• <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.

    长腿黑丝高跟| 成人特级黄色片久久久久久久| 国产成人欧美在线观看| 午夜激情福利司机影院| 在现免费观看毛片| 99在线视频只有这里精品首页| 午夜精品在线福利| 成年人黄色毛片网站| 男人和女人高潮做爰伦理| 欧美色视频一区免费| 99riav亚洲国产免费| 亚洲五月婷婷丁香| 99久久无色码亚洲精品果冻| 美女大奶头视频| 丁香六月欧美| 国产av一区在线观看免费| 成年免费大片在线观看| 蜜桃亚洲精品一区二区三区| 99热6这里只有精品| 欧美色欧美亚洲另类二区| aaaaa片日本免费| 午夜福利成人在线免费观看| 欧美日韩亚洲国产一区二区在线观看| 一卡2卡三卡四卡精品乱码亚洲| 在线看三级毛片| 老司机午夜福利在线观看视频| 亚洲av不卡在线观看| 啦啦啦观看免费观看视频高清| 国产激情偷乱视频一区二区| 成人精品一区二区免费| 在线观看av片永久免费下载| 淫秽高清视频在线观看| 国内精品久久久久久久电影| 日日摸夜夜添夜夜添av毛片 | av欧美777| 18禁在线播放成人免费| 国产精品亚洲av一区麻豆| 成人精品一区二区免费| 亚洲精品一区av在线观看| 久久中文看片网| 免费人成视频x8x8入口观看| 亚洲国产精品久久男人天堂| 亚洲av五月六月丁香网| 久久久久久久久大av| 色播亚洲综合网| 欧美3d第一页| 欧美激情久久久久久爽电影| 久久这里只有精品中国| 成人无遮挡网站| 亚洲av电影不卡..在线观看| 欧美精品啪啪一区二区三区| 色噜噜av男人的天堂激情| 最近中文字幕高清免费大全6 | 精品久久久久久成人av| 国产白丝娇喘喷水9色精品| 久久国产乱子伦精品免费另类| or卡值多少钱| 国产69精品久久久久777片| 看黄色毛片网站| 一进一出抽搐gif免费好疼| 欧美黄色片欧美黄色片| 国产麻豆成人av免费视频| 观看免费一级毛片| 精品久久久久久久人妻蜜臀av| 波野结衣二区三区在线| 国产高清视频在线播放一区| 日本 av在线| 在线观看一区二区三区| 欧美日韩中文字幕国产精品一区二区三区| 欧美一区二区国产精品久久精品| 亚洲av第一区精品v没综合| 三级毛片av免费| 亚洲第一电影网av| 少妇的逼水好多| 在线观看免费视频日本深夜| 深夜a级毛片| 亚洲国产欧洲综合997久久,| 搡老妇女老女人老熟妇| 久9热在线精品视频| 亚洲一区高清亚洲精品| 欧美成人免费av一区二区三区| 非洲黑人性xxxx精品又粗又长| 国产精品伦人一区二区| 国产久久久一区二区三区| 亚洲天堂国产精品一区在线| 美女被艹到高潮喷水动态| 一本综合久久免费| 亚洲精品一卡2卡三卡4卡5卡| 国内精品一区二区在线观看| 中文亚洲av片在线观看爽| 亚洲av二区三区四区| 欧美日韩黄片免| 日本五十路高清| 精品国产三级普通话版| АⅤ资源中文在线天堂| 欧美在线一区亚洲| 好男人在线观看高清免费视频| 亚洲欧美日韩高清在线视频| 97碰自拍视频| 日日干狠狠操夜夜爽| 精品午夜福利视频在线观看一区| 亚洲成人免费电影在线观看| 欧美日韩中文字幕国产精品一区二区三区| 成年女人毛片免费观看观看9| 内射极品少妇av片p| 亚洲成人精品中文字幕电影| 在线观看午夜福利视频| 国产伦精品一区二区三区四那| 日本免费一区二区三区高清不卡| 黄色视频,在线免费观看| 久久久久性生活片| 国产白丝娇喘喷水9色精品| 男女做爰动态图高潮gif福利片| 国产色爽女视频免费观看| 成年版毛片免费区| 一二三四社区在线视频社区8| 