Steady,laminar mixed convection inside a lid-driven square cavity filled with nanofluid is investigated numerically.We consider the case where the right and left walls are moving downwards and upwards respectively an...Steady,laminar mixed convection inside a lid-driven square cavity filled with nanofluid is investigated numerically.We consider the case where the right and left walls are moving downwards and upwards respectively and maintained at different temperatures while the other two horizontal ones are kept adiabatic and impermeable.The set of nonlinear coupled governing mass,momentum,and energy equations are solved using an extensively validated and a highly accurate finite difference method of fourth-order.Comparisons with previously conducted investigations on special configurations are performed and show an excellent agreement.Meanwhile,attention is focused on the heat transfer enhancement when different nano-particles:Cu,Ag,Al2O3,TiO2 and Fe3O4 are incorporated separately in different base fluids such as:Water,Ethylene-glycol,Methanol and Kerosene oil.In this framework,the numerical results related to several mixtures are presented and concern flow pattern and heat transfer curves for various values of Richardson number[Ri=0.1,1 and 10].It turns out that the choice of the efficient binary mixture for an optimal heat transfer depends not only on the thermophysical properties of the nanofluids but also on the range of the Richardson number.Special attention is devoted to shedding light on the effect of the shape of the nanoparticles on the heat transfer in the case of Water-Ag nanofluid.It is concluded that the spherical shape is more suitable for a better heat transfer enhancement in comparison to the cylindrical ones.展开更多
To date,there are very few studies on the transition beyond second Hopf bifurcation in a lid-driven square cavity,due to the difficulties in theoretical analysis and numerical simulations.In this paper,we study the ch...To date,there are very few studies on the transition beyond second Hopf bifurcation in a lid-driven square cavity,due to the difficulties in theoretical analysis and numerical simulations.In this paper,we study the characteristics of the third Hopf bifurcation in a driven square cavity by applying a consistent fourth-order compact finite difference scheme rectently developed by us.We numerically identify the critical Reynolds number of the third Hopf bifurcation located in the interval of(13944.7021,13946.5333)by the method of bisection.Through Fourier analysis,it is discovered that the flow becomes chaotic with a characteristic of period-doubling bifurcation when the Reynolds number is beyond the third bifurcation critical interval.Nonlinear time series analysis further ascertains the flow chaotic behaviors via the phase diagram,Kolmogorov entropy and maximal Lyapunov exponent.The phase diagram changes interestingly from a closed curve with self-intersection to an unclosed curve and the attractor eventually becomes strange when the flow becomes chaotic.展开更多
A numerical study of heat transfer problem by natural convection of a fluid inside a square cavity with two inner bodies is presented. This subject is of great interest in the engineering area, mainly in applications ...A numerical study of heat transfer problem by natural convection of a fluid inside a square cavity with two inner bodies is presented. This subject is of great interest in the engineering area, mainly in applications involving development of heat exchangers and cooling or heating systems of bodies by natural convection mechanism. Two cases have been studied. The inner bodies are square in case 1 and circular in case 2. In both cases, the bodies are solid and thermally conductive, the cavity lower and upper horizontal surfaces are isothermal with high temperature Th and low temperature Tc, respectively. Both vertical surfaces are adiabatic. A FORTRAN code using Finite Element Method (FEM) is developed to simulate the problem and solve the governing equations. The distributions of stream function, ψ, dimensionless temperature, θ, and vorticity, ω, are determined. Heat transfer is evaluated by analyzing the behavior of the average Nusselt number. The Grashof number and thermal diffusivity ratio are considered in range from 2 × 104 to 105 and from 0.1 to 100, respectively. The fluid is air with Prandtl number fixed in 0.733.展开更多
