Three-dimensional Natural Convection Research Articles

Control of Three-Dimensional Natural Convection of Graphene–Water Nanofluids Using Symmetrical Tree-Shaped Obstacle and External Magnetic Field

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%.

New higher-order accurate super-compact scheme for three-dimensional natural convection and entropy generation

Exploring natural convection in three dimensions through numerical analysis has become essential for gaining a deeper understanding of this process compared to studying it in just two dimensions. This paper presents an enhanced analysis of three-dimensional (3D) natural convection phenomena within an air-filled cubical cavity, with a primary focus on heat transfer characteristics. The distinguishing feature of this research lies in the pioneering application of the newly developed higher-order accurate super-compact finite difference scheme to study 3D natural convection and entropy generation. This numerical method is renowned for its fourth-order spatial accuracy and second-order temporal accuracy. The super-compact scheme employs 19 grid points at the current time level (nth time level) while utilizing just seven grid points from the subsequent time level [(n+1)th time level. The flow is considered to be 3D, time-varying, laminar, and incompressible. First, the newly developed numerical code has undergone validation through quantitative and qualitative comparisons with existing results. Then, we analyze the flow phenomena and heat transfer dynamics within the cavity for various Rayleigh numbers (102≤Ra≤105) with a fixed Prandtl number (Pr = 0.71) by using this scheme. Various parameters such as local Nusselt numbers, averaged Nusselt numbers, local entropy, Bejan number, streamlines, and isotherm dispersion are studied in this work. It is found that as the Rayleigh number (Ra) increases, the Bejan number (Be) decreases, while the total entropy increases. When the Ra is less than or equal to 104, the Be remains above 0.5, indicating that irreversibility primarily arises from heat transfer. However, as we transition to Ra=105, the Be falls below 0.5, signaling that irreversibility is now predominantly driven by viscous effects. To the best of our knowledge, this research marks a pioneering effort by introducing the application of the higher order super-compact (HOSC) scheme for the examination of heat transfer within a 3D cubic cavity, thus endowing our work with a truly novel and pioneering character. It is worth mentioning that, before this study, there has been no precedent in the exploration of heat transfer using the super-compact scheme, thus endowing our work with a truly novel and pioneering character.

Numerical investigation of three-dimensional natural convection heat transfer on corrugated plates of variable height

PurposeThe purpose of this study is to numerically investigate the geometric influence of different corrugation profiles (rectangular, trapezoidal and triangular) of varying heights on the flow and the natural convection heat transfer process over isothermal plates.Design/methodology/approachThis work is an extension and finalization of previous studies of the leading author. The numerical methodology was proposed and experimentally validated in previous studies. Using OpenFOAM® and other free and open-source numerical-computational tools, three-dimensional numerical models were built to simulate the flow and the natural convection heat transfer process over isothermal corrugation plates with variable and constant heights.FindingsThe influence of different geometric arrangements of corrugated plates on the flow and natural convection heat transfer over isothermal plates is investigated. The influence of the height ratio parameter, as well as the resulting concave and convex profiles, on the parameters average Nusselt number, corrected average Nusselt number and convective thermal efficiency gain, is analyzed. It is shown that the total convective heat transfer and the convective thermal efficiency gain increase with the increase of the height ratio. The numerical results confirm previous findings about the predominant effects on the predominant impact of increasing the heat transfer area on the thermal efficiency gain in corrugated surfaces, in contrast to the adverse effects caused on the flow. In corrugations with heights resulting in concave profiles, the geometry with triangular corrugations presented the highest total convection heat transfer, followed by trapezoidal and rectangular. For arrangements with the same area, it was demonstrated that corrugations of constant and variable height are approximately equivalent in terms of natural convection heat transfer.Practical implicationsThe results allowed a better understanding of the flow characteristics and the natural convection heat transfer process over isothermal plates with corrugations of variable height. The advantages of the surfaces studied in terms of increasing convective thermal efficiency were demonstrated, with the potential to be used in cooling systems exclusively by natural convection (or with reduced dependence on forced convection cooling systems), including in technological applications of microelectronics, robotics, internet of things (IoT), artificial intelligence, information technology, industry 4.0, etc.Originality/valueTo the best of the authors’ knowledge, the results presented are new in the scientific literature. Unlike previous studies conducted by the leading author, this analysis specifically analyzed the natural convection phenomenon over plates with variable-height corrugations. The obtained results will contribute to projects to improve and optimize natural convection cooling systems.

