The convective heat transfer of hybrid nanoliquids within a concentric annulus has wide engineering applications such as chemical industries, solar collectors, gas turbines, heat exchangers, nuclear reactors, and elec...The convective heat transfer of hybrid nanoliquids within a concentric annulus has wide engineering applications such as chemical industries, solar collectors, gas turbines, heat exchangers, nuclear reactors, and electronic component cooling due to their high heat transport rate. Hence, in this study, the characteristics of the heat transport mechanism in an annulus filled with the Ag-MgO/H_2O hybrid nanoliquid under the influence of quadratic thermal radiation and quadratic convection are analyzed. The nonuniform heat source/sink and induced magnetic field mechanisms are used to govern the basic equations concerning the transport of the composite nanoliquid. The dependency of the Nusselt number on the effective parameters(thermal radiation, nonlinear convection,and temperature-dependent heat source/sink parameter) is examined through sensitivity analyses based on the response surface methodology(RSM) and the face-centered central composite design(CCD). The heat transport of the composite nanoliquid for the spacerelated heat source/sink is observed to be higher than that for the temperature-related heat source/sink. The mechanisms of quadratic convection and quadratic thermal radiation are favorable for the momentum of the nanoliquid. The heat transport rate is more sensitive towards quadratic thermal radiation.展开更多
In many industrial applications,heat transfer and tangent hyperbolic fluid flow processes have been garnering increasing attention,owing to their immense importance in technology,engineering,and science.These processe...In many industrial applications,heat transfer and tangent hyperbolic fluid flow processes have been garnering increasing attention,owing to their immense importance in technology,engineering,and science.These processes are relevant for polymer solutions,porous industrial materials,ceramic processing,oil recovery,and fluid beds.The present tangent hyperbolic fluid flow and heat transfer model accurately predicts the shear-thinning phenomenon and describes the blood flow characteristics.Therefore,the entropy production analysis of a non-Newtonian tangent hyperbolic material flow through a vertical microchannel with a quadratic density temperature fluctuation(quadratic/nonlinear Boussinesq approximation)is performed in the present study.The impacts of the hydrodynamic flow and Newton’s thermal conditions on the flow,heat transfer,and entropy generation are analyzed.The governing nonlinear equations are solved with the spectral quasi-linearization method(SQLM).The obtained results are compared with those calculated with a finite element method and the bvp4c routine.In addition,the effects of key parameters on the velocity of the hyperbolic tangent material,the entropy generation,the temperature,and the Nusselt number are discussed.The entropy generation increases with the buoyancy force,the pressure gradient factor,the non-linear convection,and the Eckert number.The non-Newtonian fluid factor improves the magnitude of the velocity field.The power-law index of the hyperbolic fluid and the Weissenberg number are found to be favorable for increasing the temperature field.The buoyancy force caused by the nonlinear change in the fluid density versus temperature improves the thermal energy of the system.展开更多
The Boussinesq approximation finds more and more frequent use in geologi- cal practice. In this paper, the asymptotic behavior of solution for fractional Boussinesq approximation is studied. After obtaining some a pri...The Boussinesq approximation finds more and more frequent use in geologi- cal practice. In this paper, the asymptotic behavior of solution for fractional Boussinesq approximation is studied. After obtaining some a priori estimates with the aid of eommu- tator estimate, we apply the Galerkin method to prove the existence of weak solution in the case of periodic domain. Meanwhile, the uniqueness is also obtained. Because the results obtained are independent of domain, the existence and uniqueness of the weak solution for Cauchy problem is also true. Finally, we use the Fourier splitting method to prove the decay of weak solution in three cases respectively.展开更多
