In this work,Al-4.5wt.%Cu was selected as the research object,and a phase field-lattice Boltzmann method(PF-LBM)model based on compute unified device architecture(CUDA)was established to solve the problem of low seria...In this work,Al-4.5wt.%Cu was selected as the research object,and a phase field-lattice Boltzmann method(PF-LBM)model based on compute unified device architecture(CUDA)was established to solve the problem of low serial computing efficiency of a traditional CPU and achieve significant acceleration.This model was used to explore the evolution of dendrite growth under natural convection.Through the study of the tip velocities,it is found that the growth of the dendrite arms at the bottom is inhibited while the growth of the dendrite arms at the top is promoted by natural convection.In addition,research on the inclined dendrite under natural convection was conducted.It is observed that there is a deviation between the actual growth direction and the preferred angle of the inclined dendrite.With the increase of the preferred angle of the seed,the difference between the actual growth direction and the initial preferred angle of the inclined dendrite shows a trend of increasing at first and then decreasing.In the simulation area,the relative deflection directions of the primary dendrite arms in the top right corner and the bottom left corner of the same dendrite are almost counterclockwise,while the relative deflection directions of the other two primary dendrite arms are clockwise.展开更多
Natural convection flow in enclosure has different applications such as room ventilation, heat exchangers, the cooling system of a building etc. The Finite-Element method based on the Galerkin weighted residual approa...Natural convection flow in enclosure has different applications such as room ventilation, heat exchangers, the cooling system of a building etc. The Finite-Element method based on the Galerkin weighted residual approach is used to solve two-dimensional governing mass, momentum and energy-equations for natural convection flow in the presence of a magnetic field on a roof top with semi-circular heater. In the enclosure the horizontal lower wall was heated, the vertical two walls were adiabatic, inside the semi-circular heater, the wavy top wall cooled. The parameters Rayleigh number, Hartmann number and Prandtl number are considered. The effects of the Hartmann number and Rayleigh number on the streamlines, isotherms, velocity profiles and average Nusselt number are examined graphically. The local Nusselt number and the average Nusselt number of the heated portion of the enclosure with the semi-circular heater are presented in this paper. Finally, for the validation of the existing work, the current results are compared with published results and the auspicious agreement is achieved.展开更多
In this paper,natural heat convection inside square and equilateral triangular cavities was studied using a meshless method based on collocation local radial basis function(RBF).The nanofluids used were Cu-water or Al...In this paper,natural heat convection inside square and equilateral triangular cavities was studied using a meshless method based on collocation local radial basis function(RBF).The nanofluids used were Cu-water or Al_(2)O_(3)-water mixture with nanoparticle volume fractions range of 0≤φ≤0.2.A system of continuity,momentum,and energy partial differential equations was used in modeling the flow and temperature behavior of the fluids.Partial derivatives in the governing equations were approximated using the RBF method.The artificial compressibility model was implemented to overcome the pressure velocity coupling problem that occurs in such equations.Themain goal of this work was to present a simple and efficient method to deal with complex geometries for a variety of problem conditions.To assess the accuracy of the proposed method,several test cases of natural convection in square and triangular cavities were selected.For Rayleigh numbers ranging from 103 to 105,a validation test of natural convection of Cu-water in a square cavity was used.The numerical investigation was then extended to Rayleigh number 106,as well as Al_(2)O_(3)-water nanofluid with a volume fraction range of 0≤φ≤0.2.In a second investigation,the same nanofluids were used in a triangular cavitywith varying volume fractions to test the proposed meshless approach on non-rectangular geometries.The numerical results appear to be in agreement with those from earlier investigations.Furthermore,the suggested meshless method was found to be stable and accurate,demonstrating that it may be a viable alternative for solving natural heat transfer equations of nanofluids in enclosures with irregular geometries.展开更多
A 3D model applying temperature-and carbon concentration-dependent material properties was developed to describe the scrap melting behavior and carbon diffusion under natural convection.Simulated results agreed reason...A 3D model applying temperature-and carbon concentration-dependent material properties was developed to describe the scrap melting behavior and carbon diffusion under natural convection.Simulated results agreed reasonably well with experimental ones.Scrap melting was subdivided into four stages:formation of a solidified layer,rapid melting of the solidified layer,carburization,and carburization+normal melting.The carburization stage could not be ignored at low temperature because the carburization time for the sample investigated was 214 s at 1573 K compared to 12 s at 1723 K.The thickness of the boundary layer with significant concentration difference at 1573 K increased from 130μm at 5 s to 140μm at 60 s.The maximum velocity caused by natural convection decreased from 0.029 m·s^(−1)at 5 s to 0.009 m·s^(−1)at 634 s because the differences in temperature and density between the molten metal and scrap decreased with time.展开更多
This study numerically investigates the impact of porous materials,nano-particle types,and their concentrations on transient natural convection heat transfer of nano-fluid inside a porous chamber with a triangular sec...This study numerically investigates the impact of porous materials,nano-particle types,and their concentrations on transient natural convection heat transfer of nano-fluid inside a porous chamber with a triangular section.The governing equations of the two-phase mixture model are separated on the computational domain and solved using the Finite Volume Method,taking into account the Darcy–Brinkman model for porous medium.It was observed that convection heat transfer inside the triangular chamber consists of three stages named initial,transient,and semi-steady.The features of each step are provided in detail.The results suggested that the use of a hybrid nano-fluid(water/aluminum oxide-cooper)inside a porous glass material and an increase in volume fraction of nano-particles have adverse effects on heat transfer rate.In contrast,as the nano-particle volume fraction of the single nano-fluid(water/aluminum oxide)inside the chamber increased,convection heat transfer rate improved.At the same time,it was observed that the use of both nano-fluids(single and hybrid)in the porous environment of the aluminum foam could improve convection.展开更多