NUMERICAL STUDY FOR A THREE DIMENSIONAL LAMINAR NATURAL CONVECTION HEAT TRANSFER FROM AN ISOTHERMAL HEATED HORIZONTAL AND INCLINED SQUARE PLATE AND WITH A CIRCULAR HOLE

A theoretical study for a three-dimensional natural convection heat transfer from an isothermal horizontal , vertical and inclined heated square flat plates (with and without circular hole) has been done in the present work. The study involved the numerical solution of the transient Navier-Stokes and energy equations by using finite deference method (F.D.M.). The complete Navier-Stokes equation are transformed and expressed in terms of vorticity-vector potential. The Energy and Vorticity equations were solved by using an Alternating Direction Implicit (ADI) method because they are transient equations of parabolic portion, and the Vector potential is solved by using an equations Successive Over-Relaxation (S.O.R) method because it is from elliptic portion. The numerical solution is capable of calculating the Vector potential, three components of Vorticity and temperature field of the calculation domain. The numerical results were obtained in rang of Grashof number (103≤Gr≤5x104 ) with Prandtl number of (0.72) for square flat plate and the other consist a circle hole with ratio 0.6 and 0.8 diameter of the hole to main square side length. The numerical results showed that the main process of heat transfer is conduction for Grashof number less than 103 and convection for Grashof number larger than 103 and the results of local Nusselt number show fairly large dependence on inclination angle. For horizontal plate facing upward and downward, average Nusselt number is proportional to one-fifth power of Rayleigh number, and there is a significant difference in heat transfer rates between the upward and downward cases. For horizontal plate with circle hole facing upward for Grashof number 104 , the effect of core portion caused a limited increment in the heat transfer rate, where as for the facing downward case, the effect was larger and the maximum value of heat transfer rates is be for square flat plate with circle hole by ratio 0.6 for all inclination angles. With the increase of Grashof number to 5x104 heat transfer rates decrease except the square horizontal flat plate with circle hole by ratio 0.6 . The average Nusselt number increases with the increase of inclination of plates facing upward to reach to the higher average Nusselt number at vertical position then decrease with increase of inclination of plates. And the maximum value of average Nusselt number is depended on the ratio of diameter of the hole to main square side length, showed that the maximum temperature gradient occurs at the external edge of the horizontal plate (with and without circle hole) facing upward and at the lower external edge in inclined case. The numerical results was made through comparison with a previous numerical and experimental work, the agreement was good.

Study on the steady-oscillatory transition of three-dimensional (3D) natural convection via Hopf bifurcation

The transition from steady-state flow to periodic oscillatory flow for the natural convection by Hopf bifurcation is investigated in a three-dimensional (3D) cavity. The spectral collocation method (SCM) in combination with the artificial compressibility method (ACM), which is developed by ourselves as a numerical method SCM-ACM with high accuracy, is employed to solve the governing equations directly instead of linear stability analysis method that is commonly used for the research on flow instability. The results show that the amplitude decays exponentially with time and the decay rate is linear with the Grashof number (Gr). The critical Grashof number for steady-oscillatory transition is obtained as Grcr = 3.423 × 106. The dimensionless angular frequency ωcr = 0.24 is also determined by Fourier analysis. In this work, we also examine the heat-momentum interactions within the boundary layers, visualize the periodic oscillations of temperature and velocity amplitudes, and analyze the origin of instability from multiple angles. The results show that large oscillations of velocity and temperature are observed near the isothermal walls. The oscillation is enhanced by the increase of thermal boundary layer thickness and flow velocity at both ends of isothermal walls. The maximum velocity and temperature amplitudes appear at the lower left and upper right corners of the mid-plane (Z = 0.5), where are the origin of instability, and the spanwise walls are almost independent of oscillations. The oscillatory flow of natural convection in three-dimensional cavity originates from the continuously increasing buoyancy force, and its transition occurs by Hopf bifurcation. Moreover, the temperature amplitude exhibits a wavy distribution on the mid-plane (X = 0.5) and strongly depends on the depth Z. These results provide benchmark data for future numerical studies and engineering application.

