• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

    Influence of Non-linear Radiation Heat Flux on Rotating Maxwell Fluid over a Deformable Surface:A Numerical Study

    2018-05-02 01:51:49MustafaMushtaqHayatandAlsaedi
    Communications in Theoretical Physics 2018年4期

    M.Mustafa,A.Mushtaq,T.Hayat,and A.Alsaedi

    1School of Natural Sciences(SNS),National University of Sciences and Technology(NUST),Islamabad 44000,Pakistan

    2Research Centre for Modeling and Simulation(RCMS),National University of Sciences and Technology(NUST),Islamabad 44000,Pakistan

    3Department of Mathematics,Quaid-I-Azam University 45320,Islamabad 44000,Pakistan

    4Department of Mathematics,Faculty of Science,King Abdulaziz University,P.O.Box 80257,Jeddah 21589,Saudi Arabia

    1 Introduction

    Fluid flow problems in rotating frame have been proven fascinating as well as challenging and these are met in numerous engineering applications such as rotor-stator systems,atmospheric and oceanic circulations,rotatingdisk systems,transport engineering(automobile breaks),geothermal extraction and many others.Viscous flow in rotating frame developed by linearly stretched plate was firstly explored by Wang.[1]He derived series solutions for velocity pro files by using perturbation in rotation-strength parameter.Rajeswari and Nath[2]examined time dependent flow past a stretchable surface in a revolving fluid.Nazar et al.[3]provided numerical approximations for unsteady flow over an impulsively stretched plate in rotatingfluid using Keller-box method.They also derived asymptotic solutions valid from large time,which were shown to be consistent with the numerical findings.Boundary layer flow of Ostwald-de-Waele(power-law)fluid in rotating frame was addressed by Kumari et al.[4]for broad range of power-law index.An analytical study for rotating flow of an electrically conducting second grade fluid past a porous shrinking sheet was presented by Hayat et al.[5]Abbas et al.[6]addressed the unsteadiness in revolving flow bounded by a stretchable wall using Keller-box method.Javed et al.[7]numerically explored the revolvingflow by an exponentially stretching sheet considering space dependent angular velocity in rotating frame.Later,Zaimi et al.[8]studied t?h′eflow induced by stretching surface in rotating Walters?aAZB liquid using a numerical scheme.Khan et al.[9]reported numerical simulations for nanofluidflow by a deformable surface in rotating frame considering two different thermal conductivity models.Recently,Mustafa et al.[10]described rotational effects on the laminar flow of Fe3O4-water ferrofluid caused by stretchable surface.In another recent article,exponentially stretchedflow of Maxwell fluid in rotating frame was modeled by Mustafa et al.[11]

    Fluids which deform non-linearly upon the application of shearing forces are frequently encountered in industrial processes.Non-Newtonian behavior manifests itself in a number of ways.Shear-thinning/thickening effect is an interesting characteristic which is frequent amongst fluids such as blood,paints,polymers,colloidal solutions etc.Power-law model is a generalized Newtonian fluid model that has been widely applied for description of shearthinning or shear-thickening phenomenon. Some well-documented boundary layer problems concerning powerlaw fluids can be stated through the studies.[12?14]Another important property of non-Newtonian liquids is the retention of fading memory upon the elimination of shearing force known as fluid elasticity.Viscoelastic behavior refers to the situation in which motion of the material element not only depends on the current stress state but also on the deformation history of the element. Suchfluids display significant deviation from the Newtonian limit in terms of both physical behavior and computational complexity.Upper-convected Maxwell model is a viscoelastic fluid model that has been consistently used by the researchers due to its simplicity.Harris[15]presented the boundary layer equations for two-dimensionalflow of upper-convected Maxwell fluid.Sadeghy et al.[16]used these equations to explore Maxwell fluid flow driven by a moving rigid plate in stationary fluid.They employed numerical and perturbation approaches to determine the velocity distribution above the plate.Finite difference approach was found to be effective here in comparison to the other employed methods as it solved the problem for Deborah number as large as 2.4.Kumari and Nath[17]analyzed the Maxwell fluid flow in a region of stagnationpoint utilizing finite difference method.It was found that viscoelastic fluid parameter gives resistance to momentum transport phenomenon.Abel et al.[18]discussed the stretched flow of viscoelastic Maxwell fluid in the existence of Lorentz force.Hayat et al.[19]analytically explored the Maxwell fluid flow in the vicinity of stagnation-point with melting effects.Shateyi[20]proposed a numerical approach for tackling the Maxwell fluid flow with mixed convection and chemical reaction.Recent material in this direction can be stated through Refs.[21–30].

    The objective of this paper is to investigate non-linear radiative heat transfer over a deformable surface placed in revolving Maxwell fluid.In many papers,the authors made use of linearized Rosseland formula to attain a linear energy equation,which brings no additional computational effort(see,for example Refs.[31–33]).Here the inclusion of non-linear flux provides strongly non-linear system,which enables one to determine the features of small/large temperature differences(see Refs.[34–37]for details).Accurate similar solutions are found for broad range of embedded parameters.Emphasis has given to the effects of viscoelasticity,rotating frame and radiative heat transfer on the solutions.