The accelerating effect of natural convection on the melting of phase change material(PCM)has been extensively demonstrated.However,such an influence is directly dependent on the size and shape of domain in which phas...The accelerating effect of natural convection on the melting of phase change material(PCM)has been extensively demonstrated.However,such an influence is directly dependent on the size and shape of domain in which phase change happens,and how to quantitatively describe such an influence is still challenging.On the other hand,the simulation of natural convection process is considerably difficult,involving complex fluid flow in a region changing with time,and is typically not operable in practice.To overcome these obstacles,the present study aims to quantitatively investigate the size effect of natural convection in the melting process of PCM paraffin filled in a square latent heat storage system through experiment and simulation,and ultimately a correlation equation to represent its contribution is proposed.Firstly,the paraffin melting experiment is conducted to validate the two-dimensional finite element model based on the enthalpy method.Subsequently,a comprehensive investigation is performed numerically for various domain sizes.The results show that the melting behavior of paraffin is dominated by the thermal convection.When the melting time exceeds 50 s,a whirlpoor flow caused by natural convection appears in the upper liquid phase region close to the heating wall,and then its influencing range gradually increases to accelerate the melting of paraffin.However,its intensity gradually decreases as the distance between the melting front and the heating wall increases.Besides,it is found that the correlation between the total melting time and the domain size approximately exhibits a power law.When the domain size is less than 2 mm,the accelerating effect of natural convection becomes very weak and can be ignored in practice.Moreover,in order to simplify the complex calculation of natural convection,the equivalent thermal conductivity concept is proposed to include the contribution of natural convection to the total melting time,and an empirical correlation is given for engineering applications.展开更多
Two-dimensional transient laminar natural convection in a square cavity containing a porous medium and inclined at an angle of 30°is investigated numerically.The vertical walls are differentially heated,and the h...Two-dimensional transient laminar natural convection in a square cavity containing a porous medium and inclined at an angle of 30°is investigated numerically.The vertical walls are differentially heated,and the horizontal walls are adiabatic.The effect of Rayleigh number on heat transfer and on the road to chaos is analyzed.The natural heat transfer and the Darcy Brinkman equations are solved by using a finite volume method and a Tri Diagonal Matrix Algorithm(TDMA).The results are obtained for a porosity equal to 0.45,a Darcy number and a Prandtl respectively equal to 10^(-3)and 0.71;they are analyzed in terms of streamlines,isotherms,phase portrait,attractors,and spectra amplitude as a function of the Rayleigh number.It is found that,as Rayleigh number increases,the natural convection changes from a steady state to a time-periodic state and finally to a chaotic condition.展开更多
The natural convection heat transfer of a 60% sucrose solution in a vertical converging-diverging tube(CD) with regularly-spaced twisted tapes(RSTT) has been investigated numerically and experimentally. The effects of...The natural convection heat transfer of a 60% sucrose solution in a vertical converging-diverging tube(CD) with regularly-spaced twisted tapes(RSTT) has been investigated numerically and experimentally. The effects of wall temperature and number of RSTT on the Nusselt number were studied in detail. The distributions of velocity and temperature in the 60% sucrose solution were studied and the simulated results of CD with RSTT were compared with those of the smooth tube. The influence of Rayleigh number and RSTT on the Nusselt number was conducted experimentally. The results indicate that the Nusselt number of the 60% sucrose solution obviously increased with the number of RSTT but increased inconspicuously with 2 and more twisted tapes. The simulation shows that the distance for achieving an optimal heat transfer performance is 46 times the diameter of the tube. The mechanism of the natural convection heat transfer enhancement of the 60% sucrose solution in relationship with the CD and the RSTT was analyzed, and the change of average tangential velocity with the axial distance was presented to demonstrate that the enhancement of heat transfer was realized mainly because of the increase in tangential velocity.展开更多
Nanofluids are considered to offer important advantages over conventional heat transfer fluids. A model is developed to analyze the behavior of nanofluids taking into account the solid fraction χ. The Navier-Stokes e...Nanofluids are considered to offer important advantages over conventional heat transfer fluids. A model is developed to analyze the behavior of nanofluids taking into account the solid fraction χ. The Navier-Stokes equations are solved numerically with Alternating Direct Implicit method (ADI method) for various Grashof numbers 104 and 105;we have an excellent agreement between our numerical code and previously published works. Copper-Water nanofluid is used with Pr = 6.2 and solid volume fraction χ is varied as 0%;5%;10%;15% and 20%. The problem considered is a two-dimensional heat transfer in a square cavity. The vertical walls are differentially heated, the left is maintained at hot con- dition (sinusoidal) when the right one is cold. The horizontal walls are assumed to be insulated, non conducting and impermeable to mass transfer. The nanofluid in the enclosure is Newtonian, incompressible and laminar. The nanopar- ticles are assumed to have a uniform shape and size. Moreover, it is assumed that both the fluid phase and nanoparticles are in thermal equilibrium state and they flow at the same velocity. The thermophysical properties of the nanofluid are assumed to be constant except for the density variation in the buoyancy force, which is based on the Boussinesq approximation. Different correlations are proposed for predicting heat transfer for uniform and sinusoidal boundary thermal conditions.展开更多
