents both a theoretical and a numerical analysis of thermo-gravitational magnetic convection in electro-conductive Eringen micropolar fluids in a two-dimensional enclosure. The computational regime is bound with cold top, hot bottoms, and adiabatic side walls. The governing equations were transformed via scaled variables into dimensionless partial differential equations. A Finite volume method (FVM) is used to get a solution of the computational regime. Validation of the FVM solutions is included for non-magnetic special case from the literature. Streamline contours, isotherm contours, iso-microrotation contours (lines of constant angular velocity) and local Nusselt number at the left hot wall is depicted graphically for the impact of Hartmann (magnetic) number (Ha), Prandtl number (Pr), micropolar parameter (K) and Rayleigh number (Ra). A significant modification in internal circulation and micro-rotation in addition to temperature distribution is observed with increasing vortex viscosity parameter. Significant warping of isotherms is induced with stronger magnetic field and the mushroom-shaped core structure encountered at weak magnetic field transitions to a sigmoidal topology. [ABSTRACT FROM AUTHOR]

AbstractThis research work aims to study the effect of discrete heating on natural convective heat transfer, fluid flow, and entropy generation within a corrugated enclosure filled with water-based molybdenum disulfide (MoS2)–silicon dioxide (SiO2) hybrid nanofluid. In the study, various heights of the discrete heaters in terms of aspect ratios (AR=0.2, 0.4, 0.6, 0.8) are considered for various Rayleigh numbers (Ra=103−106) with varying nanoparticle volume fractions (ϕ=0%−4%). Stream function-vorticity formulations of two-dimensional (2D) Navier-Stokes equations and energy equation are used as the governing equations, and a higher-order compact (HOC) finite difference scheme is employed to discretize those equations. The results obtained from the current developed code are first validated with the existing numerical and experimental data. Finally, the present computed results are studied, both qualitatively and quantitatively, in terms of streamlines, isotherms, entropy generations, average Nusselt numbers, and Bejan numbers. At Ra=106 and the aspect ratio of heater length AR=0.2, a different and interesting flow and heat transfer phenomenon is observed. The results show that an increase in the aspect ratio of heater length from 0.2 to 0.8 decreases the average Nusselt number and total entropy generation by 57.49% and 13.76%, respectively, for Ra=106 and ϕ=4%. In addition, the effect of nanoparticle concentration on total entropy generation increases up to 73.40% when the aspect ratio of heater length increases to 0.8. [ABSTRACT FROM AUTHOR]

AbstractThree-dimensional numerical simulations were carried out to analyze natural convection in a differentially heated cubic cavity filled with spherical particles. Three models were considered: a fluid-only case for reference, a homogeneous porous media approximation, and a heterogeneous model that considered the actual structure of the solid particles. DEM (discrete element method) simulations were used to generate a realistic particle distribution for the construction of volumetric meshes for the heterogeneous model. The impact of thermal conduction through the solid particles was evaluated by varying the solid to fluid ratio (K*) within the range 0.02 − 50 for Rayleigh numbers between 103 and 105. Additionally, different number and diameter of the particles inside the cavity were evaluated. The results of the homogeneous approximation indicate a continuous decrease in the Nusselt number (Nu) as K* increases, associated with a higher effective thermal conductivity and the pressure drop. However, the more realistic heterogeneous model predicted the opposite trend. For K*<1, solid particles acted as thermal insulators, impeding fluid flow, while for K* > 1 conduction heat transfer between the isothermal walls and the particles was highly efficient and the particles surface area acted like extensions of the isothermal walls, facilitating heat transfer to the fluid phase, especially at lower Rayleigh values. [ABSTRACT FROM AUTHOR]