国产淫片久久久久久久久 | 少妇被粗大猛烈的视频| 亚洲成av人片免费观看| 亚洲午夜理论影院| 五月伊人婷婷丁香| 日本一二三区视频观看| 色综合婷婷激情| 亚洲乱码一区二区免费版| 两个人视频免费观看高清| 欧美极品一区二区三区四区| 成年女人看的毛片在线观看| 亚洲av日韩精品久久久久久密| 两人在一起打扑克的视频| 欧美绝顶高潮抽搐喷水| 亚洲av美国av| 一进一出抽搐动态| 国产午夜精品论理片| 少妇被粗大猛烈的视频| 久久久国产成人免费| 波多野结衣巨乳人妻| 国产精品久久久久久亚洲av鲁大| 老鸭窝网址在线观看| 中文在线观看免费www的网站| 亚洲 欧美 日韩 在线 免费| 久久人人爽人人爽人人片va | 在线a可以看的网站| 97超视频在线观看视频| 欧美色视频一区免费| 久久久久久久亚洲中文字幕 | 日韩有码中文字幕| 国产精品国产高清国产av| 我的女老师完整版在线观看| bbb黄色大片| 国产免费男女视频| 国产主播在线观看一区二区| av女优亚洲男人天堂| 少妇的逼水好多| 最好的美女福利视频网| 最近中文字幕高清免费大全6 | 亚洲三级黄色毛片| 自拍偷自拍亚洲精品老妇| 成人午夜高清在线视频| 免费观看精品视频网站| 国产一区二区在线观看日韩| 国产欧美日韩一区二区精品| 日本熟妇午夜| 亚洲熟妇中文字幕五十中出| 亚洲第一欧美日韩一区二区三区| 成年女人看的毛片在线观看| 最近中文字幕高清免费大全6 | 国产欧美日韩精品一区二区| 国内揄拍国产精品人妻在线| 亚洲成人久久爱视频| 熟妇人妻久久中文字幕3abv| 欧美一区二区精品小视频在线| 黄片小视频在线播放| 国产人妻一区二区三区在| 国产熟女xx| 色噜噜av男人的天堂激情| 中国美女看黄片| 日日夜夜操网爽| 国产真实伦视频高清在线观看 | 尤物成人国产欧美一区二区三区| 成人国产一区最新在线观看| 中国美女看黄片| av专区在线播放| 国产野战对白在线观看| www.www免费av| 日日夜夜操网爽| 深夜a级毛片| www.www免费av| 中文字幕高清在线视频| 亚洲片人在线观看| bbb黄色大片| 欧美激情久久久久久爽电影| 丰满乱子伦码专区| 又爽又黄a免费视频| 99久久久亚洲精品蜜臀av| av在线天堂中文字幕| 亚洲av不卡在线观看| 少妇高潮的动态图| 97人妻精品一区二区三区麻豆| 十八禁网站免费在线| 精品熟女少妇八av免费久了| 免费观看精品视频网站| 白带黄色成豆腐渣| 日韩成人在线观看一区二区三区| 成人特级av手机在线观看| 成年人黄色毛片网站| 内地一区二区视频在线| 黄色一级大片看看| 国产三级中文精品| 精品久久久久久久久av| 嫩草影院入口| 欧美丝袜亚洲另类 | 好看av亚洲va欧美ⅴa在| 日韩精品青青久久久久久| 欧美一级a爱片免费观看看| 淫妇啪啪啪对白视频| 亚洲一区二区三区色噜噜| 中文字幕人成人乱码亚洲影| 国产高清有码在线观看视频| 中出人妻视频一区二区| 国产高清视频在线播放一区| 一边摸一边抽搐一进一小说| 老司机深夜福利视频在线观看| 99热只有精品国产| 老司机福利观看| 每晚都被弄得嗷嗷叫到高潮| 丝袜美腿在线中文| 国产熟女xx| 他把我摸到了高潮在线观看| 精品午夜福利视频在线观看一区| 日韩欧美国产一区二区入口| 国产精品嫩草影院av在线观看 | 小说图片视频综合网站| 美女xxoo啪啪120秒动态图 | 制服丝袜大香蕉在线| 久久久久精品国产欧美久久久| 此物有八面人人有两片| 久久性视频一级片| 伦理电影大哥的女人| 哪里可以看免费的av片| 一本精品99久久精品77| 