High Explosive Anti-Tank(HEAT) warheads and ammunitions are frequently produced by explosive casting inside an axis-symmetric mold with an inverted conical geometry in the basis. In order to prevent manufacturing defe...High Explosive Anti-Tank(HEAT) warheads and ammunitions are frequently produced by explosive casting inside an axis-symmetric mold with an inverted conical geometry in the basis. In order to prevent manufacturing defects, the solidification process must be controlled. In this study, a dimensionless solidification model has been proposed to investigate the heat transfer considering the natural convection inside the liquid explosive and the numerical simulations were performed by using COMSOL Multiphysics and Modeling Software, employing trinitrotoluene(TNT) thermophysical properties. The effect of three different boundary conditions on the top of the mold have been evaluated: convection, adiabatic and isothermal. It has been observed that solidification process was faster for convection case and slower for isothermal case, while an intermediary total solidification time value was found for adiabatic case.Moreover, liquid explosive was completely surrounded by solid explosive during the solidification process for convection case and also for adiabatic case through the end of the process. Otherwise, it was not observed for isothermal case. The natural convection effects promoted a vortex inside the liquid explosive, accelerating the heat transfer process. It has been concluded that isothermal mold top boundary condition should be preferred to prevent manufacturing defects, avoiding high thermal stress.展开更多
We consider the combined effect of the magnetic field and heat transfer inside a square cavity containing a hybrid nanofluid(Cu-Al2O3-water).The upper and bottom walls of the cavity have a wavy shape.The temperature o...We consider the combined effect of the magnetic field and heat transfer inside a square cavity containing a hybrid nanofluid(Cu-Al2O3-water).The upper and bottom walls of the cavity have a wavy shape.The temperature of the vertical walls is lower,the third part in the middle of the bottom wall is kept at a constant higher temperature,and the remaining parts of the bottom wall and the upper wall are thermally insulated.The magnetic field is applied under the angleγ,an opposite clockwise direction.For the numerical simulation,the finite element technique is employed.The ranges of the characteristics are as follows:the Rayleigh number(10^3≤Ra≤10^5),the Hartmann number(0≤Ha≤100),the nanoparticle hybrid concentration(ϕAl2O3,ϕCu=0,0.025,0.05),the magnetic field orientation(0≤γ≤2π),and the Prandtl number Pr,the amplitude of wavy cavity A,and the number of waviness n are fixed at Pr=7,A=0.1,and n=3,respectively.The comparison with a reported finding in the open literature is done,and the data are observed to be in very good agreement.The effects of the governing parameters on the energy transport and fluid flow parameters are studied.The results prove that the increment of the magnetic influence determines the decrease of the energy transference because the conduction motion dominates the fluid movement.When the Rayleigh number is raised,the Nusselt number is increased,too.For moderate Rayleigh numbers,the maximum ratio of the heat transfer takes place for the hybrid nanofluid and then the Cu-nanofluid,followed by the Al2O3-nanofluid.The nature of motion and energy transport parameters has been scrutinized.展开更多
The present study concerns the modelization and numerical simulation for the heat and flow exchange characteristics in a novel configuration saturated with a nonNewtonian Ag-MgO hybrid nanofluid.The wavy shaped enclos...The present study concerns the modelization and numerical simulation for the heat and flow exchange characteristics in a novel configuration saturated with a nonNewtonian Ag-MgO hybrid nanofluid.The wavy shaped enclosure is equipped with onequarter of a conducting solid cylinder.The system of equations resulting from the mathematical modeling of the physical problem in its dimensionless form is discretized via the higher-order Galerkin-based finite element method(GFEM).The dependency of various factors and their interrelationships affecting the hydro-thermal behavior and heat exchange rate are delineated.The numerical experiments reveal that the best heat transfer rate is achieved for the pseudo-plastic hybrid nanoliquid with high Rayleigh number and thermal conductivity ratio and low Hartmann number.Besides,the power-law index has a major effect in deteriorating the heat convection at high Rayleigh number.展开更多
This study simulates natural convection flow resulting from heat partitions in an H-shaped enclosure filled with a nanofluid using an incompressible smoothed particle hydrodynamics(ISPH)method.The right area of the H-...This study simulates natural convection flow resulting from heat partitions in an H-shaped enclosure filled with a nanofluid using an incompressible smoothed particle hydrodynamics(ISPH)method.The right area of the H-shaped enclosure is saturated with non-Darcy porous media.The center variable partitions of the H-shaped enclosure walls are kept at a high-temperature Th.The left and right walls of the H-shaped enclosure are positioned at a low temperature Tc and the other walls are adiabatic.In ISPH method,the source term in pressure Poisson equation(PPE)is modified.The influences of the controlling parameters on the temperature distributions,the velocity field and average Nusselt number are discussed.The performed simulations proofed that the length of the heated partitions augments the velocity field and temperature distributions in an H-shaped enclosure.Rayleigh number rises the fluid velocity and heat transfer in an H-shaped enclosure.The porous layer on the right side of the H-shaped enclosure at a lower Darcy parameter causes a high resistance force for the fluid flow and heat transfer characteristic inside an H-shaped enclosure.Added nanoparticles reduces the velocity field and enhances the heat transfer inside an H-shaped enclosure.展开更多
In this study,the magnetohydrodynamics(MHD) natural convection heat transfer with Joule and viscous heating effects inside an iso-flux porous medium-filled inclined rectangular enclosure is studied numerically.An iso-...In this study,the magnetohydrodynamics(MHD) natural convection heat transfer with Joule and viscous heating effects inside an iso-flux porous medium-filled inclined rectangular enclosure is studied numerically.An iso-heat flux is applied for heating and cooling the two opposing walls of the enclosure while the other walls are adi-abatic. The Forchheimer extension of Darcy-Oberbeck-Boussinesq and energy equations is transformed into a dimensionless form using a set of suitable variables instead of a finite difference scheme.The governing parameters are the magnetic influence number,the modified Rayleigh number,the inclination angle,and the aspect ratio of the enclosure. The results show that viscous and Joule heating effects decrease heat transfer rates.展开更多