This study explains the entropy process of natural convective heating in the nanofluid-saturated cavity in a heated fin andmagnetic field.The temperature is constant on the Y-shaped fin,insulating the topwall while th...This study explains the entropy process of natural convective heating in the nanofluid-saturated cavity in a heated fin andmagnetic field.The temperature is constant on the Y-shaped fin,insulating the topwall while the remaining walls remain cold.All walls are subject to impermeability and non-slip conditions.The mathematical modeling of the problem is demonstrated by the continuity,momentum,and energy equations incorporating the inclined magnetic field.For elucidating the flow characteristics Finite ElementMethod(FEM)is implemented using stable FE pair.A hybrid fine mesh is used for discretizing the domain.Velocity and thermal plots concerning parameters are drawn.In addition,a detailed discussion regarding generation energy by monitoring changes in magnetic,viscous,total,and thermal irreversibility is provided.In addition,line graphs are created for the u and v components of the velocity profile to predict the flow behavior.Current simulations assume the dimensionless representative of magnetic field Hartmann number Ha between 0 and 100 and a magnetic field inclination between 0 and 90 degrees.A constant 4% volume proportion of nanoparticles is employed throughout all scenarios.展开更多
A comprehensive numerical study was conducted to investigate heat transfer enhancement during the melting process in a 2D square cavity through dispersion of nanoparticles.A paraffin-based nanofluid containing various...A comprehensive numerical study was conducted to investigate heat transfer enhancement during the melting process in a 2D square cavity through dispersion of nanoparticles.A paraffin-based nanofluid containing various volume fractions of Cu was applied.The governing equations were solved on a non-uniform mesh using a pressure-based finite volume method with an enthalpy porosity technique to trace the solid-liquid interface.The effects of nanoparticle dispersion in a pure fluid and of some significant parameters,namely nanoparticle volume fraction,cavity size and hot wall temperature,on the fluid flow,heat transfer features and melting time were studied.The results are presented in terms of temperature and velocity profiles,streamlines,isotherms,moving interface position,solid fraction and dimensionless heat flux.The suspended nanoparticles caused an increase in thermal conductivity of nano-enhanced phase change material(NEPCM)compared to conventional PCM,resulting in heat transfer enhancement and a higher melting rate.In addition,the nanofluid heat transfer rate increased and the melting time decreased as the volume fraction of nanoparticles increased.The higher temperature difference between the melting temperature and the hot wall temperature expedited the melting process of NEPCM.展开更多
This paper investigates the chaotic lid-driven square cavity flows at extreme Reynolds numbers.Several observations have been made from this study.Firstly,at extreme Reynolds numbers two principles add at the genesis ...This paper investigates the chaotic lid-driven square cavity flows at extreme Reynolds numbers.Several observations have been made from this study.Firstly,at extreme Reynolds numbers two principles add at the genesis of tiny,loose counterclockwise-or clockwise-rotating eddies.One concerns the arousing of them owing to the influence of the clockwise-or counterclockwise currents nearby;the other,the arousing of counterclockwise-rotating eddies near attached to the moving(lid)top wall which moves from left to right.Secondly,unexpectedly,the kinetic energy soon reaches the qualitative temporal limit’s pace,fluctuating briskly,randomly inside the total kinetic energy range,fluctuations which concentrate on two distinct fragments:one on its upper side,the upper fragment,the other on its lower side,the lower fragment,switching briskly,randomly from each other;and further on many small fragments arousing randomly within both,switching briskly,randomly from one another.As the Reynolds number Re→∞,both distance and then close,and the kinetic energy fluctuates shorter and shorter at the upper fragment and longer and longer at the lower fragment,displaying tall high spikes which enlarge and then disappear.As the time t→∞(at the Reynolds number Re fixed)they recur from time to time with roughly the same amplitude.For the most part,at the upper fragment the leading eddy rotates clockwise,and at the lower fragment,in stark contrast,it rotates counterclockwise.At Re=109 the leading eddy-at its qualitative temporal limit’s pace—appears to rotate solely counterclockwise.展开更多
Natural convection in a square cavity at high Rayleigh numbers is simulated by multiple relaxation time(MRT)lattice Boltzmann method(LBM)with a separate distribution function to solve the temperature.The Rayleigh numb...Natural convection in a square cavity at high Rayleigh numbers is simulated by multiple relaxation time(MRT)lattice Boltzmann method(LBM)with a separate distribution function to solve the temperature.The Rayleigh numbers examined here range from Ra=103 to Ra=10^(8).For Rayleigh numbers below 10^(8),the flow remains stationary and transition occurs beyond Ra=2×10^(8).Unsteady results at higher Rayleigh numbers(Ra=10^(9) and Ra=10^(10))are also investigated.To the best of our knowledge,this is the first accurate study which involves the high Rayleigh numbers Ra=10^(9),10^(10).展开更多