Using 3D transmission in a definite cavity with anisotropic and isotropic permeable media rotating at a fixed rotational velocity, the Rayleigh-Benard issue for a viscous, unstable, laminar, incompressible fluid heated from below a horizontal layer is extended in this paper's research. Seven controlling PDEs from the given physical configuration are similarly transformed to produce a system of non-dimensional ODEs. The Rayleigh, Taylor, and Prandtl numbers are examined for their impacts on temperature gradient and velocity in both isotropic and anisotropic conditions using the Fourier series approach. It has been discussed and determined that the results of the stream function and isotherms on a variety of factors are good. [ABSTRACT FROM AUTHOR]

The heat transfer characteristics of porous rock layers (PRLs) have significant seasonal differences. This feature has been used to protect the permafrost subgrade under highways and railways from degeneration. However, in cold sandy environments, the transformation law of heat transfer characteristics of PRLs on account of climate warming and aeolian sand filling needs to be solved. This work developed a coupled heat transfer model for the soil–PRL system aimed at analyzing the convective heat transfer process and mechanism of a closed PRL. Furthermore, the impact of climate warming and sand filling on the cooling performance of the PRL under different mean annual air temperatures (MAATs) of −3.5, −4.5, and −5.5 °C was quantified. The numerical results indicated that the natural convection of the closed PRL occurred only in winter, and the effective convective height of the rock layer decreased with the sand-filling thickness. As the thickness of sand filling increased, the critical temperature difference for the occurrence of natural convection increased, accompanied by decreases in the Rayleigh number, the duration, and intensity of natural convection. When the sand-filling thickness exceeded 80 cm, natural convection would not occur in the PRL. Under a warming scenario of 0.052 °C·a−1, the cooling performance of the PRL could offset the adverse impact of climate warming and raise the permafrost table in the first 20 years. Moreover, the closed PRL can be more effective in permafrost regions with colder MAATs. For cold sandy permafrost zones, sand-control measures should be taken to maintain the long-term cooling performance of the PRL. This study is of great significance in guiding porous rock embankment design and road maintenance along the Qinghai–Tibetan Railway. [ABSTRACT FROM AUTHOR]

An incompressible, electrically conducting, and viscous fluid flowing steadily and freely across a uniformly porous media that is partially constrained by an infinitely long vertical porous plate is studied in the present article. Additionally, chemical reaction and radiation absorption effects are seen. Here, a magnetic field of uniform strength is applied transversely to the plate, a normal suction velocity is imposed on the fluid, and the heat flux is considered to be constant. The non‐dimensional momentum and energy equations are solved using the method of perturbation. The problem has been analytically resolved, and several parameters, including the Hartmann number, porosity parameter, thermal Grashof number, mass Grashof number, and transport properties like the Sherwood number, skin friction, and plate temperature, are graphically represented. The current study reveals a spike in the radiation absorption effect causes skin friction to drop, but on the other hand, a contrary effect is observed for plate temperature. One of the notable findings of this investigation is that the Sherwood number increases as chemical reaction parameter influence increases. [ABSTRACT FROM AUTHOR]

Constructal design of vertical multiscale triangular fins in natural convection is investigated in this paper. The design consists of two parts. The first part is for single‐scale triangular fins. The objective in the first design is to reach to the highest heat transfer density from the fins for three fin angles (15°, 30°, and 45°). The single‐scale fins are placed in a horizontal array and considered as isothermal fins. The degrees of freedom are the fin angle, and the fin‐to‐fin spacing. The constraint is the fin height. The second part is for multiscale fins where small fins are placed between the large fins which are optimized in the first part. In the second part, the angles of the large and small scales fins are kept constant at (15°). The optimal fin‐to‐fin spacing which is obtained in the first part is considered a constraint in the second part. The Rayleigh numbers in this design are (Ra = 103, 104, and 105). The two‐dimensional mass, momentum, and energy equations for natural convection are solved with the finite volume method. The results show that there is a benefit of placing the small‐scale fins where the percentage increase in the heat transfer density is (10.22%) at (Ra = 103), and (50.6%) at (Ra = 105) due to existence of the small fins between the large fins. [ABSTRACT FROM AUTHOR]