    2 Problem Formulation

    Consider a laminar flow above a stretchable surface placed in a rotating viscoelastic fluid obeying upperconvected Maxwell model.The surface lying in the plane z=0 is stretched with velocity uw=ax in which a>0 denotes the stretching rate and x stands for the distance measured from the origin.Fluid rotates about the vertical axis with uniform angular velocity ω(see Fig.1).We take into account the non-linear Rosseland formula for thermal radiation.The surface temperature Twis assumed to be greater than the ambient fluid temperature T∞.Under these assumptions,conservation equations for Maxwell fluid flow and heat transfer in rotating frame are:

    Fig.1 Physical con figuration and coordinate system.

    where ρ represents fluid density,cpdenotes the specific heat of fluid,k stands for thermal conductivity,? = [0,0,ω]the angular velocity vector and qr=?(4/3aR)grad(eb)is the heat flux due to radiation in which aR[m?1]represents the mean absorption coefficient and eb[W·m?2]the black body emissive power,which is related with the absolute temperature T by the Stefan-Boltzmann law as eb= σ?T4,with σ?=5.7 × 10?5W ·m?2·K?4as Stefan-Boltzmann constant.In Eq.(2),the term(2?×V)is due to the coriolis acceleration while the expression(? × (? × r))= ??(ω2r2/2)embodies centrifugal acceleration,which balances with the pressure gradient??p.The extra stress tensor S in Maxwell fluid obeys the following relation:

    in which λ1is the fluid relaxation time,A1=(?V)+(?V)tthe first Rivlin-Ericksen tensor and D/Dt the upper-convected time derivative.Thus,component forms of Eqs.(1)–(3)under usual boundary layer approximations are given below:

    The boundary conditions in the present problem are as below:

    Introducing the following dimensionless variables

    Equation(5)is identically satis fied and Eqs.(6)–(9)become

    with transformed boundary conditions

    in which λ = ω/a is rotation-strength parameter,β = λ1a denotes the Deborah number,Pr= ν/α represents the Prandlt number,Rd=16σ?T3∞/3kaRstands for thermal radiation parameter and θw=Tw/T∞measures wall to ambient temperature ratio.When λ=0,the differential system(11)–(14)correspond to the case of non-rotating frame as discussed by Mushtaq et al.[18]Further,the case of Newtonian fluid is achieved by setting β=0. As pointed out in Ref.[29],present model reduces to linear radiation case when Rd is sufficiently small and θwapproaches unity.We define the local Nusselt number Nuxwith an aid of Fourier law as follows:

    where qwis the wall heat flux at the surface due to both convection and radiation effects.It is given by:

    Now using(16)in Eq.(15)and then invoking the transformations Eq.(10),we get

    where Rex=uwx/ν is the local Reynolds number.

    3 Numerical Results and Discussion

    We employ the standard shooting technique to treat the coupled non-linear differential system comprising of Eqs.(11)–(14)numerically.The values of missing slopes f′′(0),g′(0),and θ|prime(0)are iteratively estimated through Newton-Raphson method.The validity of numerical scheme is ascertained by comparing the values of f′′(0)and g′(0)with those of already published papers in viscous fluid case(see Table 1).Table 1 shows that current computations almost match exactly with the results of previous studies at all values of rotation-strength parameter λ.Computational results of local Nusselt number Re?1/2xNux,which is related with the heat flux from the surface,are obtained for different values of λ,θwand β in Table 2.It is clear that the wall heat flux is reduced due to the inclusion of viscoelastic effects.We also observe a significant growth in heat transfer coefficient as the difference(Tw?T∞)enlarges.Moreover,like the viscoelasticity,fluid rotation also adversely affects the heat transfer from the plate.

    The curve of f′related with the u-velocity component is computed for a variety of Deborah numbers in Fig.2.By definition,Deborah number signifies the ratio of fluid memory duration(relaxation time)to its characteristic time scale.It is encouraging that computational treatment proposed in this work can furnish convergent results up to Deborah number 1.8.It is evident that curve f′begins from unity at η =0 and tends to zero as η → ∞.Another noticeable behavior is that the velocity u approaches to zero at smaller distance from the sheet when β becomes large.In other words,hydrodynamic boundary layer shrinks as the stress relaxation duration enlarges.This result is consistent with the findings of previously published articles(see Abel et al.,[18]Shateyi,[20]Hsiao[21]etc.for details).In accordance with Ref.[21],an increasing trend in surface velocity gradient f′′(0)is apparent for growing values of Deborah number β.This follows from the fact that increasing values of parameter β implies slower recovery process,which in turn slows down the development of boundary layer.

    Figure 3 predicts the influence of rotation-strength parameter λ on the function f′.The parameter λ compares the rotation and stretching rates.It is realized that velocity field f′decreases exponentially with an increase in η in non-monotonic fashion when larger values of λ are employed.More precisely,we observe oscillatory pro file of f′for large value of λ.Further,the pro files shift towards the stretching boundary when λ enlarges indicating that boundary layer thickness is reduced due to the consideration of rotating frame.