In this paper, a fundamental advancement of the basic helix design which expands to array having good bandwidth is proposed. The helix is inserted in a cavity. The result is a new antenna design that offers the perfor...In this paper, a fundamental advancement of the basic helix design which expands to array having good bandwidth is proposed. The helix is inserted in a cavity. The result is a new antenna design that offers the performance characteristics and advantages of the conven-tional helix but in a much more compact physical size envelope. A 4-element rectangular helical array has been designed. For miniaturization and impedance matching, the helical wire is replaced by a rectangular cross sectioned strip. It has been observed that when the helix is inserted in a cavity, it behaves differently from a normal helical antenna. The effects of the cavity on the number of turns, the impedance of total antenna, and the reflection coefficient have been analyzed. The array is designed for 2.4 GHz. The return loss obtained is less than - 10 dB and the bandwidth is more than 1.3 GHz for the array.展开更多
Laminar natural convection is studied in a square cavity filled with air whose two vertical sides are subject to a temperature difference, while the other two horizontal sides are adiabatic. The hot and cold wall temp...Laminar natural convection is studied in a square cavity filled with air whose two vertical sides are subject to a temperature difference, while the other two horizontal sides are adiabatic. The hot and cold wall temperatures are kept constant. We have presented a dynamic and thermal study of pure natural convection for different values of the Rayleigh number. The numerical simulation was carried out for Rayleigh numbers ranging from 10<sup>2</sup>, 10<sup>3</sup>, …, 10<sup>5</sup> and the Prandtl number is Pr = 0.71. We used the COMSOL Multiphysic 5.1 software, which allows us to simultaneously solve the coupled physical phenomena in a square enclosure containing air under the Boussinesq approximation. For the coupling of natural convection with radiation from radiative surfaces, both horizontal faces are subjected to radiative flux, and the emissivity of the surfaces varies from ε = 0.1 to 0.8. We have seen that a circulation process is involved. The fluid that is subjected to a high temperature near the hot wall rises to the ceiling and the fluid near the cold wall sinks. This movement continues until the fluid reaches thermal equilibrium. In a natural convection-surface radiation coupling, simulation results indicate that radiative exchange decreases as a function of the Rayleigh number. Surface radiation reduces the flow in the cavity.展开更多
This work illustrates the steady state, two dimensional natural convective flow and heat transfer features in square enclosure containing heated hexagonal block maintained either at constant wall temperature(CWT) or u...This work illustrates the steady state, two dimensional natural convective flow and heat transfer features in square enclosure containing heated hexagonal block maintained either at constant wall temperature(CWT) or uniform heat flux(UHF) thermal conditions. Governing equations(mass, momentum and energy) are solved by using finite volume method(FVM) with 3rd order accurate QUICK discretization scheme and SIMPLE algorithm for range of field pertinent parameters such as, Grashof number(10~3≤ Gr ≤ 10~6), Prandtl number(1 ≤ Pr ≤ 100) and power law index(0.5 ≤ n ≤ 1.5). The analysis of momentum and heat transfer characteristics are delineated by evolution of streamlines, isotherms, variation of average Nusselt number value and Colburn factor for natural convection(j_(nH)). A remarkable change is observed on fluid flow and thermal distribution pattern in cavity for both thermal conditions. Nusselt number shows linear variation with Grashof and Prandtl numbers; while rate of heat transfer by convection decreases for power law index value. Higher heat transfer rate can be achieved by using uniform heat flux condition. A Nusselt number correlation is developed for possible utilization in engineering/scientific design purpose.展开更多
