This paper proves a new regularity criterion ω: = rotu∈L1(0,T;B·0∞,∞) for the 3D generalized MHD system with fractional diffusion terms(-Δ)αu with α >9/8 and zero magnetic diffusivity. Here u is the flu...This paper proves a new regularity criterion ω: = rotu∈L1(0,T;B·0∞,∞) for the 3D generalized MHD system with fractional diffusion terms(-Δ)αu with α >9/8 and zero magnetic diffusivity. Here u is the fluid velocity,ω is the vorticity and B·0∞,∞is the homogeneous Besov space.展开更多
In this paper, firstly, some priori estimates are obtained for the existence and uniqueness of solu-tions of a two dimensional generalized magnetohydrodynamic (MHD) system. Then the existence of the global attractor i...In this paper, firstly, some priori estimates are obtained for the existence and uniqueness of solu-tions of a two dimensional generalized magnetohydrodynamic (MHD) system. Then the existence of the global attractor is proved. Finally, the upper bound estimation of the Hausdorff and fractal dimension of attractor is got.展开更多
In this paper, we study the global regularity of the classical solution of the 2D incompressible magnetohydrodynamic equation with vertical dissipation and vertical magnetic dissipation. We show that any solution of t...In this paper, we study the global regularity of the classical solution of the 2D incompressible magnetohydrodynamic equation with vertical dissipation and vertical magnetic dissipation. We show that any solution of the second component (u2, b2) has a global L2r -bound, where r satisfies and the boundary does not grow faster than??as r increases.展开更多
In this paper,the authors study the global regularity of the 3D magnetohydrodynamics system in terms of one velocity component.In particular,they establish a new Prodi-Serrin type regularity criterion in the framework...In this paper,the authors study the global regularity of the 3D magnetohydrodynamics system in terms of one velocity component.In particular,they establish a new Prodi-Serrin type regularity criterion in the framework of weak Lebesgue spaces both in time and space variables.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
In this paper,we study the three-dimensional regularized MHD equations with fractional Laplacians in the dissipative and diffusive terms.We establish the global existence of mild solutions to this system with small in...In this paper,we study the three-dimensional regularized MHD equations with fractional Laplacians in the dissipative and diffusive terms.We establish the global existence of mild solutions to this system with small initial data.In addition,we also obtain the Gevrey class regularity and the temporal decay rate of the solution.展开更多
A toroidal soft x-ray imaging(T-SXRI)system has been developed to investigate threedimensional(3D)plasma physics on J-TEXT.This T-SXRI system consists of three sets of SXR arrays.Two sets are newly developed and locat...A toroidal soft x-ray imaging(T-SXRI)system has been developed to investigate threedimensional(3D)plasma physics on J-TEXT.This T-SXRI system consists of three sets of SXR arrays.Two sets are newly developed and located on the vacuum chamber wall at toroidal positionsφof 126.4°and 272.6°,respectively,while one set was established previously atφ=65.50.Each set of SXR arrays consists of three arrays viewing the plasma poloidally,and hence can be used separately to obtain SXR images via the tomographic method.The sawtooth precursor oscillations are measured by T-SXRI,and the corresponding images of perturbative SXR signals are successfully reconstructed at these three toroidal positions,hence providing measurement of the 3D structure of precursor oscillations.The observed 3D structure is consistent with the helical structure of the m/n=1/1 mode.The experimental observation confirms that the T-SXRI system is able to observe 3D structures in the J-TEXT plasma.展开更多
Microwave reflectometry is a powerful diagnostic that can measure the density profile and localized turbulence with high spatial and temporal resolution and will be used in ITER,so understanding the influence of plasm...Microwave reflectometry is a powerful diagnostic that can measure the density profile and localized turbulence with high spatial and temporal resolution and will be used in ITER,so understanding the influence of plasma perturbations on the reflect signal is important.The characteristics of the reflect signal from profile reflectometry,the time-of-flight(TOF)signal associated with the MHD instabilities,are investigated in EAST.Using a 1D full-wave simulation code by the Finite-DifferenceTime-Domain(FDTD)method,it is well validated that the local density flattening could induce the discontinuity of the simulated TOF signal and an obvious change of reflect amplitude.Experimental TOF signals under different types of MHD instabilities(sawtooth,sawtooth precursors and tearing mode)are studied in detail and show agreement with the simulation.Two new improved algorithms for detecting and localizing the radial positions of the low-order rational surface,the cross-correlation and gradient threshold(CGT)method and the 2D convolutional neural network approach(CNN)are presented for the first time.It is concluded that TOF signal analysis from profile reflectometry can provide a straightforward and localized measurement of the plasma perturbation from the edge to the core simultaneously and may be a complement or correction to the q-profile control,which will be beneficial for the advanced tokamak operation.展开更多