    In Fig.4,velocity pro file is plotted at different values of Deborah number β for a specified value of rotationstrength parameter λ.The velocity component g(η)is non-zero and it has a negative value signaling that fluidflows in negative y-direction only.This outcome is anticipated due to the inclusion of rotational effect.It is also clear that function g(η)has an oscillatory decaying pro file for any non-zero value of λ.The envelope of oscillations grows further as the angular velocity is enhanced.A cross over is apparent in the pro files of g(η)illustrating that velocity in y-direction increases near the wall and decreases far from the wall as parameter β enlarges.This outcome is different from the effect of viscoelastic parameter of second grade fluid.

    In Fig.5,the change in velocity pro file g(η)with the variation in λ is observed.This figure shows that the function g(η)has pro file analogous to the function ?ηexp(?η)for smaller values of λ while it decays oscillatory when larger values of λ are considered.This outcome has also be noticed by Nazar et al.[3]and Zaimi et al.[8]

    Table 1 Comparison of results for f′′(0)and g′(0)with those of Wang[1]and Zaimi et al.[8]for various values of λ when β =0.

    Table 2 Computational results of local Nusselt number Nur= ?[1+Rdθ3w]θ′(0)for different values of λ, β,and θwwhen Rd=0.5 and Pr=7.

    Fig.2 Curves of velocity field f′(η)for different values of β.

    Fig.3 Curves of velocity field f ′(η)for different values of λ.

    Fig.4 Curves of velocity field g(η)for different values of β.

    Fig.5 Curves of velocity field g(η)for different values of λ.

    Fig.6 Pro files of temperature θ(η)for different values of λ.

    Fig.7 Pro files of temperature θ(η)for different values of β.

    Figure 6 portrays temperature pro file θ at various values of rotation-strength parameter λ.There is a significant rise in temperature θ when rotation-strength parameter is varied from λ =0 to λ =10.The resistance to the fluid motion o ff ered by the rotating frame enhances the temperature.As demonstrated in Wang,[1]the entrainment velocity decreases for increasing values of λ.Thus intensity of cold fluid drawn towards the stretching surface reduces with increasing λ.As a consequence,thermal boundary layer expands when larger values of λ are accounted.

    On the other hand,temperature θ slightly rises and penetration depth grows when Deborah number β is incremented(see Fig.7).Moreover,slope of temperature pro file near the wall appears to decrease upon increasing β.This behavior is described as follows.Our computations revealed that vertical velocity is inversely proportional to the Deborah number β.It is therefore anticipated that amount of cold drawn in the vertical direction will reduce when parameter β enlarges.This in turn leads to the thickening of thermal boundary layer and enhancement in surface heat transfer rate.

    Fig.8 Pro files of temperature θ(η)for different values of θw.

    Figure 8 elucidates the behavior of temperature ratio parameter θwon the temperature pro file.As θwenlarges,that is,the parameter related with the ratio of wall temperature to the ambient temperature increases,the temperature pro file increases. From Eq.(10),it can be noticed that effective thermal diffusivity αeff=(α +16σ?T3/3ρCpk?)is temperature dependent due to the inclusion of non-linear heat flux.As also observed in Refs.[34-36],temperature distribution has S-shaped pattern against the similarity variable in the limiting case as θw→ ∞.Thus governing system(13)–(16)correspond to the adiabatic case(θ′(0)=0)when ratio(Tw/T∞)tends to in finity.

    Figure 9 shows the temperature pro files for varying radiation parameter Rd.Temperature pro files become thicker and temperature gradient at the surface enlarges when Rd is incremented.Similar behavior of radiation parameter was also figured out by Hsiao.[32?33]In linear radiation situation,temperature distribution approaches a constant finite value as Rd→0.However,such effect is not preserved in non-linear radiation model.

    Fig.9 Pro files of temperature θ(η)for different values of Rd.

    Fig.10 Pro files of local Nusselt number ?θ′(0)for different values of λ.

    In Fig.10,we plot wall temperature gradient θ′(0)as a function of Prandtl number Pr at different values of λ.Larger Prandtl number fluids are effective in heat convection compared to pure conduction.Due to this reason θ′(0)shows an increasing trend when Pr is increased and it tends to zero for vanishing Pr.Furthermore,there is a decrease in θ′(0)as β increases from β =0 to β =0.5.Interestingly,this change becomes pronounced when rotation rate becomes larger in comparison to the stretching rate.

    4 Conclusion

    In this study,Maxwell fluid flow in rotating frame is discussed in the existence of non-linear thermal radiation.Similarity solutions are found for a broad range of thermal radiation parameter.The key aspects of this work are summarized below:

    (i)Present numerical results are consistent with the previously published results for all values of rotationstrength parameter λ when β =0.

    (ii)An increase in rotation-strength parameter leads to an enhancement in the heat penetration depth.

    (iii)Dissimilar to the non-rotating frame,the decay in f′(η)with η is exponentially non-montonic.Indeed,there is an oscillatory pattern in the pro files of f′and g for non-zero values of λ.

    (iv)As wall and ambient temperature difference becomes,a decrease in wall heat transfer coefficient and an increase in heat penetration depth occurs.Also,temperature distribution becomes S-shaped or θ′(0) → 0 as θw→∞.