This work presents a simulation of the phenomena of natural convection in an enclosure with a variable heating regime by the lattice Boltzmann method(LBM).We consider a square enclosure of side H filled with air(Pr=0....This work presents a simulation of the phenomena of natural convection in an enclosure with a variable heating regime by the lattice Boltzmann method(LBM).We consider a square enclosure of side H filled with air(Pr=0.71)and heated from below,with a hot portion of length L=0.8 H,by imposing a sinusoidal temperature.The unheated segments of the bottom wall are treated as adiabatic,and one of the vertical walls features a cold region,while the remaining walls remain adiabatic.The outcomes of the two-dimensional(2D)problem are depicted through isotherms,streamlines,the temperature evolution within the enclosure,and the Nusselt number.These visualizations span various amplitude values“a”in the interval[0.2,0.8],and of the period T0 for Ra=107.The amplitude and period effect on the results is evaluated and discussed.The amplitude of the temperature at the heart of the enclosure increases with the increase in amplitude.This also increases with the period(T0)of the imposed temperature,something that is not observable on the global Nusselt number.展开更多
文摘Steady,laminar mixed convection inside a lid-driven square cavity filled with nanofluid is investigated numerically.We consider the case where the right and left walls are moving downwards and upwards respectively and maintained at different temperatures while the other two horizontal ones are kept adiabatic and impermeable.The set of nonlinear coupled governing mass,momentum,and energy equations are solved using an extensively validated and a highly accurate finite difference method of fourth-order.Comparisons with previously conducted investigations on special configurations are performed and show an excellent agreement.Meanwhile,attention is focused on the heat transfer enhancement when different nano-particles:Cu,Ag,Al2O3,TiO2 and Fe3O4 are incorporated separately in different base fluids such as:Water,Ethylene-glycol,Methanol and Kerosene oil.In this framework,the numerical results related to several mixtures are presented and concern flow pattern and heat transfer curves for various values of Richardson number[Ri=0.1,1 and 10].It turns out that the choice of the efficient binary mixture for an optimal heat transfer depends not only on the thermophysical properties of the nanofluids but also on the range of the Richardson number.Special attention is devoted to shedding light on the effect of the shape of the nanoparticles on the heat transfer in the case of Water-Ag nanofluid.It is concluded that the spherical shape is more suitable for a better heat transfer enhancement in comparison to the cylindrical ones.
基金Project supported by the National Natural Science Foundation of China(Grant No.12162001)the Natural Science Foundation of Ningxia(Grant No.2019AAC03129)the Construction Project of First-Class Disciplines in Ningxia Higher Education(Grant No.NXYLXK2017B09)。
文摘To date,there are very few studies on the transition beyond second Hopf bifurcation in a lid-driven square cavity,due to the difficulties in theoretical analysis and numerical simulations.In this paper,we study the characteristics of the third Hopf bifurcation in a driven square cavity by applying a consistent fourth-order compact finite difference scheme rectently developed by us.We numerically identify the critical Reynolds number of the third Hopf bifurcation located in the interval of(13944.7021,13946.5333)by the method of bisection.Through Fourier analysis,it is discovered that the flow becomes chaotic with a characteristic of period-doubling bifurcation when the Reynolds number is beyond the third bifurcation critical interval.Nonlinear time series analysis further ascertains the flow chaotic behaviors via the phase diagram,Kolmogorov entropy and maximal Lyapunov exponent.The phase diagram changes interestingly from a closed curve with self-intersection to an unclosed curve and the attractor eventually becomes strange when the flow becomes chaotic.
文摘A numerical study of heat transfer problem by natural convection of a fluid inside a square cavity with two inner bodies is presented. This subject is of great interest in the engineering area, mainly in applications involving development of heat exchangers and cooling or heating systems of bodies by natural convection mechanism. Two cases have been studied. The inner bodies are square in case 1 and circular in case 2. In both cases, the bodies are solid and thermally conductive, the cavity lower and upper horizontal surfaces are isothermal with high temperature Th and low temperature Tc, respectively. Both vertical surfaces are adiabatic. A FORTRAN code using Finite Element Method (FEM) is developed to simulate the problem and solve the governing equations. The distributions of stream function, ψ, dimensionless temperature, θ, and vorticity, ω, are determined. Heat transfer is evaluated by analyzing the behavior of the average Nusselt number. The Grashof number and thermal diffusivity ratio are considered in range from 2 × 104 to 105 and from 0.1 to 100, respectively. The fluid is air with Prandtl number fixed in 0.733.
