The behavior of non-Newtonian power-law nanofluids under free convection heat transfer conditions in a cooled square enclosure equipped with a heated fin is investigated numerically.In particular,the impact of nanoflu...The behavior of non-Newtonian power-law nanofluids under free convection heat transfer conditions in a cooled square enclosure equipped with a heated fin is investigated numerically.In particular,the impact of nanofluids,composed of water and Al_(2)O_(3),TiO_(2),and Cu nanoparticles,on heat transfer enhancement is examined.The aim of this research is also to analyze the influence of different parameters,including the Rayleigh number(Ra=10^(4)-10^(6)),nanoparticle volume fraction(φ=0%-20%),non-Newtonian power-law indexes(n=0.6-1.4),and fin dimensions(Ar=0.3,0.5,and 0.7).Streamlines and isotherms are used to depict flow and related heat transfer characteristics.Results indicate that thermal performance improves with increasing Rayleigh number,regardless of the nanoparticle type or nanofluid rheological behavior.This suggests that the buoyancy force has a significant impact on heat transfer,particularly near the heat source.The Nusselt number is more sensitive to variations in Cu nanoparticle volume fractions compared to Al₂O₃and TiO₂.Moreover,the average Nusselt numbers for power-law nanofluids with n<1(n>1)are greater(smaller)than for Newtonian fluids due to the decrease(increase)in viscosity with increasing(decreasing)shear rate,at the same values of Rayleigh number Ra owing to the amplification(attenuation)of the convective transfer.Notably,the most substantial enhancement is observed with Cu-water shear-thinning nanofluid,where the Nusselt number increases by 136%when changing from Newtonian to shear thinning behavior and by 154.9%when adding 16%nanoparticle volume fraction.Moreover,an even larger increase of 57%in the average Nusselt number is obtained on increasing the fin length from 0.3 to 0.7.展开更多
Natural convection is a heat transfer mechanism driven by temperature or density differences,leading to fluid motion without external influence.It occurs in various natural and engineering phenomena,influencing heat t...Natural convection is a heat transfer mechanism driven by temperature or density differences,leading to fluid motion without external influence.It occurs in various natural and engineering phenomena,influencing heat transfer,climate,and fluid mixing in industrial processes.This work aims to use the Updated Lagrangian Particle Hydrodynamics(ULPH)theory to address natural convection problems.The Navier-Stokes equation is discretized using second-order nonlocal differential operators,allowing a direct solution of the Laplace operator for temperature in the energy equation.Various numerical simulations,including cases such as natural convection in square cavities and two concentric cylinders,were conducted to validate the reliability of the model.The results demonstrate that the proposed model exhibits excellent accuracy and performance,providing a promising and effective numerical approach for natural convection problems.展开更多
The present investigation centers on the impact of viscous dissipation and ohmic heating on the plume generated by a line heat source under the impact of an aligned magnetic field.In this study,the flow model is adapt...The present investigation centers on the impact of viscous dissipation and ohmic heating on the plume generated by a line heat source under the impact of an aligned magnetic field.In this study,the flow model is adapted to incorporate ohmic heating and viscous dissipation by including the respective terms in the energy equation.A mathematical model is formulated as a system of coupled partial differential equations to analyze the flow problem.Subsequently,a numerical solution is derived with stream function formulation for the system of coupled partial differential equations,which transmutes it into ordinary differential equations.To achieve this,the numerical properties of the problem are established through the utilization of the Shooting method in tandem with the MATLAB tool bvp4c.The graphical representations of both missing and specified boundary conditions depict the effects of the magnetic parameter,viscous dissipation variable,magnetic force parameter,Prandtl number,and magnetic Prandtl number.These are accompanied by a discussion of their respective physical implications.The observed results claimed that the velocity,current density,and temperature distribution decrease for enhancing magnetic parameters.Meanwhile,the skin friction and magnetic flux drop while the heat transfer rate increases with an increment in magnetic parameters.These fluid flow and heat transfer characteristics were observed to decrease for increasing viscous dissipation.The current work is novel in incorporating ohmic heating viscous dissipation in energy equations coupled with Max-well and magnetic induction equations.展开更多
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
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
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