Cooling by evaporation through transpiring porous walls is expanding in various industrial applications such as air conditioning. It is also used to cool water in a clay jug. This process deserves to be studied, under...Cooling by evaporation through transpiring porous walls is expanding in various industrial applications such as air conditioning. It is also used to cool water in a clay jug. This process deserves to be studied, understood and valued. This paper deals with the transpiration phenomenon through a saturated porous plate coupled with heat and mass transfer by natural convection. Conservation Equations (mass, momentum, energy and concentration), associated with adequate boundary conditions, have been numerically solved using an implicit finite difference iterative method. The numerical model has been validated by experimental measurements from holographic interferometry. The used method to obtain temperature and concentration profiles was explained. They are evaluated from the refractive index of moisture air in the boundary layer. The main numerical results presented are: Nusselt and Sherwood numbers, temperature, humidity, and velocity profiles within the boundary layer as well as the different heat fluxes exchanged between the plate and the surrounding environment. Besides, the present model allows showing the important effect of the equivalent thermal conductivity and the surface emissivity on temperature and heats flux.展开更多
A detailed sensitivity study was carried out on various key parameters from a high precision numerical model of a microelectronic package cooled by natural convection, to provide rules for the thermal modeling of micr...A detailed sensitivity study was carried out on various key parameters from a high precision numerical model of a microelectronic package cooled by natural convection, to provide rules for the thermal modeling of microelectronic packages subjected to natural convection heat transfer. An accurate estimate of the junction temperature, with an error of less than 1˚C, was obtained compared to the experimental data for the vertical and horizontal orientations of the test vehicle in the JEDEC Still Air configuration. The sensitivity study showed that to have an accurate estimate of the temperature, the following elements should be present in the thermal model: radiation heat transfer in natural convection cooling;a computational fluid dynamics analysis to find realistic convection coefficients;detailed models of the high conductivity elements in the direction of the heat flow towards the environment;and finally precise values for the thicknesses of layers and the thermal properties of the substrate and the printed circuit board.展开更多
Natural convection heat transfer in open or closed cavities takes place in different engineering areas. The hemispherical cavity is a part of basic geometries although it is not widely studied. The present paper repor...Natural convection heat transfer in open or closed cavities takes place in different engineering areas. The hemispherical cavity is a part of basic geometries although it is not widely studied. The present paper reports the numerical study of natural convection in a closed hemispherical annulus delimited by two vertically eccentric hemispheres filled with Newtonian fluid (air in this case with <em>Pr</em> = 0.7) is conducted. The inner hemisphere is heated by a heat flux of constant density and the outer one is maintained isothermal. Based on the Boussinesq assumptions, the governing equations are numerically studied using unsteady natural convection formulated with vorticity and stream-function variables. These equations are written by using bispherical coordinates system and solved by using a finite difference method. The effect of the control parameters such as the Rayleigh number (<span style="white-space:nowrap;">10<sup>3</sup> ≤ <em>Ra</em> ≤ 10<sup>6</sup></span>) or the eccentricity (<em>e</em> = ±0.2, ±0.5, 0) in the dynamic and thermal behaviours of the fluid is investigated.展开更多
A numerical analysis is performed to investigate the laminar, free convection flow in an Open Enclosure Using Lattice Boltzmann Method (LBM) in the presence of Carbon nanotube and Cu nanoparticles. The problem is stud...A numerical analysis is performed to investigate the laminar, free convection flow in an Open Enclosure Using Lattice Boltzmann Method (LBM) in the presence of Carbon nanotube and Cu nanoparticles. The problem is studied for different volume fractions of nanoparticles, and aspect ratio of the cavity for various Rayligh numbers. The volume fraction of added nanoparticles to water (as base fluid) is lower than 1% to make dilute suspensions. The study presents a numerical treatment based on LBM to model convection heat transfer of Carbon nanotube based nanofluids. Results show that adding a low value of Carbon nanotube to the base fluid led to significant enhancement of convection rate. Results show that adding nanoparticles to the base fluid enhances the rate of natural convection in a cavity. Make a comparison between Carbon nanotube and Cu-nanoparticles shows that the Carbon nanotube-nano- particle has better performance to enhance convection rate at comparison with Cu- nanoparticles.展开更多
This paper shows the natural convective heat transfer in porous media over the vertical wavy surface and it assumes that the fluid is viscous and in-compressible. This model shows the effects of the inverse of Darcy n...This paper shows the natural convective heat transfer in porous media over the vertical wavy surface and it assumes that the fluid is viscous and in-compressible. This model shows the effects of the inverse of Darcy number. The dimensional partial differential equations are converted into a dimensionless form. The non-linear system of equations is obtained and these equations are solved numerically by the finite difference method. The results are obtained for inverse Darcy number, magnetic parameter, Prandtl number, amplitude of surface, parameter of heat generation and parameter of thermal conductivity, and their effects on the velocity, temperature of the fluid and Nusselt number.展开更多
Coupled natural convection and surface radiation within a square cavity, filled with air and submitted to discrete heating and cooling from all its walls, is studied numerically. The thermally active elements are cent...Coupled natural convection and surface radiation within a square cavity, filled with air and submitted to discrete heating and cooling from all its walls, is studied numerically. The thermally active elements are centrally located on the walls of the cavity. Two heating modes, called SB and SV, are considered. They correspond to bottom and vertical left elements sinusoidally heated in time, respectively, while the top and vertical right ones are constantly cooled. The remaining portions of all the walls are considered adiabatic. The parameters governing the problem are the amplitude and the period of the temporally sinusoidal temperature, the emissivity of the walls , the relative lengths of the active elements and the Rayleigh number . The effect of such parameters on flow and thermal fields and the resulting heat transfer is examined. It is shown that, during a flow cycle, the flow structure can present complex behavior, depending on the emissivity and the amplitude and period of the exciting temperature. The rate of heat transfer is generally enhanced in the case of sinusoidal heating. Also, the resonance phenomenon existence, characterized by maximum fluctuations in flow intensity and heat transfer, is proved in this study.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.52161002,51661020 and 11364024)the Postdoctoral Science Foundation of China(Grant No.2014M560371)the Funds for Distinguished Young Scientists of Lanzhou University of Technology,China(Grant No.J201304).