    (v)Fluid velocity in z-direction far from the stretching wall is reduced when rotation-strength parameter is increased.

    (vi)The amount of cold fluid drawn in the vertical direction towards the stretching surface reduces for increasing values of β.This in turn leads to a reduction in heat transfer rate.

    [1]C.Y.Wang,Zeitschrift fur Angewandte Mathematik and Physik 39(1988)177.

    [2]V.Rajeswari and G.Nath,Int.J.Eng.Sci.30(1992)747.

    [3]R.Nazar,N.Amin,and I.Pop,Mech.Res.Commun.31(2004)121.

    [4]M.Kumari,T.Grosan,and I.Pop,Tech.Mech.1(2006)11.

    [5]T.Hayat,T.Javed,and M.Sajid,Phys.Lett.A 372(2008)3264.

    [6]Z.Abbas,T.Javed,M.Sajid,and N.Ali,J.Taiwan Inst.Chem.Eng.41(2010)644.

    [7]T.Javed,Z.Abbas,M.Sajid,and N.Ali,Int.J.Numer.Meth.Heat and Fluid Flow 21(2011)903.

    [8]K.Zaimi,A.Ishak,and I.Pop,Appl.Math.Mech.-Engl.Ed.34(2013)945.

    [9]J.A.Khan,M.Mustafa,and A.Mushtaq,Int.J.Heat Mass Transf.94(2016)49.

    [10]M. Mustafa, A. Mushtaq, T. Hayat, and A. Alsaedi, PLoS ONE 11 (2016) e0149304,doi:10.1371/journal.pone.0149304.

    [11]M.Mustafa,R.Ahmad,T.Hayat,and A.Alsaedi,Neural Comput.&Appl.29(2018)493.

    [12]Y.Lin,L.Zheng,and X.Zhang,Int.J.Heat Mass Transf.77(2014)708.

    [13]Y.Lin,L.Zheng,X.Zhang,et al.,Int.J.Heat Mass Transf.84(2015)903.

    [14]S.Xun,J.Zhao,L.Zheng,et al.,Int.J.Heat Mass Transf.103(2016)1214.

    [15]J.Harris,Rheology and Non-Newtonian Flow,Longman Publishing Group(1977).

    [16]K.Sadeghy,A.H.Naja fi,and M.Saffaripour,Int.J.Nonlinear Mech.40(2005)1220.

    [17]M.Kumari and G.Nath,Int.J.Non-linear Mech.44(2009)1048.

    [18]M.S.Abel,J.V.Tawade,and M.M.Nandeppanavar,Meccanica 47(2012)385.

    [19]T.Hayat,M.Mustafa,S.A.Shehzad,and S.Obaidat,Int.J.Numer.Meth.Fluids 68(2012)233.

    [21]K.L.Hsiao,Arabian J.Sci.Eng.39(2014)4325.

    [22]A. Mushtaq, M. Mustafa, T. Hayat, and A. Alsaedi, J. Aerosp. Eng. 27 (2014) doi:org/10.1060/(ASCE)AS.1943-5525.0000361.

    [23]J.A.Khan,M.Mustafa,T.Hayat,and A.Alsaedi,PLoS ONE 9(2015)doi:10.1371/journal.pone.0137363.

    [24]M.Awais,N.Muhammad,T.Hayat,and A.Alsaedi,Int.J.Non-linear Sci.Numer.Simul.16(2015)123.

    [25]M.Mustafa,J.A.Khan,T.Hayat,and A.Alsaedi,AIP Advances 5(2015)doi:10.1063/1.4916364.

    [26]T.Salahuddin,M.Y.Malik,A.Hussain,et al.,J.Mag.Magnet.Mater.401(2016)991.

    [27]A.Mushtaq,S.Abbasbandy,M.Mustafa,et al.,AIP Advances 6(2016)doi:10.1063/1.4940133.

    [29]K.L.Hsiao,Appl.Therm.Eng.112(2017)1281.

    [30]A.Mushtaq,M.Mustafa,T.Hayat,and A.Alsaedi,Int.J.Non-linear Mech.79(2016)83.

    [31]L.Zheng,C.Zhang,X.Zhang,and J.Zhang,J.Franklin Inst.350(2013)990.

    [32]K.L.Hsiao,Energy 59(2013)494.

    [33]K.L.Hsiao,Comp.Fluids 104(2014)1.

    [34]A.Pantokratoras and T.Fang,Meccanica 49(2014)1539.

    [35]M.Mustafa,A.Mushtaq,T.Hayat,and B.Ahmad,PLoS ONE 9(2014)doi:10.1371/journal.pone.0103946.

    [36]M.Mustafa,A.Mushtaq,T.Hayat,and A.Alsaedi,J.Taiwan Inst.Chem.Eng.47(2015)43.

    [37]A.Mushtaq,M.Mustafa,T.Hayat,and A.Alsaedi,Int.J.Numer.Meth.Heat Fluid Flow 26(2016)1617.

