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Random Attractors of Stochastic non-newtonian fluids

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Acta Mathematicae Applicatae Sinica 2012年第1期28卷 165-180页

作者： Chun-xiao GUO Bo-ling GUO Yong-qian HAN Department of Mathematics China University of Mining and Technology BeijingBeijing 100083China Institute of Applied Physics and Computational Mathematics Beijing 100088China

The present paper investigates the asymptotic behavior of solutions for stochastic non-newtonian fluids in a two-dimensional domain. Firstly, we prove the existence of random attractors AH （w） in H; Secondly, we prove the existence of random attractors Ay（w） in V. Then we verify regularity of the random attractors by showing that AH（W） = Ay（w）, which implies the smoothing effect of the fluids in the sense that solution becomes eventually more regular than the initial data.

关键词： random attractors non-newtonian fluids additive noise Ornstein-Uhlenbeck process

Existence for a Class of non-newtonian fluids with a nonlocal Friction Boundary Condition

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Acta Mathematica Sinica,English Series 2006年第2期22卷 523-534页

作者： L.CONSIGLIERI Department of Mathematics and CMAF Sciences Faculty of University of Lisbon 1749-016 Lisboa Portugal

We deal with a variational inequality describing the motion of incompressible fluids, whose viscous stress tensors belong to the subdifferential of a functional at the point given by the symmetric part of the velocity gradient, with a nonlocal friction condition on a part of the boundary obtained by a generalized mollification of the stresses. We establish an existence result of a solution to the nonlocal friction problem for this class of non-newtonian flows. The result is based on the Faedo-Galerkin and Moreau Yosida methods, the duality theory of convex analysis and the Tychonov-Kakutani-Glicksberg fixed point theorem for multi-valued mappings in an appropriate functional space framework.

关键词： non-newtonian fluids Coulomb and nonlocal friction

Effects of impingement and friction of swirling air stream on prefilming airblast atomization of non-newtonian fluids

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Journal of Harbin Institute of Technology(New Series) 2007年第1期14卷 119-123页

作者：贺文智李光明姜兆华索全伶 School of Environmental Science and Engineering Tongji University Dept.of Applied Chemistry Harbin Institute of Technology Chemical Engineering School Inner Mongolia Polytechnic University

Liquids to be broken up using a prefilming airblast atomizer are usually Newton liquids with relatively low *** in some industrial processes,such as spray drying,liquids to be atomized are high concentration suspensions or non-newtonian fluids with high *** this paper,non-newtonian fluids with viscosity up to 4.4 Pa·s were effectively atomized using a specially designed prefilming airblast *** atomizer enabled liquid to extend to a thickness-adjustable film and forced the atomizing air stream to swirl with 30° or 45° through gas distributors with spiral *** liquid film was impinged by the swirling air stream resulting in the disintegration of the film into *** sizes were measured using a laser diffraction *** improved four-parameter mathematical model was established to relate the Sauter mean diameter of drops to the atomization conditions in terms of power dependencies on three dimensionless groups:Weber number,Ohnesorge number and air liquid mass *** friction on the surface of the liquid film made by swirling air stream played an important role in the prefilming atomization at the conditions of low air velocity and low liquid *** this case,the liquid film was disintegrated into drops according to the classical wavy-sheet mechanism,thus thinner liquid films and high swirl levels of the atomizing air produced smaller *** the increase of the air velocity and the liquid viscosity,the effect of the friction on the prefilming atomization relatively weakened,whereas the impingement on the liquid film made by atomizing air stream in a direction normal to the liquid film and corresponding momentum transfer gradually strengthened and eventually dominated the disruption of liquid into drops,which induced that the initial thickness of the liquid film and the swirl of atomizing air stream exercised a minor influence on the drop sizes.

关键词： atomization prefilming atomizer non-newtonian fluids impingement friction momentum transfer

Mixed convection in the heated semi-circular lid-driven cavity for non-newtonian power-law fluids: Effect of presence and shape of the block

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Chinese Journal of Chemical Engineering 2020年第5期28卷 1225-1240页

作者： Krunal M.Gangawane Hakan F.Oztop Department of Chemical Engineering National Institute of Technology RourkelaRourkela 769008OdishaIndia Department of Mechanical Engineering Engineering FacultyFirat UniversityElazig TR-23119Turkey

The present work delineates the hydrodynamics and thermal characteristics due to mixed convection in the liddriven semi-circular cavity affected by the presence of the adiabatic block at its geometric center for twodimensional,steady-state,laminar and for non-newtonian power-law *** semi-circular cavity has a diameter of *** horizontal wall/lid is sliding with a uniform horizontal velocity(u=U)and is subjugated to the ambient thermal condition;while the curved surface is subjugated to a higher isothermal *** convective characteristics inside the system is explored for the broad range of Richardson number(0.1≤Ri≤10),Prandtl number(1≤Pr≤100)and non-newtonian power-law index(0.5≤n≤1.5)at a constant Grashof number of 10~*** from this,the effect of shape(cross-section)of the inserted block,i.e.,circular,square and triangular on heat transfer characteristics has also been *** is observed that the shear thickening fluids display better cooling ***,the cavity with immersed triangular block shows better heat transfer results than the circular and square *** deviations observed in the flow and heat transfer characteristics in the cavity by inserting an adiabatic block as compared with cavity without block have been ascertained by calculating normalized Nusselt number(Nu^N).The presence of the block was found to have a diminishing effect on the heat transfer due to convection in the *** the end,the results of the study are summarized in the form of a predictive correlation exhibiting the functional dependence of average Nusselt number with Prandtl number,power-law index,and Richardson number.