The dynamics of a bilayer system filling a rectangular cuvette subjected to external heating is studied.The influence of two types of thermal exposure on the flow pattern and on the dynamic contact angle is analyzed.I...The dynamics of a bilayer system filling a rectangular cuvette subjected to external heating is studied.The influence of two types of thermal exposure on the flow pattern and on the dynamic contact angle is analyzed.In particular,the cases of local heating from below and distributed thermal load from the lateral walls are considered.The simulation is carried out within the frame of a two-sided evaporative convection model based on the Boussinesq approximation.A benzine–air system is considered as reference system.The variation in time of the contact angle is described for both heating modes.Under lateral heating,near-wall boundary layers emerge together with strong convection,whereas the local thermal load from the lower wall results in the formation of multicellular motion in the entire volume of the fluids and the appearance of transition regimes followed by a steady-state mode.The results of the present study can aid the design of equipment for thermal coating or drying and the development of methods for the formation of patterns with required structure and morphology.展开更多
This study is devoted to an analysis of natural convection and the emergence of delamination in an incompressible fluid encapsulated in a closed region heated from the side.Weak,medium and intensive modes of stationar...This study is devoted to an analysis of natural convection and the emergence of delamination in an incompressible fluid encapsulated in a closed region heated from the side.Weak,medium and intensive modes of stationary laminar thermal and thermo-concentration convection are considered.It is shown that nonlinear flow features can radically change the flow structure and characteristics of heat and mass transfer.Moreover,the temperature and concentration segregation in the center of the square region display a non-monotonic dependence on the Grashof number(flow intensity).The formation of a nonstationary periodic structure of thermal convection in boundary layers and in the core of a convective flow in the closed region is also examined.Details of the formation of countercurrents inside the region with the direction opposite to the main convective flow are given.Finally,the influence of vertical and horizontal vibrations on oscillatory convection is analyzed in detail.展开更多
Natural convection heat transfer inside horizontal rectangular enclosure filled with the anisotropic porous media, with isothermally heated bottom and cooled top while the vertical walls are adiabatic, is analyzed num...Natural convection heat transfer inside horizontal rectangular enclosure filled with the anisotropic porous media, with isothermally heated bottom and cooled top while the vertical walls are adiabatic, is analyzed numerically by applying the Brinkman model-a modified form of Darcy model giving consideration to the viscous effect. The results show that: (1)the permeability ratio (K*=Ky/Kx) is an important factor affecting natural convection heat transfer in the porous media. As K' decreases, the circulation intensity of the natural convectioncells increase significantly, resulting in an enhancement of heat transfer coefficient; (2)the increase of Darcy number (aa=Ky/H2) implies that the viscous effect is more significant. As Da≥10-, there exists a certain difference between the Darcy model and the Brinkman model. It is more significant at a lower permeability ratio. In particalar, with K*≤0. 25, the Nusselt number for Da=10-3 would differ form that of Darcy model up to an amount of 30K. The Darcy flow as depicted by Darcy model is no longer existing and an analysis neglecting the viscous effect will inevitably be of considerable error.展开更多
The simultaneous investigation on the parameters affecting the flow of electrically conductive fluids such as volumetric radiation,heat absorption,heat generation,and magnetic field(MF)is very vital due to its existen...The simultaneous investigation on the parameters affecting the flow of electrically conductive fluids such as volumetric radiation,heat absorption,heat generation,and magnetic field(MF)is very vital due to its existence in various sectors of industry and engineering.The present research focuses on mathematical modeling to simulate the cooling of a hot component through power-law(PL)nanofluid convection flow.The temperature reduction of the hot component inside a two-dimensional(2D)inclined chamber with two different cold wall shapes is evaluated.The formulation of the problem is derived with the lattice Boltzmann method(LBM)by code writing via the FORTRAN language.The variables such as the radiation parameter(0–1),the Hartmann number(0–75),the heat absorption/generation coefficient(−5–5),the fluid behavioral index(0.8–1.2),the Rayleigh number(103–105),the imposed MF angle(0°–90°),the chamber inclination angle(−90°–90°),and the cavity cold wall shape(smooth and curved)are investigated.The findings indicate that the presence of radiation increases the mean Nusselt number value for the shear-thickening,Newtonian,and shear thinning fluids by about 6.2%,4%,and 2%,respectively.In most cases,the presence of nanoparticles improves the heat transfer(HT)rate,especially in the cases where thermal conduction dominates convection.There is the lowest cooling performance index and MF effect for the cavity placed at an angle of 90°.The application in the design of electronic coolers and solar collectors is one of the practical cases of this numerical research.展开更多