In this paper,we construct a high-order discontinuous Galerkin(DG)method which can preserve the positivity of the density and the pressure for the viscous and resistive magnetohydrodynamics(VRMHD).To control the diver...In this paper,we construct a high-order discontinuous Galerkin(DG)method which can preserve the positivity of the density and the pressure for the viscous and resistive magnetohydrodynamics(VRMHD).To control the divergence error in the magnetic field,both the local divergence-free basis and the Godunov source term would be employed for the multi-dimensional VRMHD.Rigorous theoretical analyses are presented for one-dimensional and multi-dimensional DG schemes,respectively,showing that the scheme can maintain the positivity-preserving(PP)property under some CFL conditions when combined with the strong-stability-preserving time discretization.Then,general frameworks are established to construct the PP limiter for arbitrary order of accuracy DG schemes.Numerical tests demonstrate the effectiveness of the proposed schemes.展开更多
Hybrid nanofluids are remarkable functioning liquids that are intended to reduce the energy loss while maximizing the heat transmission.In the involvement of suction and nonlinear thermal radiation effects,this study ...Hybrid nanofluids are remarkable functioning liquids that are intended to reduce the energy loss while maximizing the heat transmission.In the involvement of suction and nonlinear thermal radiation effects,this study attempted to explore the energy transmission features of the inclined magnetohydrodynamic(MHD)stagnation flow of CNTs-hybrid nanofluid across the nonlinear permeable stretching or shrinking sheet.This work also included some noteworthy features like chemical reactions,variable molecular diffusivity,quadratic convection,viscous dissipation,velocity slip and heat omission assessment.Employing appropriate similarity components,the model equations were modified to ODEs and computed by using the HAM technique.The impact of various relevant flow characteristics on movement,heat and concentration profiles was investigated and plotted on a graph.Considering various model factors,the significance of drag friction,heat and mass transfer rate were also computed in tabular and graphical form.This leads to the conclusion that such factors have a considerable impact on the dynamics of fluid as well as other engineering measurements of interest.Furthermore,viscous forces are dominated by increasing the values ofλ_(p),δ_(m)andδ_(q),and as a result,F(ξ)accelerates while the opposite trend is observed for M andφ.The drag friction is boosted by the augmentation M,λ_(p)andφ,but the rate of heat transfer declined.According to our findings,hybrid nanoliquid effects dominate that of ordinary nanofluid in terms of F(ξ),Θ(ξ)andφ(ξ)profiles.The HAM and the numerical technique(shooting method)were found to be in good agreement.展开更多
A numerical calculation of a 3000MWt MHD steam combined cycle system with tail gasification is described . The research scheme has been set up and the parameters of this system have been designed. Then the efficiency ...A numerical calculation of a 3000MWt MHD steam combined cycle system with tail gasification is described . The research scheme has been set up and the parameters of this system have been designed. Then the efficiency of the combined cycle system has been calculated which is up to 53.9%.展开更多
In this study,a radiative MHD stagnation point flow over a nonlinear stretching sheet incorporating thermophoresis and Brownian motion is considered.Using a similarity method to reshape the underlying Partial differen...In this study,a radiative MHD stagnation point flow over a nonlinear stretching sheet incorporating thermophoresis and Brownian motion is considered.Using a similarity method to reshape the underlying Partial differential equations into a set of ordinary differential equations(ODEs),the implications of heat generation,and chemical reaction on the flow field are described in detail.Moreover a Homotopy analysis method(HAM)is used to interpret the related mechanisms.It is found that an increase in the magnetic and velocity exponent parameters can damp the fluid velocity,while thermophoresis and Brownian motion promote specific thermal effects.The results also demonstrate that as the Brownian motion parameter is increased,the concentration values become smaller.展开更多
文摘This paper proves a new regularity criterion ω: = rotu∈L1(0,T;B·0∞,∞) for the 3D generalized MHD system with fractional diffusion terms(-Δ)αu with α >9/8 and zero magnetic diffusivity. Here u is the fluid velocity,ω is the vorticity and B·0∞,∞is the homogeneous Besov space.