Experimental Study of Natural Convection Heat Transfer in Confined Porous Media Heated From Side

Transient three-dimensional natural convection heat transfer due to the influences of heating from one side of an enclosure filled with a saturated porous media, whereas the opposite side is maintained at a constant cold temperature, and the other four sides are adiabatic, were investigated in the present work experimentally. Silica sand was used as a porous media saturated with distilled water filled in a cubic enclosure heated from the side,using six electrical controlled heaters, at constant temperatures of (60, 70, 80, 90, and 100oC). The inverse side cooled at a constant temperature of (24oC) using an aluminum heat exchanger, consisted of 15 channels feeded with constant temperature water. Eighty thermocouples were used to control the heated and cooled sides, and to measure the temperature in the entire enclosure. Experimental results showed that the heat transfer regime was mainly conduction for all Rayleigh numbers with small influence of convection for Ra=42 and greater for Ra=55. This effect increased with the angle of inclination of the enclosure. Numerical and experimental results showed a good agreement. There was a rapid increase in the temperature at the entire media at the early time, reduced gradually until the steady state condition reached. This temperature and heat transfer to and from the porous media, were increased as the Rayleigh number and/or inclination angle increased. The Nusselt number increased directly with the angle of inclination up to o θ = 45 and then decreased. Correlation equations are obtained from the experimental investigation, showed the change of the average and local Nusselt number with time, distance, Rayleigh number, and the inclination angle.

Uncertainty quantification of a spent fuel refrigeration pool utilizing a [formula omitted] turbulence reduced order model

In this article, the uncertainty of a three-dimensional turbulent natural convection transient is quantified in a geometry representing an idealized spent fuel pool. The assessment is carried out through the creation of a surrogate fast model. This is build utilizing Proper Orthogonal Decomposition and Galerkin projection applied to a K-ϵ turbulent Navier–Stokes formulation. We discuss the uncertainties created by a uncertain heat release of the spent fuel elements. We consider the hypothesis of deviations that follow the normal distribution around a certain nominal value, with different standard deviations and sample size. The expected results and its uncertainty are henceforth computed by Monte–Carlo method, calculating hundreds of solutions of the Initial Value Problem with the surrogate model.

Stability of natural convection in a heated vertical corner

The spatial stability of three-dimensional non-parallel natural convection in a uniformly-heated vertical corner is examined for the first time. Two self-similar steady base flows are determined, which are distinguished by their behaviour far from the corner. The first solution (A) reduces to the flow induced by a heated semi-infinite vertical plate, with a crossflow component that is driven by the entrainment into the corner. The second solution (B) is new and in contrast has a crossflow that increases linearly with the spanwise coordinate. In both solutions, the crossflow is directed towards the corner, being driven by the so-called `chimney effect’. By adopting a PSE approach, we show that the computed base flows become unstable to viscous modes at sufficiently large Grashof numbers. In the case of solution A, the eigenmodes that initially dominate are well approximated by the two-dimensional stability problem for the boundary layer over a heated vertical plate. However, further downstream these modes are later overcome by modes that are corner-specific (and cannot be captured by a simpler planar far-field stability problem).