Under the combined influence of buoyancy force and constant pressure gradient, the free convection flow and heat transmission inside a channel placed vertically and consisting of two parallel walls are examined. Through the application of the Runge–Kutta fourth‐order approach and the shooting procedure, the modeled equations of the problem including nonlinear density–temperature and quadratic viscosity–temperature change at constant but different wall temperatures are numerically solved. For distinct values of the embedded parameters, the fluctuations in fluid's velocity and temperature are examined. For various situations of linear, quadratic, and nonlinear dependence of density on temperature, numerical values for heat transmission rate, volume flow rate and skin friction are determined and tabulated. The fluctuations of the Nusselt number with the Grashof number corresponding to thermal expansion coefficients are depicted through graphical interpretations. It was found that the combined effect of thermal expansion coefficients raises the values of the physical entities, Nusselt number, volume flow rate, and heat transmission rate. For the lower Reynolds number values, the Nusselt number value stays around one, indicating the same impact of conduction and convection on heat transmission. [ABSTRACT FROM AUTHOR]

With the increasing oil demand, the construction of oil energy reserves in China needs to be further strengthened. However, given that there has been no research on the main influencing factors of crude oil temperature drop in storage tanks under actual dynamically changing environments, this paper considers the influence of dynamic thermal environment and internal crude oil physical properties on the fluctuating changes in crude oil temperature. A theoretical model of the unsteady-state temperature drop heat transfer process is developed from a three-dimensional perspective. According to the temperature drop variation law of crude oil storage tank under the coupling effect of various heat transfer modes such as external forced convection, thermal radiation, and internal natural convection, the external dynamic thermal environment influence zone, the internal crude oil physical property influence zone, and the intermediate transition zone of the tank are proposed. And the multiple non-linear regression method is used to quantitatively characterize the influence of external ambient temperature, solar radiation, wind speed, internal crude oil density, viscosity, and specific heat capacity on the temperature drop of crude oil in each influencing zone. The results of this paper not only quantitatively explain the main influencing factors of the oil temperature drop in the top, wall, and bottom regions of the tank, but also provide a theoretical reference for oil security reserves under a dynamic thermal environment. [ABSTRACT FROM AUTHOR]

Abstract Natural convection in cavity with built-in plates has been widely used in fluid mechanics and heat transfer engineering, such as heat exchangers, electronics, solar collector, growing crystals, etc. However, the natural convection flow physics and heat transfer characteristics in cavity with plate arrays remain to be investigated further. In this study, numerical analysis and computational fluid dynamics simulation are conducted for natural convection in cavity with plate arrays by finite volume method. Key influence factors impacting heat transfer are analyzed, including the line dip-angle of plate arrays θ, rotary angle of plates to the array φ, with relationships comparison between the Nusselt number and Rayleigh number in different built-in plate arrays. Moreover, for illustrative application example, the natural convection in solar greenhouse with PV arrays roof is investigated, with inside temperature distribution comparison under different design parameters. The preliminary results indicate that plates spacing could remarkably impacts the number of streamlines between ”late’arrays. The dip-angle of arrays θ leads to different shape flow in the cavity, and the rotary angle of plates φ notably affects the fluid flow direction in the vicinity areas of plates, especially when φ = 90°. Solar greenhouse case study indicates that increasing array group numbers can improve air temperature distribution uniformity in the cavity, which is favorable for built environment accurate control and operation. This work can provide modeling method support and reference for natural heat convection applications. [ABSTRACT FROM AUTHOR]