Helically coiled tube-in-tube(HCTT)heat exchangers are widely applied to the process technology because of their compactness and higher heat transfer efficiency.HCTT heat exchangers play an important role in liquified...Helically coiled tube-in-tube(HCTT)heat exchangers are widely applied to the process technology because of their compactness and higher heat transfer efficiency.HCTT heat exchangers play an important role in liquified natural gas(LNG)use and cold energy recovery.The heat transfer characteristics,pressure distribution,and degree of vaporization of LNG in HCTT heat exchangers are numerically investigated.By comparing the simulation results of the computational model with existing experimental results,the effectiveness of the computational model is verified.The numerical simulation results show the vapor volume fraction of the HCTT heat exchanger is related to the inlet Reynolds number,inner tube diameters,and helix diameter.The vapor volume fraction increases rapidly from the fourth to the seventh equal division points of the helix tube length.On condition that the inlet Reynolds number is greater than 33500,the pressure drop rate gradually increases.When the magnitude of the vapor volume fraction is below 0.2,the heat transfer coefficient increase rate is greater than that when the vapor volume fraction is above 0.2.The heat exchange efficiency of HCTT heat exchangers increases with the decrease of the ratio of helix diameter to inner tube diameter.展开更多
A two-dimensional numerical study of laminar natural convection in a square enclosure filled with air with a wall partially heated on the bottom is presented.The heat source is located on the lower wall with different...A two-dimensional numerical study of laminar natural convection in a square enclosure filled with air with a wall partially heated on the bottom is presented.The heat source is located on the lower wall with different heated widths varied from 20 to 80%(ε=0.2–0.8)of the total width of the lower wall and different heights h=H/4 and H/2 of the partition.The effect of the partition height on the main system dynamics is investigated through solution of the two-dimensional Navier-Stokes equations and the energy equation by means of a finite volume method based on the SIMPLE algorithm.The influence of the Rayleigh number(Ra=10^(3) to 10^(6))and the hot wall length is also examined.It is shown that the average Nusselt number grows whenεincreases and when h decreases.For a given value ofεand h,the average Nusselt number increases as Ra increases.It is concluded that the partition height causes a decrease in the average Nusselt number.展开更多
This study examines the heat transfer enhancement from a horizontal rectangular fin embedded with triangular perforations （their bases parallel and toward the fin tip） under natural convection. The fin＇s heat dissi...This study examines the heat transfer enhancement from a horizontal rectangular fin embedded with triangular perforations （their bases parallel and toward the fin tip） under natural convection. The fin＇s heat dissipation rate is compared to that of an equivalent solid one. The parameters considered are geometrical dimensions and thermal properties of the fin and the perforations. The gain in the heat transfer enhancement and the fin weight reduction due to the perforations are considered. The study shows that the heat dissipation from the perforated fin for a certain range of triangular perforation dimensions and spaces between perforations result in improvement in the heat transfer over the equivalent solid fin. The heat transfer enhancement of the perforated fin increases as the fin thermal conductivity and its thickness are increased.展开更多
In the present study, the influence of natural convection on the lamellar eutectic growth is determined by a phase-field-lattice Boltzmann study for Al-Cu eutectic alloy. The mass difference resulting from concentrati...In the present study, the influence of natural convection on the lamellar eutectic growth is determined by a phase-field-lattice Boltzmann study for Al-Cu eutectic alloy. The mass difference resulting from concentration difference led to the fluid flow, and a robust parallel and adaptive mesh refinement algorithm was employed to improve the computational efficiency without any compromising accuracy. Results show that the existence of natural convection would affect the growth undercooling and thus control the interface shape by adjusting the lamellar width. In particular, by alternating the magnitude of the solute expansion coefficient, the strength of the natural convection is changed. Corresponding microstructure patterns are discussed and compared with those under no-convection conditions.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
The solidification microstructure of Al-Si alloy was observed in the experiment,the second dendrite arm spacing(SDAS)was measured,and the effect of temperature on the microstructure was analyzed.Phase-field(PF)model i...The solidification microstructure of Al-Si alloy was observed in the experiment,the second dendrite arm spacing(SDAS)was measured,and the effect of temperature on the microstructure was analyzed.Phase-field(PF)model incorporating natural convection caused by gravity was employed to simulate the microstructure evolution of Al-Si alloy under the experimental conditions.Good agreements between the experimental and simulation results verified the reliability of the simulation approach proposed in this study.Based on the proposed model,a series of simulation cases(2D and 3D)were performed to investigate the evolution of columnar and equiaxed dendritic structures.It was found that the solute content of the alloy had little impact on the microstructure evolution,while the solute expansion coefficient had obvious effect on the dendrite tip velocities.Significant improvement of computational efficiency was achieved via novel algorithms,making it possible to perform massive simulation for studying the evolution of solidification microstructures,which is hard to be directly observed in experiments via synchrotron radiation for Al-Si alloy.展开更多
