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Journal of Central South University 2015年第8期22卷 3189-3201页

作者： K.Ramesh M.Devakar Department of Mathematics Visvesvaraya National Institute of Technology

The intention of this investigation is to study the effects of heat transfer and inclined magnetic field on the peristaltic flow of williamson fluid in an asymmetric channel through porous medium. The governing two-dimensional equations are simplified under the assumption of long wavelength approximation. The simplified equations are solved for the stream function, temperature, and axial pressure gradient by using a regular perturbation method. The expression for pressure rise is computed numerically. The profiles of velocity, pressure gradient, temperature, heat transfer coefficient and stream function are sketched and interpreted for various embedded parameters and also the behavior of stream function for various wave forms is discussed through graphs. It is observed that the peristaltic velocity increases from porous medium to non-porous medium, the magnetic effects have increasing effect on the temperature, and the size of the trapped bolus decreases with the increasing of magnetic effects while the trend is reversed with the increasing of Darcy number. Moreover, limiting solutions of our problem are in close agreement with the corresponding results of the Newtonian fluid model.

关键词： williamson fluid heat transfer inclined magnetic field porous medium inclined asymmetric channel

Heat transfer analysis of williamson fluid over exponentially stretching surface

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Applied Mathematics and Mechanics(English Edition) 2014年第4期35卷 489-502页

作者： S.NADEEM S.T.HUSSAIN Department of Mathematics Quaid-i-Azam University

This study explores the effects of heat transfer on the williamson fluid over a porous exponentially stretching surface. The boundary layer equations of the williamson fluid model for two dimensional flow with heat transfer are presented. Two cases of heat transfer are considered, i.e., the prescribed exponential order surface temperature （PEST） case and the prescribed exponential order heat flux （PEHF） case. The highly nonlinear partial differential equations are simplified with suitable similar and non-similar variables, and finally are solved analytically with the help of the optimal homotopy analysis method （OHAM）. The optimal convergence control parameters are obtained, and the physical fea- tures of the flow parameters are analyzed through graphs and tables. The skin friction and wall temperature gradient are calculated.

关键词： optimal homotopy analysis method (OHAM) williamson fluid expo-nential stretching permeable wall heat transfer prescribed exponential order surfacetemperature (PEST) prescribed exponential order heat flux (PEHF)

Hydrodynamics and Sensitivity Analysis of a williamson fluid in Porous-Walled Wavy Channel

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Computers, Materials & Continua 2021年第9期68卷 3877-3893页

作者： A.Shahzad W.A.Khan R.Gul B.Dayyan M.Zubair Department of Mathematics COMSATS University IslamabadAbbottabad Campus22060Pakistan Department of Mechanical Engineering College of Engineering Prince Mohammad Bin Fahd UniversityAl Khobar31952Kingdom of Saudi Arabia

In this work,a steady,incompressible williamson fluid model is investigated in a porous wavy *** situation arises in the reabsorption of useful substances from the glomerular filtrate in the *** 80%reabsorption,urine is left,which behaves like a thinning *** laws of conservation of mass and momentum are used to model the physical *** analytical solution of the problem in terms of stream function is obtained by a regular perturbation expansion *** asymptotic integration method for small wave amplitudes and the RK-Fehlberg method for pressure distribution has been used inside the *** is demonstrated that the forward flow becomes fast in the narrow region(at x=0.75),which dominates the upward flow inside the *** study the impact of model parameters on outputs,we applied normalized local sensitivity analysis and noticed that the most influential parameter for the longitudinal velocity profile is the dimensionless wave *** reabsorption parameter is sensitive for transverse velocity in the narrow region,and the Weissenberg number has a strong effect on the pressure inside the ***,the least sensitive parameters for the velocity components and pressure have been identified.