Efficient monolithic immersed boundary projection method for incompressible flows with heat transfer

Efficient monolithic immersed boundary projection methods (MIBPMs) with staggered time discretization have been proposed for incompressible viscous flows with heat transfer. The main idea is to use a two-step approximate lower-upper decomposition technique to decouple the momentum and energy equations, including immersed boundary forcing. The momentum and energy forcing are treated as Lagrangian multipliers to impose divergence-free constraints and no-slip conditions at the immersed boundary surfaces. A staggered time discretization is applied with the Crank-Nicolson scheme to decouple the temperature and velocities, which means that the velocity fields are described at integer time levels (n+1), while the temperature fields are described at half-integer time levels (n+1/2). To investigate the effect of forcing schemes in monolithic formulation, several MIBPM variants based on forcing schemes are formulated and evaluated numerically. The proposed MIBPM presents an accurate imposition of no-slip conditions on the immersed boundary surface and exhibits good stability for two-dimensional forced and natural convection problems. Further, simulations with the proposed MIBPM are implemented for the three-dimensional natural convection problem. Numerical simulation results for single- and multi-particle sedimentation demonstrate the robustness of the proposed method for complex heat transfer flows over moving objects.

Frequency response of three-dimensional natural convection of nanofluids under microgravity environments with gravity modulation

The present study performed three-dimensional numerical simulations of natural convection generated by nanofluids between plates under microgravity with gravity modulation. The Rayleigh number was fixed at and the dimensionless frequency of the gravity modulation was varied from F = 0 to 102 for the volume fraction –0.05. From an unsteady analysis, we clarified the time variation of three-dimensional thermal convection structures under gravity modulation and the frequency response of the heat transfer characteristics to the gravity modulation. When the frequency of gravity modulation and the volume fraction of nanoparticles are changed, two- or three-dimensional roll-shaped thermal convection occurs, and vortex pairs form between thermal plumes. For a low volume fraction of the fluid follows the low-frequency gravity modulation of F = 1 well. Therefore, the thermal convection repeatedly develops and decays as the gravity acceleration increases and decreases. At high-frequency gravity modulation of since the followability of the fluid is poor, the convection remains during one cycle of gravity modulation. At the low frequency of F = 1 and low volume fraction of the instantaneous Nusselt number is 1.0–1.1 times higher than that at over one period. For the time-averaged characteristics, the heat transfer coefficient is lower at low frequencies than at high frequencies regardless of the volume fraction. At the low volume fraction of the average Nusselt numbers for the low frequencies of F = 1 and F = 5 are 1.0–1.01 times higher than that at and the decrease in heat transfer coefficient owing to nanoparticles is suppressed. At for each frequency, the Nusselt number is much lower than that for Therefore, for low-frequency gravity modulations that make damping difficult, using nanofluids with a low volume fraction of can prevent the decrease in the heat transfer coefficient.

Three-dimensional natural convection of fluid with temperature-dependent viscosity within a porous cube having local heater

A numerical simulation is conducted on the convective heat transfer of liquid having variable viscosity in a closed porous 3D enclosure under an influence of isothermal or heat-generating solid body. Two vertical surfaces of the chamber are considered at fixed low temperature while other surfaces are thermally insulated. The local energy source is placed on the lower surface of the chamber. The control equations are written using non-dimensional variables «vector potential functions – vorticity vector – temperature». The finite difference technique of the second order accuracy is used to work out the differential equations. The effect of control parameters including the Rayleigh number, Ostrogradsky number, Darcy number, viscosity variation parameter and time on the liquid flow structure and heat transfer inside the cavity has been studied. The obtained data show that the porous material and variable viscosity working fluid can be considered as good conditions for the heat removal from the heated element in a closed chamber. A comparison of 2D and 3D models for natural convection of fluid having temperature-dependent viscosity in chambers with local heaters of various types has shown the features of different spatial approaches and boundary conditions for heated elements.