In the present paper, we have considered the steady fully developed laminar natural convective flow in open ended vertical concentric annuli in the presence of a ra- dial magnetic field. The induced magnetic field pro...In the present paper, we have considered the steady fully developed laminar natural convective flow in open ended vertical concentric annuli in the presence of a ra- dial magnetic field. The induced magnetic field produced by the motion of an electrically conducting fluid is taken into account. The transport equations concerned with the con- sidered model are first recast in the non-dimensional form and then unified analytical solutions for the velocity, induced magnetic field and temperature field are obtained for the cases of isothermal and constant heat flux on the inner cylin- der of concentric annuli. The effects of the various phys- ical parameters appearing into the model are demonstrated through graphs and tables. It is found that the magnitude of maximum value of the fluid velocity as well as induced magnetic field is greater in the case of isothermal condition compared with the constant heat flux case when the gap be- tween the cylinders is less or equal to 1.70 times the radius of inner cylinder, while reverse trend occurs when the gap between the cylinders is greater than 1.71 times the radius of inner cylinder. These fields are almost the same when the gap between the cylinders is equal to 1.71 times the radius of inner cylinder for both the cases. It is also found that as the Hartmann number increases, there is a flattening ten- dency for both the velocity and the induced magnetic field. The influence of the induced magnetic field is to increase the velocity profiles.展开更多
The aim of the present paper is to analyze the natural convection heat and mass transfer of nanofluids over a vertical plate embedded in a saturated Darcy porous medium subjected to surface heat and nanoparticle fluxe...The aim of the present paper is to analyze the natural convection heat and mass transfer of nanofluids over a vertical plate embedded in a saturated Darcy porous medium subjected to surface heat and nanoparticle fluxes. To carry out the numerical solution, two steps are performed. The governing partial differential equations are firstly simplified into a set of highly coupled nonlinear ordinary differential equations by appropriate similarity variables, and then numerically solved by the finite difference method. The obtained similarity solution depends on four non-dimensional parameters, i.e., the Brownian motion parameter （Nb）, the buoyancy ratio （Nr）, the thermophoresis parameter （Nt）, and the Lewis number （Le）. The variations of the reduced Nusselt number and the reduced Sherwood number with Nb and Nt for various values of Le and Nr are discussed in detail. Simulation results depict that the increase in Nb, Nt, or Nr decreases the reduced Nusselt number. An increase in the Lewis number increases both of the reduced Nusselt number and the Sherwood number. The results also reveal that the nanoparticle concentration boundary layer thickness is much thinner than those of the thermal and hydrodynamic boundary layers.展开更多
The natural convective heat transfer performance of an aluminum hexagonal honeycomb acting as a novel heat sink for LED cooling is experi- mentally investigated. The concept of adding an adiabatic square chimney ex- t...The natural convective heat transfer performance of an aluminum hexagonal honeycomb acting as a novel heat sink for LED cooling is experi- mentally investigated. The concept of adding an adiabatic square chimney ex- tension for heat transfer enhancement is proposed, and the effects of chimney shape, height, and diameter are quantified. The average Nuav of a heated hon- eycomb with straight chimney is significantly higher than that without chimney, and the enhancement increases with increasing chimney height. At a given chim- ney height, honeycombs with divergent chimneys perform better than those with convergent ones. For a fixed divergent angle, the Nuav number increases mono- tonically with increasing chimney height. In contrast, with the convergent angle fixed, there exists an optimal chimney height to achieve maximum heat transfer.展开更多
The present study is devoted to numerical analysis of natural convective heat transfer and fluid flow of alumina-water nanofluid in an inclined wavy-walled cavity under the effect of non-uniform heating. A single-phas...The present study is devoted to numerical analysis of natural convective heat transfer and fluid flow of alumina-water nanofluid in an inclined wavy-walled cavity under the effect of non-uniform heating. A single-phase nanofluid model with experimental correlations for the nanofluid viscosity and thermal conductivity has been included in the mathematical model. The considered governing equations formulated in dimensionless stream function, vorticity, and temperature have been solved by the finite difference method. The cavity inclination angle and irregular walls(wavy and undulation numbers)are very good control parameters for the heat transfer and fluid flow. Nowadays, optimal parameters are necessary for the heat transfer enhancement in different practical applications. The effects of the involved parameters on the streamlines and isotherms as well as on the average Nusselt number and nanofluid flow rate have been analyzed. It has been found that the heat transfer rate and fluid flow rate are non-monotonic functions of the cavity inclination angle and undulation number.展开更多
基金financial support by Campus France within the framework of the PHC-Maghreb 45990SH Projectsupport from the Tunisian Republic Ministry of Higher Education and Scientific Research for a part of her stay in France.