    日本黄色片子视频| 国产黄片美女视频| 日产精品乱码卡一卡2卡三| 村上凉子中文字幕在线| 免费高清视频大片| 久久久色成人| 国产在线精品亚洲第一网站| 熟女电影av网| 国产成年人精品一区二区| 久久韩国三级中文字幕| 亚洲精品乱码久久久v下载方式| 国产精品99久久久久久久久| 午夜影院日韩av| 久久久久久久午夜电影| 能在线免费观看的黄片| 麻豆一二三区av精品| 三级国产精品欧美在线观看| 九色成人免费人妻av| 一边摸一边抽搐一进一小说| av在线老鸭窝| 国产精品一区二区性色av| 色吧在线观看| 久久久色成人| 国产激情偷乱视频一区二区| 插逼视频在线观看| 国产高清视频在线观看网站| 国产欧美日韩一区二区精品| 国产欧美日韩精品一区二区| 此物有八面人人有两片| 美女xxoo啪啪120秒动态图| 最近2019中文字幕mv第一页| 在线播放无遮挡| 91午夜精品亚洲一区二区三区| 久久婷婷人人爽人人干人人爱| 亚洲av一区综合| 51国产日韩欧美| 亚洲三级黄色毛片| 97碰自拍视频| 日韩欧美免费精品| 午夜福利成人在线免费观看| 看十八女毛片水多多多| 久久久成人免费电影| 亚洲aⅴ乱码一区二区在线播放| 久久精品国产99精品国产亚洲性色| 91在线观看av| 亚洲成人中文字幕在线播放| 18禁在线播放成人免费| 国产v大片淫在线免费观看| 日韩成人伦理影院| 婷婷色综合大香蕉| 久久午夜福利片| 亚洲图色成人| 不卡一级毛片| 亚洲精品国产成人久久av| 熟女人妻精品中文字幕| 国产伦在线观看视频一区| 自拍偷自拍亚洲精品老妇| 最近视频中文字幕2019在线8| 别揉我奶头~嗯~啊~动态视频| 亚洲三级黄色毛片| 亚洲真实伦在线观看| 狂野欧美激情性xxxx在线观看| 最近的中文字幕免费完整| 亚洲av中文字字幕乱码综合| 嫩草影视91久久| a级毛片免费高清观看在线播放| 国产美女午夜福利| 欧美人与善性xxx| 亚洲国产精品sss在线观看| 我要搜黄色片| 色尼玛亚洲综合影院| 99久久九九国产精品国产免费| 中文字幕av成人在线电影| 午夜福利18| 草草在线视频免费看| 亚洲精品色激情综合| 我要搜黄色片| 国产精品嫩草影院av在线观看| 美女高潮的动态| 久久人妻av系列| 久久鲁丝午夜福利片| 亚洲激情五月婷婷啪啪| 国产蜜桃级精品一区二区三区| 九色成人免费人妻av| 69av精品久久久久久| 亚洲欧美日韩高清专用| 直男gayav资源| 在线国产一区二区在线| 亚洲色图av天堂| 午夜福利在线在线| 99久久中文字幕三级久久日本| 免费大片18禁| 麻豆乱淫一区二区| 老熟妇乱子伦视频在线观看| 香蕉av资源在线| 免费观看的影片在线观看| 淫妇啪啪啪对白视频| 12—13女人毛片做爰片一| a级毛片免费高清观看在线播放| 国产日本99.免费观看| 18+在线观看网站| 最好的美女福利视频网| 日日干狠狠操夜夜爽| 内地一区二区视频在线| 亚洲成人久久性| 久久精品综合一区二区三区| 国产亚洲欧美98| 不卡视频在线观看欧美| 在线免费观看的www视频| 亚洲最大成人手机在线| 国产精品不卡视频一区二区| 久久这里只有精品中国| 给我免费播放毛片高清在线观看| 在线国产一区二区在线| 久久婷婷人人爽人人干人人爱| 禁无遮挡网站| 午夜免费男女啪啪视频观看 | 国产精品美女特级片免费视频播放器| 日韩国内少妇激情av| 亚洲欧美成人综合另类久久久 | 免费观看人在逋| 欧美另类亚洲清纯唯美| 人妻制服诱惑在线中文字幕| 国产亚洲91精品色在线| 韩国av在线不卡| 久久久久免费精品人妻一区二区| 搡女人真爽免费视频火全软件 | 亚洲国产精品合色在线| 免费高清视频大片| 精品日产1卡2卡| 日日摸夜夜添夜夜添av毛片| 久久精品国产自在天天线| 国产成人a∨麻豆精品| 最近最新中文字幕大全电影3| 99视频精品全部免费 在线| 色吧在线观看| 99热6这里只有精品| 日本熟妇午夜| 黑人高潮一二区| 少妇人妻精品综合一区二区 | 九九在线视频观看精品| av在线天堂中文字幕| 成人亚洲精品av一区二区| 日本成人三级电影网站| 国产亚洲91精品色在线| 久久草成人影院| 精品不卡国产一区二区三区| 最近视频中文字幕2019在线8| 成人亚洲精品av一区二区| 高清午夜精品一区二区三区 | 99热6这里只有精品| 久久鲁丝午夜福利片| 91麻豆精品激情在线观看国产| 