A study on the effect of fin pitch variation on the thermal performance of a bus duct conductor

The numerical results of this work provide an optimum design for a three-dimensional natural convection heat sink on the bus duct conductor's casing. The size of the fin pitch is regarded as a design variable. Using ANSYS FLUENT, a numerical model that closely resembles the experimental setup was created. The experimental data were compared to the IEC 60439-1 and IEC 60439-2 standards as a benchmark. Five potential fin pitch sizes (s1 = 1.0 mm, s2 = 1.5 mm, s3 = 2.0 mm, s4 = 3.0 mm, and s5 = 4.0 mm) were taken into consideration. It was shown that as the fin pitch gap size is reduced, the average surface temperature falls. According to the investigation, conduction resistance increased while convective resistance reduced as the fin pitch gap size grew. The overall heat resistance did, however, rise. The optimal fin pitch size, s1 = 1 mm, outperformed the other fin pitches in terms of thermal performance. The current numerical analysis expects an improved knowledge of the influence of fin pitch on a bus duct conductor's thermal performance.

Prediction of 3D natural convection heat transfer characteristics in a shallow enclosure with experimental data

This study presents an inverse computational fluid dynamics (CFD) simulation combined with the least-squares method and overdetermined experimental temperature data to predict the unknown heat transfer rate Qh and three-dimensional (3D) natural convection heat transfer characteristics in a closed shallow enclosure. This novel study belongs to the inverse convection-conduction conjugate heat transfer problem. The results show that the zero-equation turbulence model is more suitable for this study compared to other flow models. Thus, the zero-equation model is chosen as the suitable flow model because its estimates are the closest to the experimental data and existing correlation. An important finding is that, for H/L = 1/15 and Ra = 1820, Bénard convection cells and eight vortices appear in 3D and two-dimensional (2D) temperature contours, respectively. This Ra value is close to the existing critical Rayleigh number of 1708. The arrangement of these cells and vortices can be merged with each other and reorganized as H/L increases. The obtained 2D velocity patterns and air temperature contours agree with existing patterns and isotherms. The obtained h‾hi values also agree well with the existing correlation. Thus, the present results have good accuracy. A review of the literature indicates that a few studies have been conducted on using the inverse method along with overdetermined experimental temperature data to study the present problem.

Global linear instability analysis of thermal convective flow using the linearized lattice Boltzmann method

Modal global linear stability analysis of thermal convection is performed with the linearized lattice Boltzmann method (LLBM). The onset of Rayleigh–Bénard convection in rectangular cavities with conducting and adiabatic sidewalls and the instability of two-dimensional (2-D) and three-dimensional (3-D) natural convection in cavities are studied. The method of linearizing the local equilibrium probability distribution function that was first proposed by Pérez et al. (Theor. Comp. Fluid Dyn., vol. 31, 2017, pp. 643–664) is extended to solve the coupled linear Navier–Stokes equations together with the linear energy equation in this work. A multiscale analysis is also performed to recover the macroscopic linear Navier–Stokes equations from the discrete lattice Boltzmann equations for both the single and multiple relaxation time models. The present LLBM is implemented in the framework of the Palabos library. It is validated by calculating the linear critical value of 2-D natural convection that the LLBM with the multiple relaxation time model has an error less than 1 % compared with the spectral method. The instability mechanism of the flow is explained by kinetic energy transfer analysis. It is shown that the buoyancy mechanism and inertial mechanism tend to stabilize the Hopf bifurcation of the 2-D natural convection at Pr < 0.08 and Pr > 1, respectively. For 3-D natural convection, subcritical bifurcation of the Hopf type is found for low-Prandtl-number fluids (Pr < 0.1).