In this paper,the Galerkin finite element method(FEM)together with the characteristic-based split(CBS)scheme are applied to study the case of the non-linear Boussinesq approximation within sinusoidal heating inclined ...In this paper,the Galerkin finite element method(FEM)together with the characteristic-based split(CBS)scheme are applied to study the case of the non-linear Boussinesq approximation within sinusoidal heating inclined enclosures filled with a non-Darcy porous media and nanofluids.The enclosure has an inclination angle and its side-walls have varying sinusoidal temperature distributions.The working fluid is a nanofluid that is consisting of water as a based nanofluid and Al2O3 as nanoparticles.The porous medium is modeled using the Brinkman Forchheimer extended Darcy model.The obtained results are analyzed over wide ranges of the non-linear Boussinesq parameter 0≤ζ≤1,the phase deviation 00≤Φ≤1800,the inclination angle 00≤γ≤900,the nanoparticles volume fraction 0%≤φ≤4%,the amplitude ratio 0≤a≤1 and the Rayleigh number 104≤Ra≤106.The results revealed that the average Nusselt number is enhanced by 0.73%,26.46%and 35.42%at Ra=104,105 and 106,respectively,when the non-linearBoussinesq parameter is varied from 0 to 1.In addition,rate of heat transfer in the case of a non-uniformly heating is higher than that of a uniformly heating.Non-linear Boussinesq parameter rises the flow speed and heat transfer in an enclosure.Phase deviation makes clear changes on the isotherms and heat transfer rate on the right wall of an enclosure.An inclination angle varies the flow speed and it has a slight effect on heat transfer in an enclosure.展开更多
The dynamics of absolute vorticity in the Boussinesq fluid is examined. It is shown that the Boussinesq approximation only captures one of the horizontal components of the solenoidal term. Based on scaling analysis of...The dynamics of absolute vorticity in the Boussinesq fluid is examined. It is shown that the Boussinesq approximation only captures one of the horizontal components of the solenoidal term. Based on scaling analysis of typical midlatitude synoptic systems, the horizontal component of the solenoidal term neglected by the Boussinesq approximation is at least of the same order of magnitude as the one captured by the Boussinesq approximation. This leads to severe underestimation of absolute vorticity and circulation.展开更多
With the horizontal Coriolis terms included in motion equations and the influence of compressibility of seawater on Brunt-Vaeisiaelae frequency considered, a numerical method of calculating the dispersion relation for...With the horizontal Coriolis terms included in motion equations and the influence of compressibility of seawater on Brunt-Vaeisiaelae frequency considered, a numerical method of calculating the dispersion relation for linear internal waves, which is an improvement of Cai and Gan （1995）, and hence Fliegel and Hunkins （1975）, had been set up. For different models （Pacific model, Atlantic model and Arctic model）, simulations using the three different methods were compared and the following conclusions were reached： （1） the influence of horizontal Coriolis terms on dispersion relation cannot be neglected and is connected with the direction of the wave celerity, the latitude, and the modes of the wave （2） the effect of compressibility of seawater in stratification is not an important factor for the dispersion relation of linear internal wave, at least for those three models, With the improved method, the wavefunction curves for the Pacific model had also been built.展开更多
This paper investigates a numerical and experimental study about buoyant wall turbulent jet in a static homogeneous environment. A light fluid of fresh water is injected horizontally and tangentially to a plane wall i...This paper investigates a numerical and experimental study about buoyant wall turbulent jet in a static homogeneous environment. A light fluid of fresh water is injected horizontally and tangentially to a plane wall into homogenous salt water ambient. This later is given with different values of salinity and the initial fractional density is small, so the applicability of the Boussinesq approximation is valid. Since the domain temperature is assumed to be constant, the density of the mixture is a function of the salt concentration only. Mathematical model is based on the finite volume method and reports on an application of standard k- ？ turbulence model for steady flow with densimetric Froude numbers of 1-75 and Reynolds numbers of 2 000-6 000. The basic features of the model are the conservation of mass, momentum and concentration. The boundaries of jet body, the radius and cling length are determined. It is found that the jet spreading and behavior depend on the ratio between initial buoyancy flux and momentum, i.e., initial Froude number, and on the influence of wall boundary which corresponds to Coanda effect. Laboratory experiments were conducted with photographic observations of jet trajectories and numerical results are described and compared with the experiments. A good agreement with numerical and experimental results has been achieved.展开更多