直男gayav资源| 精品一区二区三区人妻视频| 两个人视频免费观看高清| 乱码一卡2卡4卡精品| 一区二区三区高清视频在线| 日日干狠狠操夜夜爽| 观看免费一级毛片| 国产精品无大码| 97热精品久久久久久| 国产精品电影一区二区三区| 黑人高潮一二区| 国产美女午夜福利| 国产白丝娇喘喷水9色精品| 国产精品人妻久久久影院| 99热6这里只有精品| 看十八女毛片水多多多| 舔av片在线| 亚洲人成网站在线播| 国产午夜福利久久久久久| 淫秽高清视频在线观看| 中文字幕人妻熟人妻熟丝袜美| 91久久精品电影网| 91在线精品国自产拍蜜月| 国产综合懂色| 婷婷色综合大香蕉| 久久精品夜色国产| 99视频精品全部免费 在线| 亚洲无线在线观看| 99热精品在线国产| 少妇被粗大猛烈的视频| 精品无人区乱码1区二区| 看十八女毛片水多多多| 欧美性猛交╳xxx乱大交人| 在线播放国产精品三级| 日日啪夜夜撸| 亚洲四区av| 亚洲,欧美,日韩| 香蕉av资源在线| 精品欧美国产一区二区三| 人人妻人人看人人澡| 男人舔女人下体高潮全视频| 99久国产av精品国产电影| 久久亚洲国产成人精品v| 婷婷六月久久综合丁香| 麻豆精品久久久久久蜜桃| 小说图片视频综合网站| 变态另类丝袜制服| 欧洲精品卡2卡3卡4卡5卡区| av中文乱码字幕在线| 免费人成视频x8x8入口观看| 可以在线观看的亚洲视频| 精品人妻一区二区三区麻豆 | 变态另类成人亚洲欧美熟女| 婷婷精品国产亚洲av在线| 国产精品日韩av在线免费观看| 麻豆成人午夜福利视频| 99热这里只有是精品50| 三级国产精品欧美在线观看| 亚州av有码| 国产成人影院久久av| 中文在线观看免费www的网站| 成年版毛片免费区| 久久这里只有精品中国| 一个人观看的视频www高清免费观看| 欧美成人精品欧美一级黄| 欧美激情国产日韩精品一区| 成人三级黄色视频| 欧美日韩乱码在线| 欧美中文日本在线观看视频| 国产探花极品一区二区| 精华霜和精华液先用哪个| 两个人视频免费观看高清| 内地一区二区视频在线| 亚洲精品一卡2卡三卡4卡5卡| 我的女老师完整版在线观看| 国产精品久久视频播放| 国产在线精品亚洲第一网站| 日本色播在线视频| 少妇人妻精品综合一区二区 | 又粗又爽又猛毛片免费看| 男女视频在线观看网站免费| av在线亚洲专区| 高清日韩中文字幕在线| 久久精品国产99精品国产亚洲性色| 亚洲欧美精品自产自拍| 99国产精品一区二区蜜桃av| 国产伦在线观看视频一区| 国产高清视频在线观看网站| av黄色大香蕉| 婷婷色综合大香蕉| 97超级碰碰碰精品色视频在线观看| 国产亚洲精品综合一区在线观看| 国产白丝娇喘喷水9色精品| ponron亚洲| 乱系列少妇在线播放| 国产精品99久久久久久久久| 午夜福利18| 欧美zozozo另类| 亚洲av电影不卡..在线观看| 国语自产精品视频在线第100页| 精华霜和精华液先用哪个| 免费搜索国产男女视频| 女的被弄到高潮叫床怎么办| 伊人久久精品亚洲午夜| 亚洲综合色惰| 最近在线观看免费完整版| 亚洲欧美成人精品一区二区| eeuss影院久久| 日韩av在线大香蕉| 午夜精品在线福利| 中文字幕久久专区| 国产男靠女视频免费网站| 夜夜爽天天搞| av专区在线播放| 国产一区二区三区av在线 | 国产精品久久久久久久电影| 精品国产三级普通话版| 美女黄网站色视频| 国产成人影院久久av| 啦啦啦啦在线视频资源| 成人综合一区亚洲| 国产黄片美女视频| 91av网一区二区| 日本a在线网址| 秋霞在线观看毛片| 啦啦啦韩国在线观看视频| 午夜福利在线观看免费完整高清在 | 六月丁香七月| 干丝袜人妻中文字幕| 免费无遮挡裸体视频| 久久久久久久久大av| 最近在线观看免费完整版| aaaaa片日本免费| 不卡视频在线观看欧美| 高清日韩中文字幕在线| 18禁裸乳无遮挡免费网站照片| 免费黄网站久久成人精品| .