美女免费视频网站| aaaaa片日本免费| 夜夜看夜夜爽夜夜摸| 18禁在线播放成人免费| 精品国内亚洲2022精品成人| 村上凉子中文字幕在线| 国产三级黄色录像| 日韩高清综合在线| 久久伊人香网站| 午夜两性在线视频| 国产蜜桃级精品一区二区三区| 欧美日韩乱码在线| 久久精品国产99精品国产亚洲性色| 99精品在免费线老司机午夜| 三级国产精品欧美在线观看| 日韩精品青青久久久久久| 欧美成人a在线观看| 久久久久久久久久成人| 村上凉子中文字幕在线| 99久久精品热视频| 精品欧美国产一区二区三| 天堂av国产一区二区熟女人妻| 国产av在哪里看| 精品免费久久久久久久清纯| 久久99热6这里只有精品| 午夜日韩欧美国产| 此物有八面人人有两片| 亚洲av熟女| 人妻久久中文字幕网| 成人高潮视频无遮挡免费网站| 久久亚洲精品不卡| 亚洲成av人片免费观看| 久久久久久久久久成人| 国产精品免费一区二区三区在线| 天美传媒精品一区二区| 亚洲av成人精品一区久久| 国产精品永久免费网站| 亚洲国产精品合色在线| 日本 av在线| 日韩欧美精品免费久久 | 国产欧美日韩精品一区二区| 精品人妻视频免费看| 少妇的逼好多水| 男插女下体视频免费在线播放| 韩国av一区二区三区四区| 久久久成人免费电影| 成人性生交大片免费视频hd| 91九色精品人成在线观看| 欧美在线黄色| 精品一区二区三区视频在线| 亚洲va日本ⅴa欧美va伊人久久| 国产精品一区二区三区四区久久| 成年免费大片在线观看| 亚洲中文字幕日韩| 国产精品自产拍在线观看55亚洲| 久久伊人香网站| 久久久久亚洲av毛片大全| 99久久无色码亚洲精品果冻| 精品一区二区三区av网在线观看| 日本成人三级电影网站| 五月玫瑰六月丁香| 免费在线观看亚洲国产| 国产毛片a区久久久久| 国产蜜桃级精品一区二区三区| 日日摸夜夜添夜夜添小说| 欧美日本视频| 国产一级毛片七仙女欲春2| 久久人人爽人人爽人人片va | 丁香六月欧美| 一区福利在线观看| 久99久视频精品免费| 国产毛片a区久久久久| 一a级毛片在线观看| 美女cb高潮喷水在线观看| 淫妇啪啪啪对白视频| 亚洲专区国产一区二区| 3wmmmm亚洲av在线观看| 一个人观看的视频www高清免费观看| 国产精华一区二区三区| 精品久久久久久久人妻蜜臀av| 精品久久久久久,| 午夜福利在线观看吧| 人妻丰满熟妇av一区二区三区| 国产精品久久久久久亚洲av鲁大| 少妇裸体淫交视频免费看高清| 久久伊人香网站| 老熟妇仑乱视频hdxx| 久久久精品欧美日韩精品| 国产精品久久电影中文字幕| 精品一区二区三区视频在线观看免费| 亚洲五月婷婷丁香| 亚洲 欧美 日韩 在线 免费| 国产亚洲av嫩草精品影院| 在线观看66精品国产| 男女之事视频高清在线观看| 亚洲va日本ⅴa欧美va伊人久久| 国产精品精品国产色婷婷| 欧美最黄视频在线播放免费| 日本 av在线| 如何舔出高潮| 午夜福利欧美成人| 99热这里只有精品一区| 久久精品国产自在天天线| 99热这里只有是精品在线观看 | 精品日产1卡2卡| 99国产极品粉嫩在线观看| 久久久国产成人免费| 精品一区二区三区视频在线观看免费| 欧美乱妇无乱码| 国产精品久久久久久久电影| 俺也久久电影网| 国产白丝娇喘喷水9色精品| 日本免费a在线| 色综合婷婷激情| 国产精品三级大全| 中文字幕高清在线视频| 午夜福利免费观看在线| 啦啦啦韩国在线观看视频| 97超视频在线观看视频| 中文在线观看免费www的网站| 村上凉子中文字幕在线| 久久草成人影院| 日韩欧美精品v在线| 三级毛片av免费| 