文摘The behavior of non-Newtonian power-law nanofluids under free convection heat transfer conditions in a cooled square enclosure equipped with a heated fin is investigated numerically.In particular,the impact of nanofluids,composed of water and Al_(2)O_(3),TiO_(2),and Cu nanoparticles,on heat transfer enhancement is examined.The aim of this research is also to analyze the influence of different parameters,including the Rayleigh number(Ra=10^(4)-10^(6)),nanoparticle volume fraction(φ=0%-20%),non-Newtonian power-law indexes(n=0.6-1.4),and fin dimensions(Ar=0.3,0.5,and 0.7).Streamlines and isotherms are used to depict flow and related heat transfer characteristics.Results indicate that thermal performance improves with increasing Rayleigh number,regardless of the nanoparticle type or nanofluid rheological behavior.This suggests that the buoyancy force has a significant impact on heat transfer,particularly near the heat source.The Nusselt number is more sensitive to variations in Cu nanoparticle volume fractions compared to Al₂O₃and TiO₂.Moreover,the average Nusselt numbers for power-law nanofluids with n<1(n>1)are greater(smaller)than for Newtonian fluids due to the decrease(increase)in viscosity with increasing(decreasing)shear rate,at the same values of Rayleigh number Ra owing to the amplification(attenuation)of the convective transfer.Notably,the most substantial enhancement is observed with Cu-water shear-thinning nanofluid,where the Nusselt number increases by 136%when changing from Newtonian to shear thinning behavior and by 154.9%when adding 16%nanoparticle volume fraction.Moreover,an even larger increase of 57%in the average Nusselt number is obtained on increasing the fin length from 0.3 to 0.7.
基金support from the National Natural Science Foundations of China(Nos.11972267 and 11802214)the Open Foundation of the Hubei Key Laboratory of Theory and Application of Advanced Materials Mechanics and the Open Foundation of Hubei Key Laboratory of Engineering Structural Analysis and Safety Assessment.
文摘Natural convection is a heat transfer mechanism driven by temperature or density differences,leading to fluid motion without external influence.It occurs in various natural and engineering phenomena,influencing heat transfer,climate,and fluid mixing in industrial processes.This work aims to use the Updated Lagrangian Particle Hydrodynamics(ULPH)theory to address natural convection problems.The Navier-Stokes equation is discretized using second-order nonlocal differential operators,allowing a direct solution of the Laplace operator for temperature in the energy equation.Various numerical simulations,including cases such as natural convection in square cavities and two concentric cylinders,were conducted to validate the reliability of the model.The results demonstrate that the proposed model exhibits excellent accuracy and performance,providing a promising and effective numerical approach for natural convection problems.
基金supported by the National Foreign Expert Project-Foreign Youth Talent Program Fund No.QN2023001001Beijing Natural Science Foundation Project-Foreign Scholar Program Fund No.IS23046/ZW001A00202301+1 种基金National Natural Science Foundation of China(NSFC)Fund No.12202019Beijing PostdoctoralResearch Activities Fund No.Q6001A00202301.
文摘The present investigation centers on the impact of viscous dissipation and ohmic heating on the plume generated by a line heat source under the impact of an aligned magnetic field.In this study,the flow model is adapted to incorporate ohmic heating and viscous dissipation by including the respective terms in the energy equation.A mathematical model is formulated as a system of coupled partial differential equations to analyze the flow problem.Subsequently,a numerical solution is derived with stream function formulation for the system of coupled partial differential equations,which transmutes it into ordinary differential equations.To achieve this,the numerical properties of the problem are established through the utilization of the Shooting method in tandem with the MATLAB tool bvp4c.The graphical representations of both missing and specified boundary conditions depict the effects of the magnetic parameter,viscous dissipation variable,magnetic force parameter,Prandtl number,and magnetic Prandtl number.These are accompanied by a discussion of their respective physical implications.The observed results claimed that the velocity,current density,and temperature distribution decrease for enhancing magnetic parameters.Meanwhile,the skin friction and magnetic flux drop while the heat transfer rate increases with an increment in magnetic parameters.These fluid flow and heat transfer characteristics were observed to decrease for increasing viscous dissipation.The current work is novel in incorporating ohmic heating viscous dissipation in energy equations coupled with Max-well and magnetic induction equations.