Abstract This study investigates the consequences of introducing a pair of oscillating elliptical obstacles on the natural convection and entropy generation within a quarter-circle cavity that is filled with a water-based hybrid nanofluid. The Galerkin Finite Element Method was utilized to perform numerical simulations on a 2-dimensional cavity, where the outer wall was set to a low temperature and the inner wall was kept at a high temperature, while the other walls were adiabatic. The hybrid nanofluid containing Cu-Al2O3 nanoparticles was used. The impact of changes in the values of dimensionless parameters, such as the Rayleigh number, heated wall length, oscillation frequency, oscillation amplitude, and oscillation period, on the flow and heat transfer within the cavity was examined. Results showed that an increase in the length of the hot source resulted in a decrease in heat transfer rate and that increasing the Rayleigh number led to a significant increase in total entropy generation and heat transfer irreversibility. A drop in the average Bejan number was noted as the Rayleigh number increased, demonstrating the prevalence of entropy caused by fluid friction. The effect of changing the amplitude had a higher impact on the average Nusselt number compared to the frequency value. At low Rayleigh numbers, the average Nusselt number was higher when the elliptical obstacles oscillated in the same direction, while the opposite trend was observed at higher Rayleigh numbers. [ABSTRACT FROM AUTHOR]

In this experimental work, heat transfer intensification using ultrasonic waves was investigated. A heat source, consisting in a parallelepiped aluminum block in which two electrical heating cartridges of 160 W each were mounted to heat four liters of distilled water contained in a tank made of Plexiglas. To demonstrate the effectiveness of heat transfer enhancement with the use of ultrasounds, three different configurations were analyzed. In the first one, considered as a reference case, the heat transfer was studied without ultrasound field. In the second configuration, ultrasonic acoustic waves were generated using one transducer vibrating at a fixed frequency of 40 kHz with a total power of 60 W. In the last configuration, ultrasounds were generated with two similar transducers mounted on two opposite walls of the water tank while maintaining the same power and frequency. The effect of the distance separating the heat source to the transducers on the convective heat transfer coefficients and the average temperature of the water in the tank were analyzed in detail. The results revealed that the natural convection heat transfer in the water tank was intensified by means of low frequency acoustic waves. Indeed, it was shown, particularly, that more the distance between the transducer and the heater is low more the heat transfer improvement is better. The heat transfer enhancement factor was estimated to 2.5 on the surface facing the transducer while it was only about 1.2 on the opposite surface in C2 configuration. In C3 configuration, the heat transfer enhancement factor is nearly the same with, however, more homogenous water temperature. The acoustic cavitation and streaming were identified as the main phenomena leading to these results. This study successfully demonstrated the feasibility of heat transfer intensification using low frequency ultrasonic waves. [ABSTRACT FROM AUTHOR]

The present article provides a three‐dimensional numerical investigation of thermal convection and entropy generation. The lattice Boltzmann method, coupled with the finite difference approach, is applied to perform numerical simulations. The validation of these numerical approaches for thermal convection simulation and entropy calculation is performed by comparing our numerical results with those in the published literature for the case of benchmark problems. The physical geometry studied in this paper concerns a hot obstacle having the shape of a plus sign (+) placed in the center of a cubic enclosure. This cube is filled with air of a Prandtl number of 0.71 and characterized by two cold vertical walls. The heat exchange between the fluid and the hot body is studied as a function of the Rayleigh number (103≤Ra≤107 ${10}^{3}\le {Ra}\le {10}^{7}$). The performed simulations show that the heat transfer rate can be increased by about 429% by switching from Ra=103 ${Ra}={10}^{3}$ to 107 ${10}^{7}$. The entropy generation due to fluid friction, heat transfer, and total entropy are also calculated and discussed. For an irreversibility coefficient φ=10−4 ${\varphi }={10}^{-4}$, the analysis of the results showed that for low values of the Rayleigh number (Ra=103 ${Ra}={10}^{3}$), the entropy production due to temperature gradients predominates over that produced by viscous effects. In the cases of Ra=104 ${Ra}={10}^{4}$ and 105 ${10}^{5}$, entropy generation is due to both fluid friction and heat transfer. However, when the Rayleigh number becomes large (Ra≥106 ${Ra}{\ge 10}^{6}$), entropy generation due to viscosity predominates over entropy production related to heat exchange. These results have important implications for the optimization and design of heat transfer systems in various industrial applications. [ABSTRACT FROM AUTHOR]