Considering the effect of horizontal Coriolis parameter and the density compactness of seawater, which were often neglected in internal waves discussion, the governing equation of linear internal waves presented by ve...Considering the effect of horizontal Coriolis parameter and the density compactness of seawater, which were often neglected in internal waves discussion, the governing equation of linear internal waves presented by vertical velocity only will be proposed. Under the assumption that the Brunt- Vaeisaelae frequency is exponential, an accurate analytic solution of it is obtained. Finally, the expressions of wave functions are also given.展开更多
The present study reveals the significance of the magnetic field or Lorentz force on the unsteady natural convection flow and heat transfer in the suddenly expanded cavity.The Lorentz force based magnetohydrodynamics(...The present study reveals the significance of the magnetic field or Lorentz force on the unsteady natural convection flow and heat transfer in the suddenly expanded cavity.The Lorentz force based magnetohydrodynamics(MHD)solver using electric potential formulation coupled with the energy equation by the means of Boussinesq approximation is developed in the open-source CFD tool OpenFOAM.The unsteady flow is generated by the buoyancy force keeping the Rayleigh number(Ra)at 109,at the fixed Prandtl number(Pr)of 0.71.The effects of the magnetic field on the flow and heat transfer are explained for various orientations of magnetic field(Bx,B45,and By)in terms of Hartmann number(Ha=0,50,100,300 and 500).The increase in the magnetic field increases the strength of the Lorentz force,which regulates the flow pattern and suppresses down the unsteady nature of flow and heat transfer into the steady-state.It is perceived that the average Nusselt number decreases as the intensity of Bx and B45 magnetic field increases.However,for By magnetic field the average Nusselt number increases up to Ha of 100 as compared to the non-MHD case(Ha=0).The distribution of Lorentz force in the domain plays a significant role in the governing of the fluid flow and heat transfer.展开更多
The two-layer fluid system and the continuous density system are based on two typical simplified stratification conditions to support the propagation of the internal solitary waves(ISWs).The aim of this study is to es...The two-layer fluid system and the continuous density system are based on two typical simplified stratification conditions to support the propagation of the internal solitary waves(ISWs).The aim of this study is to establish several extension methods of the classical ISW models across the stratification systems in an attempt to find a simple ISW structure that can propagate more stably,and to determine whether the stable ISW structure in the two typical stratification systems can be expressed in terms of a consistent nonlinear model.For the constructed ISW structures,the propagation stability has been investigated by taking the Euler equations as the evolution equations.The results show that the ISW structure constructed from the Miyata-Choi-Camassa(MCC)model undergoes two stages of instability and the re-stable ISW has a larger available potential energy and a smaller kinetic energy than the initialized condition.This illustrates the limitation of the weakly dispersive assumption in the MCC model.In contrast,the ISW structure constructed from the Dubreil-Jacotin-Long(DJL)model for the two-layer fluid system is generally stable,due to the fact that the Boussinesq approximation introduced in the derivation of the DJL model will be automatically satisfied in this system.The initial condition interpolated from the DJL model with a thin pycnocline thickness can be regarded as an appropriate ISW structure for the two-layer system and is even more stable than that initialized by the MCC model.In addition,the effect of the Boussinesq approximation is also included in the discussion.The approximation can be considered equivalent to a weakly dispersive assumption and should not be ignored for the ISW problem in the continuous density system.展开更多