亚洲色图av天堂| АⅤ资源中文在线天堂| 成年女人毛片免费观看观看9| 小说图片视频综合网站| 久久久久久久久大av| 一本久久中文字幕| 成人精品一区二区免费| www日本黄色视频网| 国产精品嫩草影院av在线观看 | 国产又黄又爽又无遮挡在线| 婷婷精品国产亚洲av在线| 久久久久九九精品影院| 国产精品国产高清国产av| 变态另类丝袜制服| 亚洲avbb在线观看| 日本免费一区二区三区高清不卡| 亚洲国产精品成人综合色| 日韩大尺度精品在线看网址| 亚洲精品一区av在线观看| 禁无遮挡网站| 欧美精品啪啪一区二区三区| 国产成人福利小说| 国产成人啪精品午夜网站| 欧美又色又爽又黄视频| 国产亚洲av嫩草精品影院| 久久精品91蜜桃| 久久九九热精品免费| 亚洲 欧美 日韩 在线 免费| 一级作爱视频免费观看| 亚洲av成人不卡在线观看播放网| 国内精品久久久久久久电影| 中文字幕av成人在线电影| 狂野欧美白嫩少妇大欣赏| 国产爱豆传媒在线观看| 国产中年淑女户外野战色| 亚洲精品在线观看二区| 亚洲第一欧美日韩一区二区三区| 国产一区二区在线观看日韩| av黄色大香蕉| 美女高潮喷水抽搐中文字幕| 日日摸夜夜添夜夜添小说| 亚洲无线在线观看| 人人妻人人看人人澡| or卡值多少钱| 国产精品乱码一区二三区的特点| 性插视频无遮挡在线免费观看| 国产伦一二天堂av在线观看| 99在线人妻在线中文字幕| 天堂网av新在线| 变态另类丝袜制服| 韩国av一区二区三区四区| 观看美女的网站| 又黄又爽又免费观看的视频| 性插视频无遮挡在线免费观看| 女同久久另类99精品国产91| 国产精品嫩草影院av在线观看 | 精品人妻视频免费看| 欧美成人免费av一区二区三区| 午夜a级毛片| 又爽又黄a免费视频| 欧美黄色片欧美黄色片| 成人美女网站在线观看视频| 色综合站精品国产| 18+在线观看网站| 99国产综合亚洲精品| 欧美成人一区二区免费高清观看| 欧美日韩综合久久久久久 | 精品无人区乱码1区二区| 亚洲精品在线观看二区| 精品午夜福利视频在线观看一区| 亚洲综合色惰| 窝窝影院91人妻| 久久久精品欧美日韩精品| 欧美乱色亚洲激情| 色精品久久人妻99蜜桃| 麻豆久久精品国产亚洲av| 美女 人体艺术 gogo| 午夜福利在线在线| 欧美另类亚洲清纯唯美| 色吧在线观看| 波多野结衣巨乳人妻| 免费看美女性在线毛片视频| 激情在线观看视频在线高清| 久久久久国内视频| 国产精品一区二区性色av| 无人区码免费观看不卡| 精华霜和精华液先用哪个| 国产久久久一区二区三区| 亚洲av免费在线观看| 啦啦啦观看免费观看视频高清| 亚洲av日韩精品久久久久久密| 国产精品不卡视频一区二区 | 亚洲中文字幕一区二区三区有码在线看| 国产精品嫩草影院av在线观看 | 午夜福利欧美成人| av在线老鸭窝| or卡值多少钱| 亚洲色图av天堂| 国产亚洲精品久久久com| 两个人的视频大全免费| .国产精品久久| 午夜老司机福利剧场| 麻豆久久精品国产亚洲av| 亚洲人成伊人成综合网2020| 男女下面进入的视频免费午夜| 国产大屁股一区二区在线视频| 九色成人免费人妻av| 色综合婷婷激情| 两个人视频免费观看高清| 在线观看免费视频日本深夜| 国产美女午夜福利| 成人三级黄色视频| 黄色丝袜av网址大全| 黄色女人牲交| 日日摸夜夜添夜夜添小说| 在线观看美女被高潮喷水网站 | 免费观看人在逋| 亚洲精品一卡2卡三卡4卡5卡| 男人和女人高潮做爰伦理| 婷婷精品国产亚洲av在线| 色av中文字幕| 亚洲熟妇中文字幕五十中出| 国产午夜精品论理片| 亚洲五月天丁香| 