文摘In this work,Al-4.5wt.%Cu was selected as the research object,and a phase field-lattice Boltzmann method(PF-LBM)model based on compute unified device architecture(CUDA)was established to solve the problem of low serial computing efficiency of a traditional CPU and achieve significant acceleration.This model was used to explore the evolution of dendrite growth under natural convection.Through the study of the tip velocities,it is found that the growth of the dendrite arms at the bottom is inhibited while the growth of the dendrite arms at the top is promoted by natural convection.In addition,research on the inclined dendrite under natural convection was conducted.It is observed that there is a deviation between the actual growth direction and the preferred angle of the inclined dendrite.With the increase of the preferred angle of the seed,the difference between the actual growth direction and the initial preferred angle of the inclined dendrite shows a trend of increasing at first and then decreasing.In the simulation area,the relative deflection directions of the primary dendrite arms in the top right corner and the bottom left corner of the same dendrite are almost counterclockwise,while the relative deflection directions of the other two primary dendrite arms are clockwise.
文摘Natural convection flow in enclosure has different applications such as room ventilation, heat exchangers, the cooling system of a building etc. The Finite-Element method based on the Galerkin weighted residual approach is used to solve two-dimensional governing mass, momentum and energy-equations for natural convection flow in the presence of a magnetic field on a roof top with semi-circular heater. In the enclosure the horizontal lower wall was heated, the vertical two walls were adiabatic, inside the semi-circular heater, the wavy top wall cooled. The parameters Rayleigh number, Hartmann number and Prandtl number are considered. The effects of the Hartmann number and Rayleigh number on the streamlines, isotherms, velocity profiles and average Nusselt number are examined graphically. The local Nusselt number and the average Nusselt number of the heated portion of the enclosure with the semi-circular heater are presented in this paper. Finally, for the validation of the existing work, the current results are compared with published results and the auspicious agreement is achieved.
基金supported through the Annual Funding Track by the Deanship of Scientific Research,Vice Presidency for Graduate Studies and Scientific Research,King Faisal University,Saudi Arabia[Project No.AN000675].
文摘In this paper,natural heat convection inside square and equilateral triangular cavities was studied using a meshless method based on collocation local radial basis function(RBF).The nanofluids used were Cu-water or Al_(2)O_(3)-water mixture with nanoparticle volume fractions range of 0≤φ≤0.2.A system of continuity,momentum,and energy partial differential equations was used in modeling the flow and temperature behavior of the fluids.Partial derivatives in the governing equations were approximated using the RBF method.The artificial compressibility model was implemented to overcome the pressure velocity coupling problem that occurs in such equations.Themain goal of this work was to present a simple and efficient method to deal with complex geometries for a variety of problem conditions.To assess the accuracy of the proposed method,several test cases of natural convection in square and triangular cavities were selected.For Rayleigh numbers ranging from 103 to 105,a validation test of natural convection of Cu-water in a square cavity was used.The numerical investigation was then extended to Rayleigh number 106,as well as Al_(2)O_(3)-water nanofluid with a volume fraction range of 0≤φ≤0.2.In a second investigation,the same nanofluids were used in a triangular cavitywith varying volume fractions to test the proposed meshless approach on non-rectangular geometries.The numerical results appear to be in agreement with those from earlier investigations.Furthermore,the suggested meshless method was found to be stable and accurate,demonstrating that it may be a viable alternative for solving natural heat transfer equations of nanofluids in enclosures with irregular geometries.
基金the National Key R&D Program of China(No.2019YFC1905701)the National Natural Science Foundation of China(Nos.51674022,51734003)the Key projects of NSFC(No.U1960201).
文摘A 3D model applying temperature-and carbon concentration-dependent material properties was developed to describe the scrap melting behavior and carbon diffusion under natural convection.Simulated results agreed reasonably well with experimental ones.Scrap melting was subdivided into four stages:formation of a solidified layer,rapid melting of the solidified layer,carburization,and carburization+normal melting.The carburization stage could not be ignored at low temperature because the carburization time for the sample investigated was 214 s at 1573 K compared to 12 s at 1723 K.The thickness of the boundary layer with significant concentration difference at 1573 K increased from 130μm at 5 s to 140μm at 60 s.The maximum velocity caused by natural convection decreased from 0.029 m·s^(−1)at 5 s to 0.009 m·s^(−1)at 634 s because the differences in temperature and density between the molten metal and scrap decreased with time.