文摘In this paper, firstly, some priori estimates are obtained for the existence and uniqueness of solu-tions of a two dimensional generalized magnetohydrodynamic (MHD) system. Then the existence of the global attractor is proved. Finally, the upper bound estimation of the Hausdorff and fractal dimension of attractor is got.
文摘In this paper, we study the global regularity of the classical solution of the 2D incompressible magnetohydrodynamic equation with vertical dissipation and vertical magnetic dissipation. We show that any solution of the second component (u2, b2) has a global L2r -bound, where r satisfies and the boundary does not grow faster than??as r increases.
基金supported by Zhejiang Province Science fund(No.LY21A010009)。
文摘In this paper,the authors study the global regularity of the 3D magnetohydrodynamics system in terms of one velocity component.In particular,they establish a new Prodi-Serrin type regularity criterion in the framework of weak Lebesgue spaces both in time and space variables.
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.
基金supported by the Opening Project of Guangdong Province Key Laboratory of Cyber-Physical System(20168030301008)supported by the National Natural Science Foundation of China(11126266)+4 种基金the Natural Science Foundation of Guangdong Province(2016A030313390)the Quality Engineering Project of Guangdong Province(SCAU-2021-69)the SCAU Fund for High-level University Buildingsupported by the National Key Research and Development Program of China(2020YFA0712500)the National Natural Science Foundation of China(11971496,12126609)。
文摘In this paper,we study the three-dimensional regularized MHD equations with fractional Laplacians in the dissipative and diffusive terms.We establish the global existence of mild solutions to this system with small initial data.In addition,we also obtain the Gevrey class regularity and the temporal decay rate of the solution.
基金supported by the National Magnetic Confinement Fusion Energy R&D Program of China(Nos.2018YFE0309100 and 2019YFE03010004)National Natural Science Foundation of China(No.51821005)。
文摘A toroidal soft x-ray imaging(T-SXRI)system has been developed to investigate threedimensional(3D)plasma physics on J-TEXT.This T-SXRI system consists of three sets of SXR arrays.Two sets are newly developed and located on the vacuum chamber wall at toroidal positionsφof 126.4°and 272.6°,respectively,while one set was established previously atφ=65.50.Each set of SXR arrays consists of three arrays viewing the plasma poloidally,and hence can be used separately to obtain SXR images via the tomographic method.The sawtooth precursor oscillations are measured by T-SXRI,and the corresponding images of perturbative SXR signals are successfully reconstructed at these three toroidal positions,hence providing measurement of the 3D structure of precursor oscillations.The observed 3D structure is consistent with the helical structure of the m/n=1/1 mode.The experimental observation confirms that the T-SXRI system is able to observe 3D structures in the J-TEXT plasma.
基金supported by the Open Fund of Magnetic Confinement Laboratory of Anhui Province(No.2023 AMF03005)the China Postdoctoral Science Foundation(No.2021M703256)+4 种基金the Director Funding of Hefei Institutes of Physical Science,Chinese Academy of Sciences(No.YZJJ2022QN16)the National Key R&D Program of China(Nos.2022YFE03050003,2019YFE03080200,2019Y FE03040002,and 2022YFE03070004)National Natural Science Foundation of China(Nos.12075284,12175277,12275315 and 12275311)the National Magnetic Confinement Fusion Science Program of China(No.2022YFE03040001)the Science Foundation of the Institute of Plasma Physics,Chinese Academy of Sciences(No.DSJJ-2021-08)。
文摘Microwave reflectometry is a powerful diagnostic that can measure the density profile and localized turbulence with high spatial and temporal resolution and will be used in ITER,so understanding the influence of plasma perturbations on the reflect signal is important.The characteristics of the reflect signal from profile reflectometry,the time-of-flight(TOF)signal associated with the MHD instabilities,are investigated in EAST.Using a 1D full-wave simulation code by the Finite-DifferenceTime-Domain(FDTD)method,it is well validated that the local density flattening could induce the discontinuity of the simulated TOF signal and an obvious change of reflect amplitude.Experimental TOF signals under different types of MHD instabilities(sawtooth,sawtooth precursors and tearing mode)are studied in detail and show agreement with the simulation.Two new improved algorithms for detecting and localizing the radial positions of the low-order rational surface,the cross-correlation and gradient threshold(CGT)method and the 2D convolutional neural network approach(CNN)are presented for the first time.It is concluded that TOF signal analysis from profile reflectometry can provide a straightforward and localized measurement of the plasma perturbation from the edge to the core simultaneously and may be a complement or correction to the q-profile control,which will be beneficial for the advanced tokamak operation.