This study focuses on the steady free convection of an electrically conducting viscous and incompressible fluid in a vertically oriented porous channel with a line/point heat source/sink (point/line heat generation/absorption) at different channel positions in the coexistence of magnetic and suction/injection parameters. The constant heat source/sink parameters, which mathematically define the line heat source/sink, are modeled using the Heaviside step function. The Laplace transform procedure was applied to find the precise expression for the dimensionless governing equations that make up the flow model. Investigations were conducted on flow patterns with line graphs to visually depict the function of the magnetic, suction/injection, and heat generation parameters. The tabular simulations of results demonstrate that increasing the suction/injection parameter can result in a decrease in the mass flow rate by 8.9%. Similarly, increasing the magnetic parameter causes the mass flow rate to drop by almost 27%. Furthermore, with an improvement in the magnetic and suction/injection parameters, frictional force and mass flux values declined. An upsurge in the magnetic fieldand suction/injection parameters causes a rise in skin friction and mass flux near the left surface and a decline at around the right surface as the point heat source extends over a region. [ABSTRACT FROM AUTHOR]

We report one of the first experimental investigation on simultaneous mapping of whole field temperature and velocity data to demonstrate the potential of thermographic PIV (or LIP/PIV) in the context of natural convection for a back-wall heated open square cavity. As part of the validation exercise, LIP/PIV-based results are compared with corresponding numerically simulated and interferometry-based whole field data. The study holds its importance as it successfully captures the flow physics associated with the buoyancy-driven convective phenomena in the cavity at varying temperature differences using a single imaging technique instead of two separate sets of optical diagnostics. [ABSTRACT FROM AUTHOR]

An experimental setup has been developed to measure the thermal state of a conical antenna cooled by means of porous media saturated with water-based copper nanofluid. Thermal conductivity of the used porous materials varies between 4 and 41.2 times that of the water which constitutes the base fluid of the nanofluid whose volume fraction ranges from 0% (pure water) to 5%. The antenna is placed in the center of a coaxial concentric cavity of the same shape. Aspect ratio of the enclosure varies between 0.2 and 0.6. Its base is inclined with respect to the horizontal plane with an angle ranging between 0° and 180° corresponding to a horizontal circular base with the top of the cone oriented upwards and downwards, respectively. Measurements validate the calculations obtained in a recent numerical approach based on the finite volume method. They confirm that the Maxwell and Brinkman models remain valid for the ranges of the Rayleigh number considered here (3.32 x 10 5 − 6.74 x 10 7) and Water based-Copper nanofluid volume fraction (0–5%). This work also confirms the effectiveness of porous materials saturated with nanofluids to ensure the thermoregulation of electronic equipment dissipating a large amount of thermal power. [ABSTRACT FROM AUTHOR]

Investigating natural convection heat transfer of nanofluids in various geometries has garnered significant attention due to its potential applications across several disciplines. This study presents a numerical simulation of the natural convection heat transfer and entropy generation process in an E-shaped porous cavity filled with nanofluids, implementing Buongiorno's simulation model. Analyzing the behavior of individual nanoparticles, or even the entire nanofluid system at the molecular level, can be extremely computationally intensive. Symmetry is a fundamental concept in science that can help reduce this computational burden considerably. In this study, nanofluids are frequently conceived of as a combination of water and Al2O3 nanoparticles at a concentration of up to 4% by volume. A unique correlation was proposed to model the effective thermal conductivity of nanofluids. The average Nusselt number, entropy production, and Rayleigh number have been illustrated to exhibit a decreasing trend when the volume concentration of nanoparticles inside the porous cavity rises; the 4% vol. water–alumina NFs yield 17.35% less average Nu number compared to the base water. [ABSTRACT FROM AUTHOR]