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.
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.
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.
文摘The dynamics of a bilayer system filling a rectangular cuvette subjected to external heating is studied.The influence of two types of thermal exposure on the flow pattern and on the dynamic contact angle is analyzed.In particular,the cases of local heating from below and distributed thermal load from the lateral walls are considered.The simulation is carried out within the frame of a two-sided evaporative convection model based on the Boussinesq approximation.A benzine–air system is considered as reference system.The variation in time of the contact angle is described for both heating modes.Under lateral heating,near-wall boundary layers emerge together with strong convection,whereas the local thermal load from the lower wall results in the formation of multicellular motion in the entire volume of the fluids and the appearance of transition regimes followed by a steady-state mode.The results of the present study can aid the design of equipment for thermal coating or drying and the development of methods for the formation of patterns with required structure and morphology.
基金the Russian Science Foundation Grant 24-29-00101.
文摘This study is devoted to an analysis of natural convection and the emergence of delamination in an incompressible fluid encapsulated in a closed region heated from the side.Weak,medium and intensive modes of stationary laminar thermal and thermo-concentration convection are considered.It is shown that nonlinear flow features can radically change the flow structure and characteristics of heat and mass transfer.Moreover,the temperature and concentration segregation in the center of the square region display a non-monotonic dependence on the Grashof number(flow intensity).The formation of a nonstationary periodic structure of thermal convection in boundary layers and in the core of a convective flow in the closed region is also examined.Details of the formation of countercurrents inside the region with the direction opposite to the main convective flow are given.Finally,the influence of vertical and horizontal vibrations on oscillatory convection is analyzed in detail.
文摘Natural convection heat transfer inside horizontal rectangular enclosure filled with the anisotropic porous media, with isothermally heated bottom and cooled top while the vertical walls are adiabatic, is analyzed numerically by applying the Brinkman model-a modified form of Darcy model giving consideration to the viscous effect. The results show that: (1)the permeability ratio (K*=Ky/Kx) is an important factor affecting natural convection heat transfer in the porous media. As K' decreases, the circulation intensity of the natural convectioncells increase significantly, resulting in an enhancement of heat transfer coefficient; (2)the increase of Darcy number (aa=Ky/H2) implies that the viscous effect is more significant. As Da≥10-, there exists a certain difference between the Darcy model and the Brinkman model. It is more significant at a lower permeability ratio. In particalar, with K*≤0. 25, the Nusselt number for Da=10-3 would differ form that of Darcy model up to an amount of 30K. The Darcy flow as depicted by Darcy model is no longer existing and an analysis neglecting the viscous effect will inevitably be of considerable error.
文摘The simultaneous investigation on the parameters affecting the flow of electrically conductive fluids such as volumetric radiation,heat absorption,heat generation,and magnetic field(MF)is very vital due to its existence in various sectors of industry and engineering.The present research focuses on mathematical modeling to simulate the cooling of a hot component through power-law(PL)nanofluid convection flow.The temperature reduction of the hot component inside a two-dimensional(2D)inclined chamber with two different cold wall shapes is evaluated.The formulation of the problem is derived with the lattice Boltzmann method(LBM)by code writing via the FORTRAN language.The variables such as the radiation parameter(0–1),the Hartmann number(0–75),the heat absorption/generation coefficient(−5–5),the fluid behavioral index(0.8–1.2),the Rayleigh number(103–105),the imposed MF angle(0°–90°),the chamber inclination angle(−90°–90°),and the cavity cold wall shape(smooth and curved)are investigated.The findings indicate that the presence of radiation increases the mean Nusselt number value for the shear-thickening,Newtonian,and shear thinning fluids by about 6.2%,4%,and 2%,respectively.In most cases,the presence of nanoparticles improves the heat transfer(HT)rate,especially in the cases where thermal conduction dominates convection.There is the lowest cooling performance index and MF effect for the cavity placed at an angle of 90°.The application in the design of electronic coolers and solar collectors is one of the practical cases of this numerical research.