A natural convection horizontal straight-fin heat sink design problem to enhance heat dissipation performance

An optimized design for a three-dimensional natural convection horizontal straight-fin heat sink (SFHS) is numerically and experimentally examined in this study. The fin heights and shift displacement of the fins are considered as design variables, and this study aims to determine the optimal values of the design variables using the Levenberg–Marquardt method (LMM) to yield the minimum base surface temperature of the heat sink and thus enhance the heat dissipation performance of the system. Three design models (A, B and C) are examined, and the design parameters are considered to be the fin heights, the shift displacement of the fins, and both together. Numerical results show that the thermal resistance of designs A, B and C can be reduced by 5.7%, 14.4% and 15.6% compared to that of the original SFHS. These results imply that the shift displacement of the fin is a more effective design variable than the fin heights with regard to improving the heat sink's thermal performance. When both variables are considered as design variables, computational time increased tremendously, and the contribution of the fin height was trivial. Therefore, design B is recommended for practical application. Experiments were then performed on the manufactured original SFHS and design B heat sink to verify the validity of the optimal designs. Results showed that the error between the computed and measured base surface temperatures of the heat sink is small (less than 2%). The validity of using the proposed optimization algorithm to design the optimized shape of the natural convection SFHS is thus confirmed.

Three-Dimensional Natural Convection of Fluid with Temperature-Dependent Viscosity within a Porous Cube Having Local Heater

Three-Dimensional Natural Convection of Fluid with Temperature-Dependent Viscosity within a Porous Cube Having Local Heater

An Interpolated Bounce Back Thermable Method for Simulating Solid Particles Dynamics in a Viscous Medium

In this paper we discuss the mathematical and computer modeling of non-isothermal two-phase flows with suspended particles. Natural convection between an outer cubical cavity and an inner hot sphere is investigated. To simulate heat fluxes loaded with particles, a thermal model of the lattice Boltzmann equation in combination with the interpolated bounce back method (TLBM-IBB) has been developed. In TLBM-IBB, IBB is used to process liquid-solid interfaces, and TLBM is used to simulate the heat flow of a fluid. The momentum exchange method is used to calculate the hydrodynamic force on the particle surface. Simulation performed for a range of Rayleigh numbers . The accuracy and efficiency of the existing method is demonstrated by the example of solving the test problem of natural convection around a stationary particle and three-dimensional compressible natural convection in a square cavity filled with air, which has a hot wall on the left and a cold wall on the right, and two horizontal walls are adiabatic. The results obtained are in good agreement with the experimental and numerical results of other authors.

Study of Natural Convection of Lithium-Ion Battery Module Employing Phase Change Material

When the Lithium-ion battery operates at high temperature, it would bring about short circuit; if it reaches a critical temperature, it will explode. It is important to reduce its maximum temperature by appropriate heat transfer technique. When it operates without an external force for cooling, it needs natural convection technique to take away heat dissipation. Therefore, this study numerically examines three-dimensional transient natural convection of cylindrical lithium-ion batteries inside a rectangular pack with air between cylinders. The heat transfer technique in this study applies PCM (phase change material) between cylinders without or with fin array on top changing distance between cells. The results indicated that for no fin array, the package adopting the PCM could achieve the peak temperature 14.2 °C smaller than the package adopting the air. However, the package adopting the PCM with fin array vertical to the top of the package can best enhance average Nusselt number by 120% compared with using air and no fin array. Replacing the air by the PCM can keep the peak temperature of the batteries within the desirable operation range.

Transient Three-Dimensional Natural Convection in Confined Porous Media with Time-Periodic Boundary Conditions

Transient three-dimensional natural convection in confined fluid-saturated porous media had been investigated numerically through this work. The geometry selected is a box with time-periodic temperature variation at the vertical sides and constant wall temperature at the top and bottom. In this investigation, the momentum equation of flow through fluid-saturated porous media had been transformed to a vector potential form and solved numerically using the Successive Over Relaxation method while the energy equation is solved using the three-dimensional Alternating Direction Implicit method. The values of the Rayleigh number under investigation are (150, 200, 250 and 300). The results are presented in a form of contour maps for the temperature and a velocity vector maps for the velocity. The results reveal that the temperature within the box is increased as the time or Rayleigh number increase.The Nusselt number varies inversely with the time and directly with the Rayleigh number. Two cell convective patterns are obtained in the y-z

Natural convection in a partially heated cylinder: A numerical study

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