关键词： Sensitivity analysis williamson fluid regular perturbation method asymptotic approximation RK-Fehlberg method kidney flow

MHD Stagnation Point Flow of williamson fluid over a Stretching Cylinder with Variable Thermal Conductivity and Homogeneous/Heterogeneous Reaction

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Communications in Theoretical Physics 2017年第6期67卷 688-696页

作者： M.Bilal M.Sagheer S.Hussain Y.Mehmood Department of Mathematics Capital University of Science and Technology

The present study reveals the effect of homogeneous/hetereogeneous reaction on stagnation point flow of williamson fluid in the presence of magnetohydrodynamics and heat generation/absorption coefficient over a stretching cylinder. Further the effects of variable thermal conductivity and thermal stratification are also considered. The governing partial differential equations are converted to ordinary differential equations with the help of similarity *** system of coupled non-linear ordinary differential equations is then solved by shooting technique. MATLAB shooting code is validated by comparison with the previously published work in limiting case. Results are further strengthened when the present results are compared with MATLAB built-in function bvp4c. Effects of prominent parameters are deliberated graphically for the velocity, temperature and concentration profiles. Skin-friction coefficient and Nusselt number for the different parameters are investigated with the help of tables.

关键词： stagnation point flow homogeneous/heterogeneous reaction williamson fluid stretching cylinder variable thermal conductivity thermal stratification

Peristaltic flow of williamson fluid in a convected walls channel with Soret and Dufour effects

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International Journal of Biomathematics 2016年第1期9卷 223-241页

作者： T. Hayat H. Yasmin A. Alsaedt M. Ayub Department of MathematicsQuaid-I-Azam University 45320 Islamabad 44000 Pakistan Department of Mathematics Faculty of Science King Abdulaziz University Jeddah 21589 Saudi Arabia Department of MathematicsCOMSATS Institute of Information Technology G. T. Road Wah Cantt 47040 Pakistan

Peristaltic flow of magnetohydrodynamic （MHD） williamson fluid in a symmetric chan- nel is addressed. Modeling is given with Sorer and Dufour effects. Channel walls have compliant properties. Analysis has been carried out through long wavelength and low Reynolds number approach. The obtained series solutions for small Weissenberg number are developed. Impact of variables reflecting the salient features of wall properties, Blot numbers and Soret and Dufour on the velocity, temperature and concentration has been point out. Trapping phenomenon is also analyzed.

关键词： williamson fluid compliant walls convective conditions Soret and Dufoureffects.

Mathematical study for peristaltic flow of williamson fluid in a curved channel

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International Journal of Biomathematics 2015年第1期8卷 59-68页

作者： E. N. Maraj Noreen Sher Akbar S. Nadeem NICE (SCEE) National University of Sciences and Technology Islamabad Pakistan DBS H CEME National University of Sciences and Technology Islamabad Pakistan Department of Mathematics Quaid-i-Azam University Islamabad 44000 Pakistan

In this paper, we have investigated the peristaltic flow of williamson fluid in a curved channel. The governing equations of williamson fluid model for curved channel are derived including the effects of curvature. The highly nonlinear partial differential equa- tions are simplified by using the wave frame transformation, long wavelength and low Reynolds number assumptions. The reduced nonlinear partial differential equation is solved analytically with the help of homotopy perturbation method. The physical features of pertinent parameters have been discussed by plotting the graphs of pressure rise, velocity profile and stream functions.

关键词： Peristaltic flow williamson fluid curved channel

Convective heat and mass transfer analysis on peristaltic flow of williamson fluid with Hall effects and Joule heating

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International Journal of Biomathematics 2014年第5期7卷 201-227页

作者： Humaira Yasmin T. Hayat Naif Alotaibi Huijun Gao Department of MathematicsQuaid-I-Azam University 45320 Islamabad 44000 Pakistan Department of Electrical and Computer Engineering Faculty of Engineering King Abdulaziz University Jeddah 21589 Saudi Arabia Research Institute of Intelligent Control and Systems Harbin Institute of Technology Harbin 150080 P. R. China

This paper deals with the peristaltic flow of an incompressible and electrically conducting williamson fluid in a symmetric planar channel with heat and mass transfer. Hall effects, viscous dissipation and Joule heating are also taken into consideration. Mathematical model is presented by using the long wavelength and low Reynolds number approximations. The differential equations governing the flow are highly nonlinear and thus perturbation solution for small Weissenberg number （0 〈 We 〈 1） is presented. Effects of the heat and mass transfer Biot numbers and Hall parameter on the longitudinal velocity, temperature, concentration and pumping characteristics are studied in detail. Main observations are presented in the concluding section, The streamlines pattern and trapping are also given due attention.