基金supported by the NSFC Grant 11901555,12271499the Cyrus Tang Foundationsupported by the NSFC Grant 11871448 and 12126604.
文摘In this paper,we construct a high-order discontinuous Galerkin(DG)method which can preserve the positivity of the density and the pressure for the viscous and resistive magnetohydrodynamics(VRMHD).To control the divergence error in the magnetic field,both the local divergence-free basis and the Godunov source term would be employed for the multi-dimensional VRMHD.Rigorous theoretical analyses are presented for one-dimensional and multi-dimensional DG schemes,respectively,showing that the scheme can maintain the positivity-preserving(PP)property under some CFL conditions when combined with the strong-stability-preserving time discretization.Then,general frameworks are established to construct the PP limiter for arbitrary order of accuracy DG schemes.Numerical tests demonstrate the effectiveness of the proposed schemes.
基金funded by King Mongkut’s University of Technology North Bangkok with Contract no.KMUTNB-Post-65-07。
文摘Hybrid nanofluids are remarkable functioning liquids that are intended to reduce the energy loss while maximizing the heat transmission.In the involvement of suction and nonlinear thermal radiation effects,this study attempted to explore the energy transmission features of the inclined magnetohydrodynamic(MHD)stagnation flow of CNTs-hybrid nanofluid across the nonlinear permeable stretching or shrinking sheet.This work also included some noteworthy features like chemical reactions,variable molecular diffusivity,quadratic convection,viscous dissipation,velocity slip and heat omission assessment.Employing appropriate similarity components,the model equations were modified to ODEs and computed by using the HAM technique.The impact of various relevant flow characteristics on movement,heat and concentration profiles was investigated and plotted on a graph.Considering various model factors,the significance of drag friction,heat and mass transfer rate were also computed in tabular and graphical form.This leads to the conclusion that such factors have a considerable impact on the dynamics of fluid as well as other engineering measurements of interest.Furthermore,viscous forces are dominated by increasing the values ofλ_(p),δ_(m)andδ_(q),and as a result,F(ξ)accelerates while the opposite trend is observed for M andφ.The drag friction is boosted by the augmentation M,λ_(p)andφ,but the rate of heat transfer declined.According to our findings,hybrid nanoliquid effects dominate that of ordinary nanofluid in terms of F(ξ),Θ(ξ)andφ(ξ)profiles.The HAM and the numerical technique(shooting method)were found to be in good agreement.
文摘A numerical calculation of a 3000MWt MHD steam combined cycle system with tail gasification is described . The research scheme has been set up and the parameters of this system have been designed. Then the efficiency of the combined cycle system has been calculated which is up to 53.9%.
文摘In this study,a radiative MHD stagnation point flow over a nonlinear stretching sheet incorporating thermophoresis and Brownian motion is considered.Using a similarity method to reshape the underlying Partial differential equations into a set of ordinary differential equations(ODEs),the implications of heat generation,and chemical reaction on the flow field are described in detail.Moreover a Homotopy analysis method(HAM)is used to interpret the related mechanisms.It is found that an increase in the magnetic and velocity exponent parameters can damp the fluid velocity,while thermophoresis and Brownian motion promote specific thermal effects.The results also demonstrate that as the Brownian motion parameter is increased,the concentration values become smaller.