Abstract In the present article, magneto-double-diffusive density driven convection accompanied by an entropy optimization analysis of Al2O3-water nanofluid filled in a horizontal coaxial annular space is numerically addressed. The double-diffusive natural nanofluid flow which is produced due to the maintaining of constant and different temperature and solute on the inner and outer cylinders is affected by a uniform vertical magnetic field. Dimensionless governed equations which are developed through law of conservation of mass, momentum, and energy are numerically solved via finite volume approach, and parametric control analysis is developed. By using Corcione empirical correlations considering the Brownian diffusion of 4% of Al2O3 nanoparticles in water, the thermal conductivity and viscosity of the mixture nanofluid are determined. Results are performed and interpreted in detail for wide range of relevant variables: Rayleigh (102 ≤ Ra ≤ 105), Hartmann (0 ≤ Ha ≤ 30), Lewis numbers (0 ≤ Le ≤ 10), and Buoyancy ratio (−4 ≤ N ≤ 4) to evaluate the double-diffusive convective nanofluid flow, heat and solute transfer rates as well as entropies produced in the system. [ABSTRACT FROM AUTHOR]

This study numerically simulates optimal thermal convection and entropy production minimization in a steady magnetohydrodynamic micropolar hybrid nanofluid (Ag–Al2O3/H2O) flow through an annulus region bounded between an elliptical cylinder (inner) and a square cylinder (outer) with partially insulated and partially heated walls. Four different configurations with heater locations were considered when the heater was placed continuously or discretely at different locations along the annulus' boundaries. The governing equations were derived from the Navier–Stokes equations along with the angular momentum equation of microrotation. The flow domain, bounded between two dissimilar geometrical surfaces, was transformed into a computational domain. The modeled set of equations was solved using an in-house developed MATLAB program code based on the finite difference method with the succesive over relaxation, succesive under relaxation, and Gauss–Seidel iteration techniques. The impacts of the Hartmann number, Rayleigh number, volume fraction of nanoparticles, and vortex viscosity parameter on the streamlines, isotherms, average Nusselt number, average Bejan number, and entropy generation number were computed to analyze the flow dynamics and convective heat transfer mechanism. The average Nusselt number increased linearly with ϕhnf, higher for the inner elliptic cylinder. As K0 rises, heat convection declines. In contrast to Cases II and I, Cases III and IV exhibit a greater attenuation of heat convection at the inner elliptical cylinder. The Nuo declines rapidly for Cases I and III compared to Cases II and IV. Increasing the concentration of nanoparticles improved heat convection. Both Nui and Nuo increase linearly with ϕhnf, but the rise is more pronounced from the inner elliptical cylinder than the outer square cylinder. It is found that Cases II and III have the highest and lowest Beavg values, while Cases III and I have the highest and lowest Ns values. Beavg diminishes and the total entropy generation Ns increases with Ha, Ra, and ϕhnf, while reverse effect of vortex viscosity Ko. [ABSTRACT FROM AUTHOR]

In the present work, the effect of natural convection caused by immiscible intermediate fluid on melting process in a horizontal shell-and-tube latent heat storage is examined numerically. The intermediate fluid is placed between the section filled with phase change material and the storage outer hot wall (as heat source). Water is considered as the intermediate fluid to transfer heat from the hot wall to PCM (n-octadecane) by the buoyancy impact of heated water. Water and the liquid phase of the n-octadecane are immiscible. Numerical analysis is performed employing the enthalpy-porosity method with the assistance of a commercial CFD code, ANSYS FLUENT 18.2, based on the finite volume method. The present work consists of two parts. In the first part, a simple 2D latent heat storage with various volume proportions of water as intermediate fluid, including; 25, 50, 75, and 100%, is considered. In the second part, the effect of the number and arrangement of heat transfer fluid channels is evaluated and analyzed. In all investigated models, the volume of the storage is constant and the amount of the PCM varies. The solid PCM was subcooled to 1 ℃, and the temperature of the surface of the storage was maintained at 329 K. The pertinent dimensionless parameters, including; Prandtl, Rayleigh, and Stefan numbers, are 59.5, 6.3 × 108, and 0.27, respectively. The results depicted that the maximum saved energy inside the proposed latent heat storage belongs to the case with 50% of storage volume capacity filled by water. Moreover, the case with four heat transfer fluid tubes indicated the highest absorbed energy, and among them, the four tubes with diamond pattern arrangement stored the highest amount of energy. [ABSTRACT FROM AUTHOR]

