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Mechanism of Thermally Radiative Prandtl Nanofluids and Double-Diffusive Convection in Tapered Channel on peristaltic flow with Viscous Dissipation and Induced Magnetic Field

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Computer Modeling in Engineering & Sciences 2024年第2期138卷 1501-1520页

作者： Yasir Khan Safia Akram Maria Athar Khalid Saeed Alia Razia A.Alameer Department of Mathematics University of Hafr Al-BatinHafr Al-Batin31991Saudi Arabia MCS National University of Sciences and TechnologyIslamabadPakistan SEECS National University of Sciences and TechnologyIslamabadPakistan College of Aeronautical Engineering National University of Sciences and TechnologyIslamabadPakistan

The application of mathematical modeling to biological fluids is of utmost importance, as it has diverse applicationsin medicine. The peristaltic mechanism plays a crucial role in understanding numerous biological flows. In thispaper, we present a theoretical investigation of the double diffusion convection in the peristaltic transport of aPrandtl nanofluid through an asymmetric tapered channel under the combined action of thermal radiation andan induced magnetic field. The equations for the current flow scenario are developed, incorporating relevantassumptions, and considering the effect of viscous dissipation. The impact of thermal radiation and doublediffusion on public health is of particular interest. For instance, infrared radiation techniques have been used totreat various skin-related diseases and can also be employed as a measure of thermotherapy for some bones toenhance blood circulation, with radiation increasing blood flow by approximately 80%. To solve the governingequations, we employ a numerical method with the aid of symbolic software such as Mathematica and MATLAB.The velocity, magnetic force function, pressure rise, temperature, solute (species) concentration, and nanoparticlevolume fraction profiles are analytically derived and graphically displayed. The results outcomes are compared withthe findings of limiting situations for verification.

关键词： Double diffusion convection thermal radiation induced magnetic field peristaltic flow tapered asymmetric channel viscous dissipation Prandtl nanofluid

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Impact of Magnetic Field on a peristaltic flow with Heat Transfer of a Fractional Maxwell Fluid in a Tube

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Computers, Materials & Continua 2022年第9期72卷 6141-6153页

作者： Hanan S.Gafel Department of Mathematics Faculty of ScienceTaif UniversitySaudi Arabia

Magnetic field and the fractional Maxwell fluids’impacts on peristaltic flows within a circular cylinder tube with heat transfer was evaluated while assuming that they are preset with a low-Reynolds number and a long wavelength.Utilizing,the fractional calculus method,the problem was solved analytically.It was deduced for temperature,axial velocity,tangential stress,and heat transfer coefficient.Many emerging parameters and their effects on the aspects of the flow were illustrated,and the outcomes were expressed via graphs.A special focus was dedicated to some criteria,such as the wave amplitude’s effect,Hartman and Grashof numbers,radius and relaxation–retardation ratios,and heat source,which were under discussions on the axial velocity,tangential stress,heat transfer,and temperature coefficients across one wavelength.Multiple graphs of physical interest were provided.The outcomes state that the effect of the criteria mentioned beforehand(the Hartman and Grashof numbers,wave amplitude,radius ratio,heat source,and relaxation–retardation ratio)were quite evident.

关键词： peristaltic flow fractional maxwell fluid mass and heat transfer magneto-hydrodynamic flow

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peristaltic flow of Sisko fluid in a uniform inclined tube

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Acta Mechanica Sinica 2010年第5期26卷 675-683页

作者： Sohail Nadeem Noreen Sher Akbar Department of Mathematics Quaid-i-Azam University 45320

We have analyzed an incompressible Sisko fluid through an axisymmetric uniform tube with a sinusoidal wave propagating down its walls. The present analysis of non- Newtonian fluid is investigated under the considerations of long wavelength and low Reynolds number approximation. The analytic solution is obtained using （i） the regular perturbation method （ii） the Homotopy analysis method （HAM）. The comparison of both the solutions is presented graphically. The results for the pressure rise, frictional force and pressure gradient have been calculated numerically and the results are studied for various values of the physical parameters of interest, such as α （angle of inclination）, b^＊（Sisko fluid parameter）, Ф （amplitude ratio） and n （power law index）. Trapping phenomena is discussed at the end of the article.

关键词： peristaltic flow Sisko fluid Perturbation method Homotopy analysis method

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peristaltic flow of MHD Jeffrey fluid through finite length cylindrical tube

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Applied Mathematics and Mechanics(English Edition) 2011年第10期32卷 1231-1244页

作者： D.TRIPATHI N.ALI T.HAYAT M.K.CHAUBE A.A.HENDI Birla Institute of Technology and Science Pilani Hyderabad CampusHyderabad 500078India Department of Mathematics and Statistics International Islamic UniversityIslamabad 46000Pakistan Department of Mathematics Quaid-i-Azam UniversityIslamabad 45320Pakistan Department of Physics Faculty of ScienceKing Saud UniversityP.O.Box 1846Riyadh 11320Saudi Arabia Department of Applied Mathematics IT-BHUVaranasi 221005India

The present investigation studies the peristaltic flow of the Jeffrey fluid through a tube of finite length. The fluid is electrically conducting in the presence of an applied magnetic field. Analysis is carried out under the assumption of long wavelength and low Reynolds number approximations. Expressions of the pressure gradient, volume flow rate, average volume flow rate, and local wall shear stress are obtained. The effects of relaxation time, retardation time, Hartman number on pressure, local wall shear stress, and mechanical efficiency of peristaltic pump are studied. The reflux phenomenon is also investigated. The case of propagation of a non-integral number of waves along the tube walls, which are inherent characteristics of finite length vessels, is also examined.