文摘This study numerically investigates the impact of porous materials,nano-particle types,and their concentrations on transient natural convection heat transfer of nano-fluid inside a porous chamber with a triangular section.The governing equations of the two-phase mixture model are separated on the computational domain and solved using the Finite Volume Method,taking into account the Darcy–Brinkman model for porous medium.It was observed that convection heat transfer inside the triangular chamber consists of three stages named initial,transient,and semi-steady.The features of each step are provided in detail.The results suggested that the use of a hybrid nano-fluid(water/aluminum oxide-cooper)inside a porous glass material and an increase in volume fraction of nano-particles have adverse effects on heat transfer rate.In contrast,as the nano-particle volume fraction of the single nano-fluid(water/aluminum oxide)inside the chamber increased,convection heat transfer rate improved.At the same time,it was observed that the use of both nano-fluids(single and hybrid)in the porous environment of the aluminum foam could improve convection.
基金supported by the National Natural Science Foundation of China(Grant Nos.51908197 and 12072107)the Tackle Key Problems in Science and Technology Project of Henan Province,China(Grant No.202102310262)+1 种基金the Program for Innovative Research Team of Science&Technology of Henan Province,China(Grant No.19IRTSTHN020)the Key Research Project of Higher Education Institutions of Henan Province,China(Grant No.20B580001).
文摘The accelerating effect of natural convection on the melting of phase change material(PCM)has been extensively demonstrated.However,such an influence is directly dependent on the size and shape of domain in which phase change happens,and how to quantitatively describe such an influence is still challenging.On the other hand,the simulation of natural convection process is considerably difficult,involving complex fluid flow in a region changing with time,and is typically not operable in practice.To overcome these obstacles,the present study aims to quantitatively investigate the size effect of natural convection in the melting process of PCM paraffin filled in a square latent heat storage system through experiment and simulation,and ultimately a correlation equation to represent its contribution is proposed.Firstly,the paraffin melting experiment is conducted to validate the two-dimensional finite element model based on the enthalpy method.Subsequently,a comprehensive investigation is performed numerically for various domain sizes.The results show that the melting behavior of paraffin is dominated by the thermal convection.When the melting time exceeds 50 s,a whirlpoor flow caused by natural convection appears in the upper liquid phase region close to the heating wall,and then its influencing range gradually increases to accelerate the melting of paraffin.However,its intensity gradually decreases as the distance between the melting front and the heating wall increases.Besides,it is found that the correlation between the total melting time and the domain size approximately exhibits a power law.When the domain size is less than 2 mm,the accelerating effect of natural convection becomes very weak and can be ignored in practice.Moreover,in order to simplify the complex calculation of natural convection,the equivalent thermal conductivity concept is proposed to include the contribution of natural convection to the total melting time,and an empirical correlation is given for engineering applications.
基金This work was done at the LTPMP Laboratory,USTHB,Algeria.
文摘Two-dimensional transient laminar natural convection in a square cavity containing a porous medium and inclined at an angle of 30°is investigated numerically.The vertical walls are differentially heated,and the horizontal walls are adiabatic.The effect of Rayleigh number on heat transfer and on the road to chaos is analyzed.The natural heat transfer and the Darcy Brinkman equations are solved by using a finite volume method and a Tri Diagonal Matrix Algorithm(TDMA).The results are obtained for a porosity equal to 0.45,a Darcy number and a Prandtl respectively equal to 10^(-3)and 0.71;they are analyzed in terms of streamlines,isotherms,phase portrait,attractors,and spectra amplitude as a function of the Rayleigh number.It is found that,as Rayleigh number increases,the natural convection changes from a steady state to a time-periodic state and finally to a chaotic condition.
基金the Major Science and Technology Projects of Guangdong Province (No. 2011A080804012)
文摘The natural convection heat transfer of a 60% sucrose solution in a vertical converging-diverging tube(CD) with regularly-spaced twisted tapes(RSTT) has been investigated numerically and experimentally. The effects of wall temperature and number of RSTT on the Nusselt number were studied in detail. The distributions of velocity and temperature in the 60% sucrose solution were studied and the simulated results of CD with RSTT were compared with those of the smooth tube. The influence of Rayleigh number and RSTT on the Nusselt number was conducted experimentally. The results indicate that the Nusselt number of the 60% sucrose solution obviously increased with the number of RSTT but increased inconspicuously with 2 and more twisted tapes. The simulation shows that the distance for achieving an optimal heat transfer performance is 46 times the diameter of the tube. The mechanism of the natural convection heat transfer enhancement of the 60% sucrose solution in relationship with the CD and the RSTT was analyzed, and the change of average tangential velocity with the axial distance was presented to demonstrate that the enhancement of heat transfer was realized mainly because of the increase in tangential velocity.