In order to improve convective flow, this study primarily used techniques including curved surfaces and a strong magnetic force. Cold temperatures and even flow are experienced by both the circular outer wall and the sinusoidal inner wall. FHD can have a bigger effect when combined with iron oxide in the base fluid. The electric current-carrying wire was positioned close to the interior wall in order to produce Kelvin force. A novel modeling approach was chosen to ascertain the number of scalars throughout the entire domain, and the process was validated using earlier numerical work. Gravity forces, ferrofluid concentrations, and the Kelvin force serve as the main pillars of current research. Conduction features increase and the Nu rises by 12.44% when nanopowders are used. Due to gravity and magnetic forces, the nanofluid can move more easily through the container. At Ra=1e3 and 1e4, respectively, Nu increases by 93.04% and 35.43%; with an increase in MnF. Additionally, Nu rises with Ra at MnF=0 and MnF=4000 by 43.55% and 0.71%, respectively. [ABSTRACT FROM AUTHOR]

The purpose of this article is to study the convergence of a low order finite element approximation for a natural convection problem. We prove that the discretization based on P 1 polynomials for every variable (velocity, pressure and temperature) is well-posed if used with a penalty term in the divergence equation, to compensate the loss of an inf-sup condition. With mild assumptions on the pressure regularity, we recover convergence for the Navier-Stokes-Boussinesq system, provided the penalty term is chosen in accordance with the mesh size. We express conditions to obtain optimal order of convergence. We illustrate theoretical convergence results with extensive examples. The computational cost that can be saved by this approach is also assessed. [ABSTRACT FROM AUTHOR]

Abstract The buoyancy-driven thermofluid dynamics of a solid/hollow cylinder with concave surfaces have been studied in a laminar regime ( 10 4 ≤ R a ≤ 10 8 ) using the finite-volume method to analyze the effects of L / D ( 2 ≤ L / D ≤ 10 ) , and D t h / D   ( 0.2 ≤ D t h / D ≤ 0.9 ) . Conservation equations for mass, momentum, and energy have also been solved in a 2-D axisymmetric geometry . Second-order upwind and central difference schemes have been deployed to discretize the convective and diffusive terms. Heat dissipation increases with R a irrespective of L / D for both cylinders. However, the N u ¯ total remains constant with the L / D ratio for a hollow concave cylinder N u ¯ i n increases with D t h / D ; whereas, N u ¯ out decreases. Multiple vortices appear at the outside surface at a low D t h / D (i.e. = 0.2), and these vortices almost disappear at high D t h / D (i.e. = 0.6), affecting the outside average Nusselt number from low to high. In all cases, N u ¯ out is higher than N u ¯ i n . The thermofluid dynamics of solid and hollow cylinders have been delineated through different countour and vector plots, and two correlations for Nu have been deveoped. [ABSTRACT FROM AUTHOR]

The power-law nanofluid natural convection in a chamber with a thermally generating unit and a solid ribbed structure has been studied in this work. A mixture of carboxymethylcellulose with water and copper nanoparticles is a working fluid illustrating pseudoplastic properties. The effective properties of the nanoliquid have been described by experimental correlations reflecting the temperature effect. The governing equations have been formulated on the basis of the conservation laws of mass, momentum and energy employing non-primitive parameters such as stream function and vorticity. The defined boundary value problem has been worked out by the finite difference technique using an independently developed calculation system. The Rayleigh number is fixed for analysis (Ra = 105). The paper analyzes the influence of the nanoparticles volume fraction, an increase in which reduces the temperature in the case of the one edge presence. An analysis of the rib height has shown that its growth leads to a weakening of the convective heat transfer, but at the same time, the source temperature also decreases. Increasing the number of fins from 1 to 3 also helps to reduce the average temperature of the heat-generated element by 15%. [ABSTRACT FROM AUTHOR]