基金supported by Innovative Team Introduction Projects for New Universities in Jinan City(No.2021GXRC075).
文摘Helically coiled tube-in-tube(HCTT)heat exchangers are widely applied to the process technology because of their compactness and higher heat transfer efficiency.HCTT heat exchangers play an important role in liquified natural gas(LNG)use and cold energy recovery.The heat transfer characteristics,pressure distribution,and degree of vaporization of LNG in HCTT heat exchangers are numerically investigated.By comparing the simulation results of the computational model with existing experimental results,the effectiveness of the computational model is verified.The numerical simulation results show the vapor volume fraction of the HCTT heat exchanger is related to the inlet Reynolds number,inner tube diameters,and helix diameter.The vapor volume fraction increases rapidly from the fourth to the seventh equal division points of the helix tube length.On condition that the inlet Reynolds number is greater than 33500,the pressure drop rate gradually increases.When the magnitude of the vapor volume fraction is below 0.2,the heat transfer coefficient increase rate is greater than that when the vapor volume fraction is above 0.2.The heat exchange efficiency of HCTT heat exchangers increases with the decrease of the ratio of helix diameter to inner tube diameter.
文摘A two-dimensional numerical study of laminar natural convection in a square enclosure filled with air with a wall partially heated on the bottom is presented.The heat source is located on the lower wall with different heated widths varied from 20 to 80%(ε=0.2–0.8)of the total width of the lower wall and different heights h=H/4 and H/2 of the partition.The effect of the partition height on the main system dynamics is investigated through solution of the two-dimensional Navier-Stokes equations and the energy equation by means of a finite volume method based on the SIMPLE algorithm.The influence of the Rayleigh number(Ra=10^(3) to 10^(6))and the hot wall length is also examined.It is shown that the average Nusselt number grows whenεincreases and when h decreases.For a given value ofεand h,the average Nusselt number increases as Ra increases.It is concluded that the partition height causes a decrease in the average Nusselt number.
文摘This study examines the heat transfer enhancement from a horizontal rectangular fin embedded with triangular perforations （their bases parallel and toward the fin tip） under natural convection. The fin＇s heat dissipation rate is compared to that of an equivalent solid one. The parameters considered are geometrical dimensions and thermal properties of the fin and the perforations. The gain in the heat transfer enhancement and the fin weight reduction due to the perforations are considered. The study shows that the heat dissipation from the perforated fin for a certain range of triangular perforation dimensions and spaces between perforations result in improvement in the heat transfer over the equivalent solid fin. The heat transfer enhancement of the perforated fin increases as the fin thermal conductivity and its thickness are increased.
基金supported by the National Natural Science Foundation of China[grant number U1537202]the TsinghuaGeneral Motor International collaboration project[grant number 20153000354]+1 种基金the UK Royal Society through the Newton International Fellowship Schemethe National Laboratory for Information Science and Technology in Tsinghua University for access to supercomputing facilities
文摘In the present study, the influence of natural convection on the lamellar eutectic growth is determined by a phase-field-lattice Boltzmann study for Al-Cu eutectic alloy. The mass difference resulting from concentration difference led to the fluid flow, and a robust parallel and adaptive mesh refinement algorithm was employed to improve the computational efficiency without any compromising accuracy. Results show that the existence of natural convection would affect the growth undercooling and thus control the interface shape by adjusting the lamellar width. In particular, by alternating the magnitude of the solute expansion coefficient, the strength of the natural convection is changed. Corresponding microstructure patterns are discussed and compared with those under no-convection conditions.
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.
基金financial supports from the National Key R&D Program of China(No.2016YFB0701201)the Fostering Project in Innovation Funds of China Academy of Engineering Physics(No.PY2019078)financial support from China Scholarship Council。
文摘The solidification microstructure of Al-Si alloy was observed in the experiment,the second dendrite arm spacing(SDAS)was measured,and the effect of temperature on the microstructure was analyzed.Phase-field(PF)model incorporating natural convection caused by gravity was employed to simulate the microstructure evolution of Al-Si alloy under the experimental conditions.Good agreements between the experimental and simulation results verified the reliability of the simulation approach proposed in this study.Based on the proposed model,a series of simulation cases(2D and 3D)were performed to investigate the evolution of columnar and equiaxed dendritic structures.It was found that the solute content of the alloy had little impact on the microstructure evolution,while the solute expansion coefficient had obvious effect on the dendrite tip velocities.Significant improvement of computational efficiency was achieved via novel algorithms,making it possible to perform massive simulation for studying the evolution of solidification microstructures,which is hard to be directly observed in experiments via synchrotron radiation for Al-Si alloy.