关键词： Heat transfer enhancement Semi-circular cavity Adiabatic block non-newtonian fluids

Fully Developed Convective Heat Transfer of Power Law fluids in a Circular Tube

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Chinese Physics Letters 2008年第1期25卷 195-197页

作者：郑连存张欣欣马连喜 Department of Mathematics and Mechanics University of Science and Technology Beijing Beijing 100083 School of Mechanical Engineering University of Science and Technology Beijing Beijing 100083 Department of Physics Texas A & M University College Station Texas 77843-4242 USA

We present a theoretical analysis for fully developed convective beat transfer in a circular tube for power law fluids by assuming that the thermal diffusivity is a function of temperature gradient. The analytical eolution is obtained and the heat transfer behaviour is investigated under a constant heat flux boundary condition. It is shown that the Nusselt number strongly depends on the value of power law index n. The Nusselt number sharply decreases in the range of 0 〈 n 〈 0.1. However, for n 〉 0.5, the Nusselt number decreases monotonically with the increasing n, and for n 〉 20, the values of Nusselt number approach a constant.

关键词： non-newtonian fluids CONTINUOUS MOVING SURFACE BOUNDARY-VALUE PROBLEM MIXED CONVECTION PSEUDOPLASTIC fluids VERTICAL PLATE LAYER-FLOW MOMENTUM INJECTION WALL

On the Regularity of Shear Thickening Viscous fluids

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Chinese Annals of Mathematics,Series B 2009年第3期30卷 273-280页

作者： Francesca CRISPO Dipartimento di Matematica Applicata "U.Dini" Università di PisaVia Buonarroti 1/c56127 PisaItaly.

The aim of this note is to improve the regularity results obtained by H. Beirao da Veiga in 2008 for a class of p-fluid flows in a cubic domain. The key idea is exploiting the better regularity of solutions in the tan... 详细信息

关键词： non-newtonian fluids Shear dependent viscosity Boundary regularity

Shallow water equations for power law and Bingham fluids Dedicated to the NSFC-CNRS Chinese-French summer institute on fluid mechanics in 2010

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Science China Mathematics 2012年第2期55卷 277-283页

作者： FERNANDEZ-NIETO Enrique D. NOBLE Pascal VILA Jean-Paul Departamento de Matemdtica Aplicada I Universidad de Sevilla 41012 Sevilla Spain Universite de Lyon Universitd Lyon1 Institut Camille Jordan UMR CNRS 520843 blvd du 11 novembre 1918 F-69622 ViUeurbanne Cedex France Institut de Mathdmatiques de Toulouse UMR CNRS 5219 INSA de Toulouse 135 avenue de Rangueil 31077 Toulouse Cedex 4 France

In this note, we provide a consistant thin layer theory for power law and Bingham incompressible fluids flowing down an inclined plane under the effect of gravity. The derivation of such equations is based on formal asymptotic expansions of solutions of Cauchy momentum equations in the shallow water scaling and in the neighbourhood of steady solutions so that we can close the average equations on the fluid height h and the total discharge rate q.

关键词： shallow water equations asymptotic analysis non-newtonian fluids

Uniqueness results for monopolar fluids

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Communications in nonlinear Science and Numerical Simulation 2000年第1期5卷 21-23页

作者： Guoguang LIN Department of Mathematics, Yunnan University, Kunming 650091, China, e-mail: gglin@ynu. edu. cn Department of Mathematics Yunnan University Kunming 650091 China

We prove a unique property for weak solutions of monopolar fluid equations.

关键词： monopolar fluid equations non-newtonian fluids uniqueness of weak solutions

Coupled MRT Lattice Boltzmann Study of Electrokinetic Mixing of Power-Law fluids in Microchannels with Heterogeneous Surface Potential

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Advances in Applied Mathematics and Mechanics 2018年第6期10卷 1478-1496页

作者： Xuguang Yang Lei Wang Baochang Shi School of Mathematics and Computational Science Hunan First Normal UniversityChangsha 410205HunanChina Department of Applied Mathematics The Hong Kong Polytechnic UniversityHung HomHong Kong School of Mathematics and Physics China University of GeosciencesWuhan430074HubeiChina School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074HubeiChina

The electrokinetic mixing,as a powerful technique in microfluidic devices,is widely used in many *** this study,a more general dynamic model,which consists of Poisson equation,Nernst-Planck equation and Navier-Stokes equations,is used to describe the electrokinetic mixing of non-newtonian fluids in ***,a coupled multiple-relaxation-time(MRT)lattice Boltzmann(LB)framework is developed to solve this complicated multi-physics transport *** numerical simulations,we mainly consider the effects of the arrangement of nonuniform surface potentials and the power-law index on the mixing efficiency and the volumetric flow *** results show that the mixing efficiency and the volumetric flow rate of shear-thinning fluids are higher than that of shear-thickening fluids under the same *** is also shown that for both types of fluids,there should be a balance between the mixing and liquid transport in electrokinetic microfluidics.

关键词： Lattice Boltzmann method electrokinetic mixing non-newtonian fluids