文摘This study explains the entropy process of natural convective heating in the nanofluid-saturated cavity in a heated fin andmagnetic field.The temperature is constant on the Y-shaped fin,insulating the topwall while the remaining walls remain cold.All walls are subject to impermeability and non-slip conditions.The mathematical modeling of the problem is demonstrated by the continuity,momentum,and energy equations incorporating the inclined magnetic field.For elucidating the flow characteristics Finite ElementMethod(FEM)is implemented using stable FE pair.A hybrid fine mesh is used for discretizing the domain.Velocity and thermal plots concerning parameters are drawn.In addition,a detailed discussion regarding generation energy by monitoring changes in magnetic,viscous,total,and thermal irreversibility is provided.In addition,line graphs are created for the u and v components of the velocity profile to predict the flow behavior.Current simulations assume the dimensionless representative of magnetic field Hartmann number Ha between 0 and 100 and a magnetic field inclination between 0 and 90 degrees.A constant 4% volume proportion of nanoparticles is employed throughout all scenarios.
文摘A comprehensive numerical study was conducted to investigate heat transfer enhancement during the melting process in a 2D square cavity through dispersion of nanoparticles.A paraffin-based nanofluid containing various volume fractions of Cu was applied.The governing equations were solved on a non-uniform mesh using a pressure-based finite volume method with an enthalpy porosity technique to trace the solid-liquid interface.The effects of nanoparticle dispersion in a pure fluid and of some significant parameters,namely nanoparticle volume fraction,cavity size and hot wall temperature,on the fluid flow,heat transfer features and melting time were studied.The results are presented in terms of temperature and velocity profiles,streamlines,isotherms,moving interface position,solid fraction and dimensionless heat flux.The suspended nanoparticles caused an increase in thermal conductivity of nano-enhanced phase change material(NEPCM)compared to conventional PCM,resulting in heat transfer enhancement and a higher melting rate.In addition,the nanofluid heat transfer rate increased and the melting time decreased as the volume fraction of nanoparticles increased.The higher temperature difference between the melting temperature and the hot wall temperature expedited the melting process of NEPCM.
基金supported in part by the National Science Foundation Grants No.DMS-0906440 and No.DMS-1206438.
文摘This paper investigates the chaotic lid-driven square cavity flows at extreme Reynolds numbers.Several observations have been made from this study.Firstly,at extreme Reynolds numbers two principles add at the genesis of tiny,loose counterclockwise-or clockwise-rotating eddies.One concerns the arousing of them owing to the influence of the clockwise-or counterclockwise currents nearby;the other,the arousing of counterclockwise-rotating eddies near attached to the moving(lid)top wall which moves from left to right.Secondly,unexpectedly,the kinetic energy soon reaches the qualitative temporal limit’s pace,fluctuating briskly,randomly inside the total kinetic energy range,fluctuations which concentrate on two distinct fragments:one on its upper side,the upper fragment,the other on its lower side,the lower fragment,switching briskly,randomly from each other;and further on many small fragments arousing randomly within both,switching briskly,randomly from one another.As the Reynolds number Re→∞,both distance and then close,and the kinetic energy fluctuates shorter and shorter at the upper fragment and longer and longer at the lower fragment,displaying tall high spikes which enlarge and then disappear.As the time t→∞(at the Reynolds number Re fixed)they recur from time to time with roughly the same amplitude.For the most part,at the upper fragment the leading eddy rotates clockwise,and at the lower fragment,in stark contrast,it rotates counterclockwise.At Re=109 the leading eddy-at its qualitative temporal limit’s pace—appears to rotate solely counterclockwise.
文摘Natural convection in a square cavity at high Rayleigh numbers is simulated by multiple relaxation time(MRT)lattice Boltzmann method(LBM)with a separate distribution function to solve the temperature.The Rayleigh numbers examined here range from Ra=103 to Ra=10^(8).For Rayleigh numbers below 10^(8),the flow remains stationary and transition occurs beyond Ra=2×10^(8).Unsteady results at higher Rayleigh numbers(Ra=10^(9) and Ra=10^(10))are also investigated.To the best of our knowledge,this is the first accurate study which involves the high Rayleigh numbers Ra=10^(9),10^(10).