文摘Nanofluids are considered to offer important advantages over conventional heat transfer fluids. A model is developed to analyze the behavior of nanofluids taking into account the solid fraction χ. The Navier-Stokes equations are solved numerically with Alternating Direct Implicit method (ADI method) for various Grashof numbers 104 and 105;we have an excellent agreement between our numerical code and previously published works. Copper-Water nanofluid is used with Pr = 6.2 and solid volume fraction χ is varied as 0%;5%;10%;15% and 20%. The problem considered is a two-dimensional heat transfer in a square cavity. The vertical walls are differentially heated, the left is maintained at hot con- dition (sinusoidal) when the right one is cold. The horizontal walls are assumed to be insulated, non conducting and impermeable to mass transfer. The nanofluid in the enclosure is Newtonian, incompressible and laminar. The nanopar- ticles are assumed to have a uniform shape and size. Moreover, it is assumed that both the fluid phase and nanoparticles are in thermal equilibrium state and they flow at the same velocity. The thermophysical properties of the nanofluid are assumed to be constant except for the density variation in the buoyancy force, which is based on the Boussinesq approximation. Different correlations are proposed for predicting heat transfer for uniform and sinusoidal boundary thermal conditions.
文摘High Explosive Anti-Tank(HEAT) warheads and ammunitions are frequently produced by explosive casting inside an axis-symmetric mold with an inverted conical geometry in the basis. In order to prevent manufacturing defects, the solidification process must be controlled. In this study, a dimensionless solidification model has been proposed to investigate the heat transfer considering the natural convection inside the liquid explosive and the numerical simulations were performed by using COMSOL Multiphysics and Modeling Software, employing trinitrotoluene(TNT) thermophysical properties. The effect of three different boundary conditions on the top of the mold have been evaluated: convection, adiabatic and isothermal. It has been observed that solidification process was faster for convection case and slower for isothermal case, while an intermediary total solidification time value was found for adiabatic case.Moreover, liquid explosive was completely surrounded by solid explosive during the solidification process for convection case and also for adiabatic case through the end of the process. Otherwise, it was not observed for isothermal case. The natural convection effects promoted a vortex inside the liquid explosive, accelerating the heat transfer process. It has been concluded that isothermal mold top boundary condition should be preferred to prevent manufacturing defects, avoiding high thermal stress.
文摘We consider the combined effect of the magnetic field and heat transfer inside a square cavity containing a hybrid nanofluid(Cu-Al2O3-water).The upper and bottom walls of the cavity have a wavy shape.The temperature of the vertical walls is lower,the third part in the middle of the bottom wall is kept at a constant higher temperature,and the remaining parts of the bottom wall and the upper wall are thermally insulated.The magnetic field is applied under the angleγ,an opposite clockwise direction.For the numerical simulation,the finite element technique is employed.The ranges of the characteristics are as follows:the Rayleigh number(10^3≤Ra≤10^5),the Hartmann number(0≤Ha≤100),the nanoparticle hybrid concentration(ϕAl2O3,ϕCu=0,0.025,0.05),the magnetic field orientation(0≤γ≤2π),and the Prandtl number Pr,the amplitude of wavy cavity A,and the number of waviness n are fixed at Pr=7,A=0.1,and n=3,respectively.The comparison with a reported finding in the open literature is done,and the data are observed to be in very good agreement.The effects of the governing parameters on the energy transport and fluid flow parameters are studied.The results prove that the increment of the magnetic influence determines the decrease of the energy transference because the conduction motion dominates the fluid movement.When the Rayleigh number is raised,the Nusselt number is increased,too.For moderate Rayleigh numbers,the maximum ratio of the heat transfer takes place for the hybrid nanofluid and then the Cu-nanofluid,followed by the Al2O3-nanofluid.The nature of motion and energy transport parameters has been scrutinized.
文摘The present study concerns the modelization and numerical simulation for the heat and flow exchange characteristics in a novel configuration saturated with a nonNewtonian Ag-MgO hybrid nanofluid.The wavy shaped enclosure is equipped with onequarter of a conducting solid cylinder.The system of equations resulting from the mathematical modeling of the physical problem in its dimensionless form is discretized via the higher-order Galerkin-based finite element method(GFEM).The dependency of various factors and their interrelationships affecting the hydro-thermal behavior and heat exchange rate are delineated.The numerical experiments reveal that the best heat transfer rate is achieved for the pseudo-plastic hybrid nanoliquid with high Rayleigh number and thermal conductivity ratio and low Hartmann number.Besides,the power-law index has a major effect in deteriorating the heat convection at high Rayleigh number.
基金The authors would like to extend their appreciations to the Deanship of Scientific Research at King Khalid University,Abha,Saudi Arabia,for funding this work through the Research Group Project under Grant Number(R.G.P 2/70/41).
文摘This study simulates natural convection flow resulting from heat partitions in an H-shaped enclosure filled with a nanofluid using an incompressible smoothed particle hydrodynamics(ISPH)method.The right area of the H-shaped enclosure is saturated with non-Darcy porous media.The center variable partitions of the H-shaped enclosure walls are kept at a high-temperature Th.The left and right walls of the H-shaped enclosure are positioned at a low temperature Tc and the other walls are adiabatic.In ISPH method,the source term in pressure Poisson equation(PPE)is modified.The influences of the controlling parameters on the temperature distributions,the velocity field and average Nusselt number are discussed.The performed simulations proofed that the length of the heated partitions augments the velocity field and temperature distributions in an H-shaped enclosure.Rayleigh number rises the fluid velocity and heat transfer in an H-shaped enclosure.The porous layer on the right side of the H-shaped enclosure at a lower Darcy parameter causes a high resistance force for the fluid flow and heat transfer characteristic inside an H-shaped enclosure.Added nanoparticles reduces the velocity field and enhances the heat transfer inside an H-shaped enclosure.