亚洲中文字幕一区二区三区有码在线看| 狂野欧美白嫩少妇大欣赏| 美女免费视频网站| 国产精品一区二区免费欧美| 综合色av麻豆| 国产精品国产高清国产av| 国产亚洲av嫩草精品影院| 久久久久亚洲av毛片大全| 91麻豆av在线| 黄片小视频在线播放| 在线国产一区二区在线| 欧美zozozo另类| 999久久久精品免费观看国产| 亚洲欧美激情综合另类| 日本 av在线| 免费在线观看日本一区| 免费大片18禁| 国产亚洲精品久久久久久毛片| 久久久色成人| 少妇人妻一区二区三区视频| 欧美高清性xxxxhd video| avwww免费| 精品日产1卡2卡| 中文字幕人成人乱码亚洲影| 中文字幕免费在线视频6| 五月伊人婷婷丁香| 99热6这里只有精品| h日本视频在线播放| 国产精品三级大全| 久99久视频精品免费| 搡老熟女国产l中国老女人| www.色视频.com| 极品教师在线免费播放| 欧美成人a在线观看| 啦啦啦观看免费观看视频高清| 色在线成人网| 久久午夜福利片| 亚洲av成人精品一区久久| 国产野战对白在线观看| 亚洲精华国产精华精| 色综合婷婷激情| 精品一区二区免费观看| 狂野欧美白嫩少妇大欣赏| 婷婷亚洲欧美| 国产一区二区亚洲精品在线观看| 校园春色视频在线观看| 在线观看av片永久免费下载| 日本 欧美在线| 一本综合久久免费| 一二三四社区在线视频社区8| 精品午夜福利视频在线观看一区| 亚洲片人在线观看| 日本一本二区三区精品| 搡老妇女老女人老熟妇| 我的老师免费观看完整版| 国产单亲对白刺激| 一二三四社区在线视频社区8| 伊人久久精品亚洲午夜| 久9热在线精品视频| eeuss影院久久| 99热精品在线国产| av视频在线观看入口| 91久久精品电影网| 国产久久久一区二区三区| 淫秽高清视频在线观看| 一级黄色大片毛片| 夜夜夜夜夜久久久久| 亚洲av美国av| 在线十欧美十亚洲十日本专区| 亚洲国产色片| 久久这里只有精品中国| 亚洲成av人片在线播放无| 十八禁人妻一区二区| av在线观看视频网站免费| 久久国产精品人妻蜜桃| 日本a在线网址| 永久网站在线| 老司机福利观看| 琪琪午夜伦伦电影理论片6080| av福利片在线观看| 国内精品久久久久久久电影| 在线免费观看的www视频| 日韩国内少妇激情av| 真人一进一出gif抽搐免费| 18禁黄网站禁片免费观看直播| 免费人成在线观看视频色| 老鸭窝网址在线观看| av天堂在线播放| 老师上课跳d突然被开到最大视频 久久午夜综合久久蜜桃 | 99久国产av精品| 久久精品影院6| 国产黄片美女视频| 精品无人区乱码1区二区| 国产精品,欧美在线| 国产精品乱码一区二三区的特点| 久99久视频精品免费| 色综合亚洲欧美另类图片| 亚洲一区二区三区不卡视频| 1024手机看黄色片| 男女下面进入的视频免费午夜| 午夜免费男女啪啪视频观看 | 亚洲七黄色美女视频| 悠悠久久av| 亚洲第一电影网av| 观看美女的网站| 久久久久久九九精品二区国产| 在线播放国产精品三级| 欧美日韩乱码在线| 国内少妇人妻偷人精品xxx网站| 亚洲第一电影网av| 日本免费a在线| 午夜福利高清视频| 亚洲第一电影网av| 国产黄色小视频在线观看| 亚洲专区中文字幕在线| 国产综合懂色| 国产伦人伦偷精品视频| 两个人的视频大全免费| 久久久久精品国产欧美久久久| 性色av乱码一区二区三区2| 日韩欧美 国产精品| 国产精品久久电影中文字幕| 国产精品精品国产色婷婷| 每晚都被弄得嗷嗷叫到高潮| 尤物成人国产欧美一区二区三区| 一夜夜www| 日韩欧美国产一区二区入口|