By using two-dimensional dynamical equations in x-z plane with Boussinesq approximation,the effects of the second-order vertical shear of the basic flow ■ and the horizontal gradient of temperature (M) on the gravity...By using two-dimensional dynamical equations in x-z plane with Boussinesq approximation,the effects of the second-order vertical shear of the basic flow ■ and the horizontal gradient of temperature (M) on the gravity wave and the isolated gravity wave are discussed.The magnitudes of ■ and M corresponding to the linear and nonlinear stabilities of the gravity waves are worked out,respectively.The results show that amplitude and width of the isolated gravity wave are closely related to ■ and M.It is indicated that the isolated gravity wave with a width of about 10 km can be motivated by the disturbance of sub-synoptic scale in the certain ranges of flow field shear and temperature gra- dient,while the motivated waves may be associated with the cold surge ahead of a cold front and the other mesoscale synoptic systems.展开更多
文摘The convective heat transfer of hybrid nanoliquids within a concentric annulus has wide engineering applications such as chemical industries, solar collectors, gas turbines, heat exchangers, nuclear reactors, and electronic component cooling due to their high heat transport rate. Hence, in this study, the characteristics of the heat transport mechanism in an annulus filled with the Ag-MgO/H_2O hybrid nanoliquid under the influence of quadratic thermal radiation and quadratic convection are analyzed. The nonuniform heat source/sink and induced magnetic field mechanisms are used to govern the basic equations concerning the transport of the composite nanoliquid. The dependency of the Nusselt number on the effective parameters(thermal radiation, nonlinear convection,and temperature-dependent heat source/sink parameter) is examined through sensitivity analyses based on the response surface methodology(RSM) and the face-centered central composite design(CCD). The heat transport of the composite nanoliquid for the spacerelated heat source/sink is observed to be higher than that for the temperature-related heat source/sink. The mechanisms of quadratic convection and quadratic thermal radiation are favorable for the momentum of the nanoliquid. The heat transport rate is more sensitive towards quadratic thermal radiation.
文摘In many industrial applications,heat transfer and tangent hyperbolic fluid flow processes have been garnering increasing attention,owing to their immense importance in technology,engineering,and science.These processes are relevant for polymer solutions,porous industrial materials,ceramic processing,oil recovery,and fluid beds.The present tangent hyperbolic fluid flow and heat transfer model accurately predicts the shear-thinning phenomenon and describes the blood flow characteristics.Therefore,the entropy production analysis of a non-Newtonian tangent hyperbolic material flow through a vertical microchannel with a quadratic density temperature fluctuation(quadratic/nonlinear Boussinesq approximation)is performed in the present study.The impacts of the hydrodynamic flow and Newton’s thermal conditions on the flow,heat transfer,and entropy generation are analyzed.The governing nonlinear equations are solved with the spectral quasi-linearization method(SQLM).The obtained results are compared with those calculated with a finite element method and the bvp4c routine.In addition,the effects of key parameters on the velocity of the hyperbolic tangent material,the entropy generation,the temperature,and the Nusselt number are discussed.The entropy generation increases with the buoyancy force,the pressure gradient factor,the non-linear convection,and the Eckert number.The non-Newtonian fluid factor improves the magnitude of the velocity field.The power-law index of the hyperbolic fluid and the Weissenberg number are found to be favorable for increasing the temperature field.The buoyancy force caused by the nonlinear change in the fluid density versus temperature improves the thermal energy of the system.
基金Sponsored by the Fundamental Research Funds for the Central Universities(2010QS04)the National Science Foundation of China(11201475,11126160,11201185)Zhejiang Provincial Natural Science Foundation of China under Grant(LQ12A01013)
文摘The Boussinesq approximation finds more and more frequent use in geologi- cal practice. In this paper, the asymptotic behavior of solution for fractional Boussinesq approximation is studied. After obtaining some a priori estimates with the aid of eommu- tator estimate, we apply the Galerkin method to prove the existence of weak solution in the case of periodic domain. Meanwhile, the uniqueness is also obtained. Because the results obtained are independent of domain, the existence and uniqueness of the weak solution for Cauchy problem is also true. Finally, we use the Fourier splitting method to prove the decay of weak solution in three cases respectively.