文摘In the present paper, we have considered the steady fully developed laminar natural convective flow in open ended vertical concentric annuli in the presence of a ra- dial magnetic field. The induced magnetic field produced by the motion of an electrically conducting fluid is taken into account. The transport equations concerned with the con- sidered model are first recast in the non-dimensional form and then unified analytical solutions for the velocity, induced magnetic field and temperature field are obtained for the cases of isothermal and constant heat flux on the inner cylin- der of concentric annuli. The effects of the various phys- ical parameters appearing into the model are demonstrated through graphs and tables. It is found that the magnitude of maximum value of the fluid velocity as well as induced magnetic field is greater in the case of isothermal condition compared with the constant heat flux case when the gap be- tween the cylinders is less or equal to 1.70 times the radius of inner cylinder, while reverse trend occurs when the gap between the cylinders is greater than 1.71 times the radius of inner cylinder. These fields are almost the same when the gap between the cylinders is equal to 1.71 times the radius of inner cylinder for both the cases. It is also found that as the Hartmann number increases, there is a flattening ten- dency for both the velocity and the induced magnetic field. The influence of the induced magnetic field is to increase the velocity profiles.
基金Shahid Chamran University of Ahvaz for its support of this paper
文摘The aim of the present paper is to analyze the natural convection heat and mass transfer of nanofluids over a vertical plate embedded in a saturated Darcy porous medium subjected to surface heat and nanoparticle fluxes. To carry out the numerical solution, two steps are performed. The governing partial differential equations are firstly simplified into a set of highly coupled nonlinear ordinary differential equations by appropriate similarity variables, and then numerically solved by the finite difference method. The obtained similarity solution depends on four non-dimensional parameters, i.e., the Brownian motion parameter （Nb）, the buoyancy ratio （Nr）, the thermophoresis parameter （Nt）, and the Lewis number （Le）. The variations of the reduced Nusselt number and the reduced Sherwood number with Nb and Nt for various values of Le and Nr are discussed in detail. Simulation results depict that the increase in Nb, Nt, or Nr decreases the reduced Nusselt number. An increase in the Lewis number increases both of the reduced Nusselt number and the Sherwood number. The results also reveal that the nanoparticle concentration boundary layer thickness is much thinner than those of the thermal and hydrodynamic boundary layers.
基金supported by the National 111 Project of China(B06024)the National Basic Research Program of China(2011CB610305)the National Natural Science Foundation of China(51206128)
文摘The natural convective heat transfer performance of an aluminum hexagonal honeycomb acting as a novel heat sink for LED cooling is experi- mentally investigated. The concept of adding an adiabatic square chimney ex- tension for heat transfer enhancement is proposed, and the effects of chimney shape, height, and diameter are quantified. The average Nuav of a heated hon- eycomb with straight chimney is significantly higher than that without chimney, and the enhancement increases with increasing chimney height. At a given chim- ney height, honeycombs with divergent chimneys perform better than those with convergent ones. For a fixed divergent angle, the Nuav number increases mono- tonically with increasing chimney height. In contrast, with the convergent angle fixed, there exists an optimal chimney height to achieve maximum heat transfer.
基金supported by the Ministry of Education and Science of the Russian Federation(No.13.6542.2017/6.7)supported from the grant PN-III-P4-ID-PCE-2016-0036,UEFISCDI,Romania
文摘The present study is devoted to numerical analysis of natural convective heat transfer and fluid flow of alumina-water nanofluid in an inclined wavy-walled cavity under the effect of non-uniform heating. A single-phase nanofluid model with experimental correlations for the nanofluid viscosity and thermal conductivity has been included in the mathematical model. The considered governing equations formulated in dimensionless stream function, vorticity, and temperature have been solved by the finite difference method. The cavity inclination angle and irregular walls(wavy and undulation numbers)are very good control parameters for the heat transfer and fluid flow. Nowadays, optimal parameters are necessary for the heat transfer enhancement in different practical applications. The effects of the involved parameters on the streamlines and isotherms as well as on the average Nusselt number and nanofluid flow rate have been analyzed. It has been found that the heat transfer rate and fluid flow rate are non-monotonic functions of the cavity inclination angle and undulation number.