The current investigation deals numerically with a two-dimensional steady laminar flow natural convection heat transfer of a dilute suspension of a base fluid and suspension of Nano Encapsulated Phase Change Materials (NEPCMs) nanoparticles saturated inside an inclined square enclosure with a centered internal conducting square block with a ratio of 0.5. The enclosure inclination angle varies from 0° to 90° with increments of 15°, and block thermal conductivity to the host fluid has been chosen to be 0.2 and 5. The obtained results are in excellent agreement with those available in the literature for validation. The findings reveal that the heat transfer depends considerably on the inclination angle, block thermal conductivity ratio, and Stefan number for all considered ranges. The present results suggest that the average Nusselt number rate is notably enhanced as the inclination angle rises from 0° to 90° for thermal conductivity KR = 0.2 and KR = 5; this enhancement is more evident as the Rayleigh number is increased. The average Nusselt number improves by 5%, 153%, 558%, and 1120% for Rayleigh numbers of 103, 104, 105, and 106, respectively, when the inclination angle varies from 0° to 90° for a thermal conductivity ratio of 0.2. This improvement is somewhat reduced in the case of a thermal conductivity of 5, where the average Nusselt number grows by around 0.4%, 27%, 213%, and 537% for Rayleigh numbers 103, 104, 105, and 106, respectively. The higher value of the latent heat capacity of encapsulated particles enhances the heat transfer rate; the decreased Stefan number induces a notable improvement in the average Nusselt number. This enhancement is more evident as the inclination angle increases. The findings clearly show a considerable influence on the isotherms and heat capacity ratio distributions for all considered block thermal conductivities and Rayleigh numbers. [ABSTRACT FROM AUTHOR]

An interaction of natural convection and surface radiation in a rotating cubic cabinet is scrutinized in this article. The cavity has differentially heated walls, namely opposite heated and cooled walls, while the remaining boundaries are adiabatic. The key equations have been written employing the mass, momentum, and energy conservation laws combined with nonprimitive dimensionless variables including vector potential functions and vorticity vector. The resulting set of equations with the corresponding restrictions has been discretized and resolved employing the finite difference procedure employing a uniform grid. The outcomes have been analyzed for a wide range of key characteristics, including the surface emissivity and the Rayleigh and Taylor numbers. The temperature distributions have been shown during a complete revolution of the chamber. The influence of the governing parameters has been described by changing the mean convective and radiative Nusselt numbers. The results have shown that rotation and radiation can be used as key mechanisms to control the energy transport. Moreover, employing the Boussinesq approach the thermal centrifugal force can be neglected for moderate Rayleigh and Taylor numbers. [ABSTRACT FROM AUTHOR]

In order to consider the influence of thermal radiation and winding insulation paper on the temperature field of transformer natural convection in practice, a physical calculation model of transformer hot-spot and temperature-rise including gasket, insulation paper cylinder, pressing plate, winding insulation paper and black body thermal radiation was established based on an oil immersed transformer SSZ20- 63000/ 110. The influence of thermal radiation and winding insulation paper on the temperature field of transformer natural convection was studied through a finite element method. The results show that in the case of natural convection, thermal radiation will make the winding temperature of hot-spot and temperature-rise slightly, while the winding surface insulating paper will make the winding temperature of hot-spot and temperature-rise significantly. The thermal radiation will not affect the distribution of hot-spot, while the winding insulation paper will make the distribution of hot-spot move down. Although the thermal radiation has little effect on the temperature of hot-spot of the winding, it has a greater effect when considered together with the winding insulating paper. It can be seen that the thermal radiation and winding insulation layer should not be ignored in the simulation calculation, otherwise the difference with the actual value is too large. [ABSTRACT FROM AUTHOR]