文摘In this paper, a fundamental advancement of the basic helix design which expands to array having good bandwidth is proposed. The helix is inserted in a cavity. The result is a new antenna design that offers the performance characteristics and advantages of the conven-tional helix but in a much more compact physical size envelope. A 4-element rectangular helical array has been designed. For miniaturization and impedance matching, the helical wire is replaced by a rectangular cross sectioned strip. It has been observed that when the helix is inserted in a cavity, it behaves differently from a normal helical antenna. The effects of the cavity on the number of turns, the impedance of total antenna, and the reflection coefficient have been analyzed. The array is designed for 2.4 GHz. The return loss obtained is less than - 10 dB and the bandwidth is more than 1.3 GHz for the array.
文摘Laminar natural convection is studied in a square cavity filled with air whose two vertical sides are subject to a temperature difference, while the other two horizontal sides are adiabatic. The hot and cold wall temperatures are kept constant. We have presented a dynamic and thermal study of pure natural convection for different values of the Rayleigh number. The numerical simulation was carried out for Rayleigh numbers ranging from 10<sup>2</sup>, 10<sup>3</sup>, …, 10<sup>5</sup> and the Prandtl number is Pr = 0.71. We used the COMSOL Multiphysic 5.1 software, which allows us to simultaneously solve the coupled physical phenomena in a square enclosure containing air under the Boussinesq approximation. For the coupling of natural convection with radiation from radiative surfaces, both horizontal faces are subjected to radiative flux, and the emissivity of the surfaces varies from ε = 0.1 to 0.8. We have seen that a circulation process is involved. The fluid that is subjected to a high temperature near the hot wall rises to the ceiling and the fluid near the cold wall sinks. This movement continues until the fluid reaches thermal equilibrium. In a natural convection-surface radiation coupling, simulation results indicate that radiative exchange decreases as a function of the Rayleigh number. Surface radiation reduces the flow in the cavity.
文摘This work illustrates the steady state, two dimensional natural convective flow and heat transfer features in square enclosure containing heated hexagonal block maintained either at constant wall temperature(CWT) or uniform heat flux(UHF) thermal conditions. Governing equations(mass, momentum and energy) are solved by using finite volume method(FVM) with 3rd order accurate QUICK discretization scheme and SIMPLE algorithm for range of field pertinent parameters such as, Grashof number(10~3≤ Gr ≤ 10~6), Prandtl number(1 ≤ Pr ≤ 100) and power law index(0.5 ≤ n ≤ 1.5). The analysis of momentum and heat transfer characteristics are delineated by evolution of streamlines, isotherms, variation of average Nusselt number value and Colburn factor for natural convection(j_(nH)). A remarkable change is observed on fluid flow and thermal distribution pattern in cavity for both thermal conditions. Nusselt number shows linear variation with Grashof and Prandtl numbers; while rate of heat transfer by convection decreases for power law index value. Higher heat transfer rate can be achieved by using uniform heat flux condition. A Nusselt number correlation is developed for possible utilization in engineering/scientific design purpose.
文摘This work presents a simulation of the phenomena of natural convection in an enclosure with a variable heating regime by the lattice Boltzmann method(LBM).We consider a square enclosure of side H filled with air(Pr=0.71)and heated from below,with a hot portion of length L=0.8 H,by imposing a sinusoidal temperature.The unheated segments of the bottom wall are treated as adiabatic,and one of the vertical walls features a cold region,while the remaining walls remain adiabatic.The outcomes of the two-dimensional(2D)problem are depicted through isotherms,streamlines,the temperature evolution within the enclosure,and the Nusselt number.These visualizations span various amplitude values“a”in the interval[0.2,0.8],and of the period T0 for Ra=107.The amplitude and period effect on the results is evaluated and discussed.The amplitude of the temperature at the heart of the enclosure increases with the increase in amplitude.This also increases with the period(T0)of the imposed temperature,something that is not observable on the global Nusselt number.