关键词： williamson fluid convective heat and mass transfer Joule heating Halleffects pumping and trapping.

Entropy optimization in cubic autocatalysis chemical reactive flow of williamson fluid subjected to viscous dissipation and uniform magnetic field

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Journal of Central South University 2019年第5期26卷 1218-1232页

作者： M. IJAZ KHAN Sania JAVED Tasawar HAYAT M. WAQAS Ahmed ALSAEDI Department of Mathematics Quaid-I-Azam UniversityIslamabad 44000Pakistan Nonlinear Analysis and Applied Mathematics (NAAM) Research Group Department of MathematicsFaculty of ScienceKing Abdulaziz UniversityJeddah 21589Saudi Arabia

This research elaborates magnetohydrodynamics (MHD) impact on non-Newtonian (williamson) fluid flow by stretchable rotating *** disks are rotating with different angular velocities and different stretching *** dissipation aspect is considered for energy expression *** generation analysis is described via implementation of thermodynamic second *** processes (heterogeneous and homogeneous) subjected to entropy generation are introduced first time in ***-layer approach is employed for *** variables are introduced for non-dimensionalization of governing *** procedure yields convergence of solutions subjected to computations of highly nonlinear *** significant characteristics of sundry factors against thermal,velocity and solutal fields are described ***,tabular results are addressed for engineering quantities (skin-friction coefficient,Nusselt number).The outcomes certify an increment in temperature distribution for Weissenberg (We) and Eckert (Ec) numbers.

关键词： entropy generation viscous dissipation williamson fluid uniform magnetic felid quartic autocatalysis chemical reaction

Mixed convection analysis for blood flow through arteries on williamson fluid model

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International Journal of Biomathematics 2015年第4期8卷 53-72页

作者： Noreen Sher Akbar DBSg_4H, CEME National University of Sciences and Technology Islamabad Pakistan

In this paper, the blood flow through a tapered artery with a stenosis by considering axially non-symmetric but radially symmetric mild stenosis on blood flow characteris- tics is analyzed, assuming the flow is steady and blood is treated as williamson fluid. The effects of mixed convection heat and mass transfer are also carried out. Perturbation solutions have been calculated for velocity, temperature, concentration, resistance impedance, wall shear stress and shearing stress at the stenosis throat. The graphical results of different types of tapered arteries （i.e. converging tapering, diverging tapering, non-tapered artery） have been examined for different parameters of interest. Streamlines have been plotted at the end of the paper.

关键词： williamson fluid blood flow tapered artery stenosis perturbation solution mixed convection heat and mass transfer.

Darcy–Forchheimer Three-Dimensional Flow of williamson Nanofluid over a Convectively Heated Nonlinear Stretching Surface

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Communications in Theoretical Physics 2017年第9期67卷 387-394页

作者： Tasawar Hayat Arsalan Aziz Taseer Muhammad Ahmed Alsaedi Department of Mathematics Quaid-I-Azam University Nonlinear Analysis and Applied Mathematics (NAAM) Research Group Department of Mathematics Faculty of ScienceKing Abdulaziz University

The present study elaborates three-dimensional flow of williamson nanoliquid over a nonlinear stretchable surface. fluid flow obeys Darcy–Forchheimer porous medium. A bidirectional nonlinear stretching surface generates the flow. Convective surface condition of heat transfer is taken into consideration. Further the zero nanoparticles mass flux condition is imposed at the boundary. Effects of thermophoresis and Brownian diffusion are considered. Assumption of boundary layer has been employed in the problem formulation. Convergent series solutions for the nonlinear governing system are established through the optimal homotopy analysis method(OHAM). Graphs have been sketched in order to analyze that how the velocity, temperature and concentration distributions are affected by distinct emerging flow parameters. Skin friction coefficients and local Nusselt number are also computed and discussed.

关键词： three-dimensional flow williamson fluid nanoparticles Darcy-Forchheimer porous medium con-vective boundary condition nonlinear stretching surface