国产精品久久| 99久久精品热视频| 亚洲四区av| 久久久欧美国产精品| 男女下面进入的视频免费午夜| 久久久色成人| 婷婷亚洲欧美| 国产欧美日韩精品亚洲av| 国产真实伦视频高清在线观看| 日日干狠狠操夜夜爽| 久久久精品大字幕| 日韩一本色道免费dvd| 深爱激情五月婷婷| 国产乱人偷精品视频| av中文乱码字幕在线| 99久久无色码亚洲精品果冻| 中文字幕久久专区| 亚洲真实伦在线观看| 十八禁网站免费在线| 简卡轻食公司| 国产成人freesex在线 | 免费看av在线观看网站| 成人亚洲欧美一区二区av| 日韩欧美三级三区| 免费看av在线观看网站| 悠悠久久av| 精品久久久久久久末码| 91在线观看av| 亚洲av免费在线观看| 国产精品一二三区在线看| 三级男女做爰猛烈吃奶摸视频| 国产成人福利小说| 极品教师在线视频| 寂寞人妻少妇视频99o| 欧美性猛交╳xxx乱大交人| 天堂影院成人在线观看| 99国产极品粉嫩在线观看| 久久天躁狠狠躁夜夜2o2o| 黄色欧美视频在线观看| 三级国产精品欧美在线观看| 日本爱情动作片www.在线观看 | 99久久中文字幕三级久久日本| 久久精品夜色国产| .国产精品久久| 狂野欧美激情性xxxx在线观看| 级片在线观看| 村上凉子中文字幕在线| 99久国产av精品国产电影| 一个人看的www免费观看视频| 国产精品精品国产色婷婷| 真实男女啪啪啪动态图| 国产av在哪里看| 国产精品三级大全| 99热6这里只有精品| 欧美区成人在线视频| 欧美性猛交╳xxx乱大交人| 成人美女网站在线观看视频| 99国产极品粉嫩在线观看| 日韩精品青青久久久久久| 变态另类丝袜制服| 国产91av在线免费观看| 日韩人妻高清精品专区| 99久久精品国产国产毛片| 三级经典国产精品| 菩萨蛮人人尽说江南好唐韦庄 | 欧美日韩一区二区视频在线观看视频在线 | 国产亚洲欧美98| 一进一出抽搐gif免费好疼| 99久久无色码亚洲精品果冻| 伦精品一区二区三区| 免费看a级黄色片| 国产成人福利小说| 高清毛片免费看| 国产极品精品免费视频能看的| 高清日韩中文字幕在线| 99久国产av精品| 人人妻人人澡欧美一区二区| 乱系列少妇在线播放| 日本-黄色视频高清免费观看| 偷拍熟女少妇极品色| 男女那种视频在线观看| 欧美+亚洲+日韩+国产| 欧美成人a在线观看| 欧美中文日本在线观看视频| 免费看日本二区| 精品不卡国产一区二区三区| 美女黄网站色视频| 麻豆精品久久久久久蜜桃| 亚洲第一区二区三区不卡| 久久精品影院6| 亚洲av.av天堂| 特大巨黑吊av在线直播| 深夜a级毛片| 久久精品夜色国产| 亚洲成人久久性| 一本一本综合久久| 精品不卡国产一区二区三区| 嫩草影院入口| 成人一区二区视频在线观看| 国产精品av视频在线免费观看| 日韩 亚洲 欧美在线| 欧美绝顶高潮抽搐喷水| 亚洲欧美成人综合另类久久久 | 久久久a久久爽久久v久久| 国产午夜福利久久久久久| 69人妻影院| 国产精品野战在线观看| 久久久成人免费电影| 久久99热6这里只有精品| 国产一级毛片七仙女欲春2| 日韩欧美精品免费久久| 日韩,欧美,国产一区二区三区 | 亚洲精品一卡2卡三卡4卡5卡| 深爱激情五月婷婷| 可以在线观看毛片的网站| 99热网站在线观看| 亚洲成人久久爱视频| 欧美中文日本在线观看视频| av.在线天堂| 六月丁香七月| 免费人成在线观看视频色| 国产精品一及| 51国产日韩欧美| 伊人久久精品亚洲午夜| 久久久久久大精品| 在线播放国产精品三级| av天堂在线播放| 能在线免费观看的黄片| 亚洲色图av天堂| 国产高清有码在线观看视频| 色5月婷婷丁香| 欧美一区二区亚洲| 可以在线观看毛片的网站| 久久精品国产亚洲av香蕉五月| 久久精品国产99精品国产亚洲性色| 日产精品乱码卡一卡2卡三| 亚洲四区av| 国产精品1区2区在线观看.| 中国国产av一级| 成人一区二区视频在线观看| av免费在线看不卡| 直男gayav资源| 成人三级黄色视频| 中文字幕精品亚洲无线码一区| 在线观看免费视频日本深夜| 91久久精品国产一区二区成人| 国产欧美日韩精品一区二区| 此物有八面人人有两片| 欧美一区二区亚洲| 久久精品影院6| 色av中文字幕| 日本与韩国留学比较| 国产人妻一区二区三区在| 变态另类成人亚洲欧美熟女| 成年女人永久免费观看视频| 国产精品久久电影中文字幕| 日韩人妻高清精品专区| 男人和女人高潮做爰伦理| 国产老妇女一区| 亚洲欧美日韩卡通动漫| 伊人久久精品亚洲午夜| 观看美女的网站| 在线播放无遮挡| 精品久久久久久久久av| 天堂影院成人在线观看| 成人国产麻豆网| 午夜福利在线观看吧| 国产成人freesex在线 | 成人鲁丝片一二三区免费| 日韩一本色道免费dvd| 能在线免费观看的黄片| 日本黄大片高清| 午夜免费激情av| 