基金the Deanship of Scientific Research at King Khalid University for funding this work through research groups program under Grant Number(R.G.P2/72/41).
文摘In this paper,the Galerkin finite element method(FEM)together with the characteristic-based split(CBS)scheme are applied to study the case of the non-linear Boussinesq approximation within sinusoidal heating inclined enclosures filled with a non-Darcy porous media and nanofluids.The enclosure has an inclination angle and its side-walls have varying sinusoidal temperature distributions.The working fluid is a nanofluid that is consisting of water as a based nanofluid and Al2O3 as nanoparticles.The porous medium is modeled using the Brinkman Forchheimer extended Darcy model.The obtained results are analyzed over wide ranges of the non-linear Boussinesq parameter 0≤ζ≤1,the phase deviation 00≤Φ≤1800,the inclination angle 00≤γ≤900,the nanoparticles volume fraction 0%≤φ≤4%,the amplitude ratio 0≤a≤1 and the Rayleigh number 104≤Ra≤106.The results revealed that the average Nusselt number is enhanced by 0.73%,26.46%and 35.42%at Ra=104,105 and 106,respectively,when the non-linearBoussinesq parameter is varied from 0 to 1.In addition,rate of heat transfer in the case of a non-uniformly heating is higher than that of a uniformly heating.Non-linear Boussinesq parameter rises the flow speed and heat transfer in an enclosure.Phase deviation makes clear changes on the isotherms and heat transfer rate on the right wall of an enclosure.An inclination angle varies the flow speed and it has a slight effect on heat transfer in an enclosure.
文摘The dynamics of absolute vorticity in the Boussinesq fluid is examined. It is shown that the Boussinesq approximation only captures one of the horizontal components of the solenoidal term. Based on scaling analysis of typical midlatitude synoptic systems, the horizontal component of the solenoidal term neglected by the Boussinesq approximation is at least of the same order of magnitude as the one captured by the Boussinesq approximation. This leads to severe underestimation of absolute vorticity and circulation.
基金the Knowledge Innovation Program of the Chinese Academy of Sciences (KZCX2-YW-201).
文摘With the horizontal Coriolis terms included in motion equations and the influence of compressibility of seawater on Brunt-Vaeisiaelae frequency considered, a numerical method of calculating the dispersion relation for linear internal waves, which is an improvement of Cai and Gan （1995）, and hence Fliegel and Hunkins （1975）, had been set up. For different models （Pacific model, Atlantic model and Arctic model）, simulations using the three different methods were compared and the following conclusions were reached： （1） the influence of horizontal Coriolis terms on dispersion relation cannot be neglected and is connected with the direction of the wave celerity, the latitude, and the modes of the wave （2） the effect of compressibility of seawater in stratification is not an important factor for the dispersion relation of linear internal wave, at least for those three models, With the improved method, the wavefunction curves for the Pacific model had also been built.
文摘This paper investigates a numerical and experimental study about buoyant wall turbulent jet in a static homogeneous environment. A light fluid of fresh water is injected horizontally and tangentially to a plane wall into homogenous salt water ambient. This later is given with different values of salinity and the initial fractional density is small, so the applicability of the Boussinesq approximation is valid. Since the domain temperature is assumed to be constant, the density of the mixture is a function of the salt concentration only. Mathematical model is based on the finite volume method and reports on an application of standard k- ？ turbulence model for steady flow with densimetric Froude numbers of 1-75 and Reynolds numbers of 2 000-6 000. The basic features of the model are the conservation of mass, momentum and concentration. The boundaries of jet body, the radius and cling length are determined. It is found that the jet spreading and behavior depend on the ratio between initial buoyancy flux and momentum, i.e., initial Froude number, and on the influence of wall boundary which corresponds to Coanda effect. Laboratory experiments were conducted with photographic observations of jet trajectories and numerical results are described and compared with the experiments. A good agreement with numerical and experimental results has been achieved.