文摘In this study,the magnetohydrodynamics(MHD) natural convection heat transfer with Joule and viscous heating effects inside an iso-flux porous medium-filled inclined rectangular enclosure is studied numerically.An iso-heat flux is applied for heating and cooling the two opposing walls of the enclosure while the other walls are adi-abatic. The Forchheimer extension of Darcy-Oberbeck-Boussinesq and energy equations is transformed into a dimensionless form using a set of suitable variables instead of a finite difference scheme.The governing parameters are the magnetic influence number,the modified Rayleigh number,the inclination angle,and the aspect ratio of the enclosure. The results show that viscous and Joule heating effects decrease heat transfer rates.
文摘Cooling by evaporation through transpiring porous walls is expanding in various industrial applications such as air conditioning. It is also used to cool water in a clay jug. This process deserves to be studied, understood and valued. This paper deals with the transpiration phenomenon through a saturated porous plate coupled with heat and mass transfer by natural convection. Conservation Equations (mass, momentum, energy and concentration), associated with adequate boundary conditions, have been numerically solved using an implicit finite difference iterative method. The numerical model has been validated by experimental measurements from holographic interferometry. The used method to obtain temperature and concentration profiles was explained. They are evaluated from the refractive index of moisture air in the boundary layer. The main numerical results presented are: Nusselt and Sherwood numbers, temperature, humidity, and velocity profiles within the boundary layer as well as the different heat fluxes exchanged between the plate and the surrounding environment. Besides, the present model allows showing the important effect of the equivalent thermal conductivity and the surface emissivity on temperature and heats flux.
文摘A detailed sensitivity study was carried out on various key parameters from a high precision numerical model of a microelectronic package cooled by natural convection, to provide rules for the thermal modeling of microelectronic packages subjected to natural convection heat transfer. An accurate estimate of the junction temperature, with an error of less than 1˚C, was obtained compared to the experimental data for the vertical and horizontal orientations of the test vehicle in the JEDEC Still Air configuration. The sensitivity study showed that to have an accurate estimate of the temperature, the following elements should be present in the thermal model: radiation heat transfer in natural convection cooling;a computational fluid dynamics analysis to find realistic convection coefficients;detailed models of the high conductivity elements in the direction of the heat flow towards the environment;and finally precise values for the thicknesses of layers and the thermal properties of the substrate and the printed circuit board.
文摘Natural convection heat transfer in open or closed cavities takes place in different engineering areas. The hemispherical cavity is a part of basic geometries although it is not widely studied. The present paper reports the numerical study of natural convection in a closed hemispherical annulus delimited by two vertically eccentric hemispheres filled with Newtonian fluid (air in this case with <em>Pr</em> = 0.7) is conducted. The inner hemisphere is heated by a heat flux of constant density and the outer one is maintained isothermal. Based on the Boussinesq assumptions, the governing equations are numerically studied using unsteady natural convection formulated with vorticity and stream-function variables. These equations are written by using bispherical coordinates system and solved by using a finite difference method. The effect of the control parameters such as the Rayleigh number (<span style="white-space:nowrap;">10<sup>3</sup> ≤ <em>Ra</em> ≤ 10<sup>6</sup></span>) or the eccentricity (<em>e</em> = ±0.2, ±0.5, 0) in the dynamic and thermal behaviours of the fluid is investigated.
文摘A numerical analysis is performed to investigate the laminar, free convection flow in an Open Enclosure Using Lattice Boltzmann Method (LBM) in the presence of Carbon nanotube and Cu nanoparticles. The problem is studied for different volume fractions of nanoparticles, and aspect ratio of the cavity for various Rayligh numbers. The volume fraction of added nanoparticles to water (as base fluid) is lower than 1% to make dilute suspensions. The study presents a numerical treatment based on LBM to model convection heat transfer of Carbon nanotube based nanofluids. Results show that adding a low value of Carbon nanotube to the base fluid led to significant enhancement of convection rate. Results show that adding nanoparticles to the base fluid enhances the rate of natural convection in a cavity. Make a comparison between Carbon nanotube and Cu-nanoparticles shows that the Carbon nanotube-nano- particle has better performance to enhance convection rate at comparison with Cu- nanoparticles.
文摘This paper shows the natural convective heat transfer in porous media over the vertical wavy surface and it assumes that the fluid is viscous and in-compressible. This model shows the effects of the inverse of Darcy number. The dimensional partial differential equations are converted into a dimensionless form. The non-linear system of equations is obtained and these equations are solved numerically by the finite difference method. The results are obtained for inverse Darcy number, magnetic parameter, Prandtl number, amplitude of surface, parameter of heat generation and parameter of thermal conductivity, and their effects on the velocity, temperature of the fluid and Nusselt number.
文摘Coupled natural convection and surface radiation within a square cavity, filled with air and submitted to discrete heating and cooling from all its walls, is studied numerically. The thermally active elements are centrally located on the walls of the cavity. Two heating modes, called SB and SV, are considered. They correspond to bottom and vertical left elements sinusoidally heated in time, respectively, while the top and vertical right ones are constantly cooled. The remaining portions of all the walls are considered adiabatic. The parameters governing the problem are the amplitude and the period of the temporally sinusoidal temperature, the emissivity of the walls , the relative lengths of the active elements and the Rayleigh number . The effect of such parameters on flow and thermal fields and the resulting heat transfer is examined. It is shown that, during a flow cycle, the flow structure can present complex behavior, depending on the emissivity and the amplitude and period of the exciting temperature. The rate of heat transfer is generally enhanced in the case of sinusoidal heating. Also, the resonance phenomenon existence, characterized by maximum fluctuations in flow intensity and heat transfer, is proved in this study.