精品不卡国产一区二区三区| av卡一久久| 国产精品乱码一区二三区的特点| 一级毛片电影观看 | 青春草视频在线免费观看| 亚洲无线观看免费| 男女边吃奶边做爰视频| 成人综合一区亚洲| 色吧在线观看| 国产v大片淫在线免费观看| 少妇的逼好多水| 国产精品美女特级片免费视频播放器| 一区二区三区高清视频在线| 麻豆国产av国片精品| 日韩欧美 国产精品| 国产亚洲av嫩草精品影院| 免费无遮挡裸体视频| 嫩草影院新地址| 国产亚洲精品综合一区在线观看| 亚洲av成人av| 欧美高清性xxxxhd video| 久久久午夜欧美精品| 久久99热6这里只有精品| 欧美日本亚洲视频在线播放| 精品人妻熟女av久视频| 91久久精品电影网| 亚洲国产精品成人久久小说 | 久久久精品大字幕| 男女做爰动态图高潮gif福利片| 一进一出抽搐动态| 麻豆久久精品国产亚洲av| 97热精品久久久久久| 亚洲无线观看免费| 激情 狠狠 欧美| 免费人成在线观看视频色| 亚州av有码| 又爽又黄a免费视频| 久久精品国产亚洲av香蕉五月| 最近在线观看免费完整版| 亚洲电影在线观看av| 日韩欧美精品免费久久| .国产精品久久| 天天躁日日操中文字幕| 国产精品99久久久久久久久| 激情 狠狠 欧美| 欧美高清成人免费视频www| 欧美性猛交黑人性爽| 免费观看精品视频网站| av免费在线看不卡| 国内久久婷婷六月综合欲色啪| 日本 av在线| 成人亚洲精品av一区二区| 91av网一区二区| 色av中文字幕| 日本 av在线| 日本三级黄在线观看| 国产 一区精品| 晚上一个人看的免费电影| av中文乱码字幕在线| 国产日本99.免费观看| 午夜福利在线在线| 三级毛片av免费| 国产精品久久久久久亚洲av鲁大| 日韩 亚洲 欧美在线| 国产高潮美女av| 能在线免费观看的黄片| 高清午夜精品一区二区三区 | 两个人视频免费观看高清| 国产伦在线观看视频一区| 校园人妻丝袜中文字幕| 夜夜夜夜夜久久久久| 97碰自拍视频| 亚洲成a人片在线一区二区| 97碰自拍视频| 99热6这里只有精品| 国产av在哪里看| 中出人妻视频一区二区| 五月伊人婷婷丁香| 欧洲精品卡2卡3卡4卡5卡区| 草草在线视频免费看| 色视频www国产| 国产男靠女视频免费网站| 麻豆成人午夜福利视频| 日韩一本色道免费dvd| 国产精品嫩草影院av在线观看| 精品熟女少妇av免费看| 男插女下体视频免费在线播放| 精品不卡国产一区二区三区| 午夜免费激情av| 国产极品精品免费视频能看的| 午夜免费激情av| 小说图片视频综合网站| 久久久久九九精品影院| 日本-黄色视频高清免费观看| 久久午夜亚洲精品久久| 精品一区二区三区视频在线观看免费| 99久久精品国产国产毛片| 不卡一级毛片| 别揉我奶头~嗯~啊~动态视频| 1000部很黄的大片| 国产片特级美女逼逼视频| 12—13女人毛片做爰片一| 在线免费十八禁| 中文字幕av成人在线电影| 亚洲成人久久爱视频| 亚洲av中文av极速乱| 韩国av在线不卡| www日本黄色视频网| 精品99又大又爽又粗少妇毛片| av中文乱码字幕在线| 欧美3d第一页| 欧美日韩精品成人综合77777| 成人亚洲精品av一区二区| avwww免费| 国产乱人偷精品视频| 国产淫片久久久久久久久| 插逼视频在线观看| 亚洲国产精品成人久久小说 | 国产成人精品久久久久久| 国产精品嫩草影院av在线观看| 亚洲欧美精品自产自拍| 可以在线观看的亚洲视频| 人人妻人人澡欧美一区二区| 最新在线观看一区二区三区| 国产精品福利在线免费观看| 久久人人爽人人片av| 午夜福利在线在线| 99热这里只有是精品在线观看| 婷婷精品国产亚洲av在线| 一级黄片播放器| 久久久午夜欧美精品| 麻豆乱淫一区二区| 国产男靠女视频免费网站| 国产视频内射| 国产午夜精品久久久久久一区二区三区 | 在线免费观看的www视频| 国产大屁股一区二区在线视频| 九九久久精品国产亚洲av麻豆| 别揉我奶头 嗯啊视频| 久久婷婷人人爽人人干人人爱| 亚洲国产精品久久男人天堂| 久久久久久伊人网av| 日韩大尺度精品在线看网址| 哪里可以看免费的av片| 免费一级毛片在线播放高清视频| 变态另类丝袜制服| 久久久久久久久中文| 深爱激情五月婷婷| 一个人看的www免费观看视频| 亚洲四区av| 91午夜精品亚洲一区二区三区| 一级av片app|