文摘Considering the effect of horizontal Coriolis parameter and the density compactness of seawater, which were often neglected in internal waves discussion, the governing equation of linear internal waves presented by vertical velocity only will be proposed. Under the assumption that the Brunt- Vaeisaelae frequency is exponential, an accurate analytic solution of it is obtained. Finally, the expressions of wave functions are also given.
文摘The present study reveals the significance of the magnetic field or Lorentz force on the unsteady natural convection flow and heat transfer in the suddenly expanded cavity.The Lorentz force based magnetohydrodynamics(MHD)solver using electric potential formulation coupled with the energy equation by the means of Boussinesq approximation is developed in the open-source CFD tool OpenFOAM.The unsteady flow is generated by the buoyancy force keeping the Rayleigh number(Ra)at 109,at the fixed Prandtl number(Pr)of 0.71.The effects of the magnetic field on the flow and heat transfer are explained for various orientations of magnetic field(Bx,B45,and By)in terms of Hartmann number(Ha=0,50,100,300 and 500).The increase in the magnetic field increases the strength of the Lorentz force,which regulates the flow pattern and suppresses down the unsteady nature of flow and heat transfer into the steady-state.It is perceived that the average Nusselt number decreases as the intensity of Bx and B45 magnetic field increases.However,for By magnetic field the average Nusselt number increases up to Ha of 100 as compared to the non-MHD case(Ha=0).The distribution of Lorentz force in the domain plays a significant role in the governing of the fluid flow and heat transfer.
基金supported by the National Natural Science Foundation of China(Grant Nos.52231011,52071056)This work was supported by the Liaoning Revitalization Talents Program(XLYC2007109)+1 种基金Dalian Science and Technology Innovation Fund(Grant No.2020JJ25CY012)the Marine S&T Fund of Shandong Province for Pilot National Laboratory for Marine Science and Technology(Qingdao)(Grant No.2021QNLM020003-5).
文摘The two-layer fluid system and the continuous density system are based on two typical simplified stratification conditions to support the propagation of the internal solitary waves(ISWs).The aim of this study is to establish several extension methods of the classical ISW models across the stratification systems in an attempt to find a simple ISW structure that can propagate more stably,and to determine whether the stable ISW structure in the two typical stratification systems can be expressed in terms of a consistent nonlinear model.For the constructed ISW structures,the propagation stability has been investigated by taking the Euler equations as the evolution equations.The results show that the ISW structure constructed from the Miyata-Choi-Camassa(MCC)model undergoes two stages of instability and the re-stable ISW has a larger available potential energy and a smaller kinetic energy than the initialized condition.This illustrates the limitation of the weakly dispersive assumption in the MCC model.In contrast,the ISW structure constructed from the Dubreil-Jacotin-Long(DJL)model for the two-layer fluid system is generally stable,due to the fact that the Boussinesq approximation introduced in the derivation of the DJL model will be automatically satisfied in this system.The initial condition interpolated from the DJL model with a thin pycnocline thickness can be regarded as an appropriate ISW structure for the two-layer system and is even more stable than that initialized by the MCC model.In addition,the effect of the Boussinesq approximation is also included in the discussion.The approximation can be considered equivalent to a weakly dispersive assumption and should not be ignored for the ISW problem in the continuous density system.
文摘By using two-dimensional dynamical equations in x-z plane with Boussinesq approximation,the effects of the second-order vertical shear of the basic flow ■ and the horizontal gradient of temperature (M) on the gravity wave and the isolated gravity wave are discussed.The magnitudes of ■ and M corresponding to the linear and nonlinear stabilities of the gravity waves are worked out,respectively.The results show that amplitude and width of the isolated gravity wave are closely related to ■ and M.It is indicated that the isolated gravity wave with a width of about 10 km can be motivated by the disturbance of sub-synoptic scale in the certain ranges of flow field shear and temperature gra- dient,while the motivated waves may be associated with the cold surge ahead of a cold front and the other mesoscale synoptic systems.