关键词： peristaltic flow magnetohydrodynamics Jeffrey fluid finite length tube mechanical efficiency reflux

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peristaltic flow of Walter’s B fluid in endoscope

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Applied Mathematics and Mechanics(English Edition) 2011年第6期32卷 689-700页

作者： S.NADEEM N.S.AKBAR T.HAYAT A.A.HENDI Department of Mathematics Quaid-i-Azam University Department of Physics Faculty of ScienceKing Saud University

The peristaltic flow of a Walter＇s B fluid in an endoscope is studied. The problem is modeled in a cylindrical coordinate system. The main theme of the present analysis is to study the endoscopic effects on the peristaltic flow of the Waiter＇s B fluid. To the best of the authors＇ knowledge, no investigation has been made so far in the literatures to study the Walter＇s B fluid in an endoscope. Analytical solutions axe obtained using the regular perturbation method by taking 5 as a perturbation parameter. The approximate analytical solutions for the pressure rise and friction forces are evaluated using numerical integration. The effects of emerging parameters of the Waiter＇s B fluid are presented graphically.

关键词： peristaltic flow Walter＇s B fluid endoscope perturbation solution.

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Analysis of Combined Convective and Viscous Dissipation Effects for peristaltic flow of Rabinowitsch Fluid Model

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Journal of Bionic Engineering 2017年第1期14卷 182-190页

作者： Hina Sadaf Sohail Nadeem Department of Mathematics Quaid-i-Azam University Islamabad 44000 Pakistan

In this article, mathematical modeling for peristaltic flow of Rabinowitsch fluid model is considered in a non-uniform tube with combined effects of viscous dissipation and convective boundary conditions. Wall properties analysis is also taken into account. Non-dimensional differential equations are simplified by using the well-known assumptions of low Reynolds number and long wavelength. The influence of various parameters connected with this flow problem such as rigidity parameter E1, stiffness parameter E2, viscous damping force parameter E3, Brickman number and Biot number are plotted for velocity distribution, temperature profile and for stream function. Results are plotted and discussed in detail for shear thinning, shear thickening and for viscous fluid. It is found that velocity profile is an increasing function of rigidity parameter, stiffness parameter, and viscous damping force parameter for shear thinning and for viscous fluid, due to the less resistance offered by the walls but, quite opposite behavior is depicted for shear thickening fluids. It is seen that Brickman number relates to the viscous dissipation effects, so it contributes in enhancing fluid temperature for all cases.

关键词： peristaltic flow non-uniform tube viscous dissipation convective boundary condition exact solution,non-newtonian fluid

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Effects of rotation and magnetic field on the nonlinear peristaltic flow of a second-order fluid in an asymmetric channel through a porous medium

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Chinese Physics B 2013年第7期22卷 303-313页

作者： A. M. Abd-Alla S. M. Abo-Dahab H. D. El-Shahrany Department of Mathematics Faculty of ScienceTaif University Department of Mathematics Faculty of Science Department of Mathematics Faculty of ScienceSouth Valley University

In this paper, the effects of both rotation and magnetic field of the peristaltic transport of a second-order fluid through a porous medium in a channel are studied analytically and computed numerically. The material is represented by the constitutive equations for a second-order fluid. Closed-form solutions under the consideration of long wavelength and low Reynolds number is presented. The analytical expressions for the pressure gradient, pressure rise, friction force, stream function, shear stress, and velocity are obtained in the physical domain. The effects of the non-dimensional wave amplitude, porosity, magnetic field, rotation, and the dimensionless time-mean flow in the wave frame are analyzed theoretically and computed numerically. Numerical results are given and illustrated graphically in each case considered. Comparison was made with the results obtained in the presence and absence of rotation, magnetic field, and porosity. The results indicate that the effects of the non-dimensional wave amplitude, porosity, magnetic field, rotation, and the dimensionless time-mean flow are very pronounced in the phenomena.

关键词： peristaltic flow second-order fluid magnetic field porous medium

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Numerical Simulation of MHD peristaltic flow with Variable Electrical Conductivity and Joule Dissipation Using Generalized Differential Quadrature Method

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Communications in Theoretical Physics 2019年第5期71卷 509-518页

作者： Muhammad Qasim Zafar Ali Abderrahim Wakif Zoubair Boulahia Department of Mathematics COMSATS University Islamabad (CUI) Laboratory of Mechanics Faculty of Sciences Ain Chock Hassan Ⅱ University

In this paper, the MHD peristaltic flow inside wavy walls of an asymmetric channel is investigated, where the walls of the channel are moving with peristaltic wave velocity along the channel length. During this investigation,the electrical conductivity both in Lorentz force and Joule heating is taken to be temperature dependent. Also, the long wavelength and low Reynolds number assumptions are utilized to reduce the governing partial differential equations into a set of coupled nonlinear ordinary differential equations. The new set of obtained equations is then numerically solved using the generalized differential quadrature method(GDQM). This is the first attempt to solve the nonlinear equations arising in the peristaltic flows using this method in combination with the Newton-Raphson technique. Moreover, in order to check the accuracy of the proposed numerical method, our results are compared with the results of built-in Mathematica command NDSolve. Taking Joule heating and viscous dissipation into account, the effects of various parameters appearing in the problem are used to discuss the fluid flow characteristics and heat transfer in the electrically conducting fluids graphically. In presence of variable electrical conductivity, velocity and temperature profiles are highly decreasing in nature when the intensity of the electrical conductivity parameter is strengthened.

关键词： peristaltic flow MHD variable electrical conductivity Joule dissipation generalized differential quadrature method(GDQM)

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Heat transfer on peristaltic flow of fourth grade fluid in inclined asymmetric channel with partial slip

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Applied Mathematics and Mechanics(English Edition) 2012年第10期33卷 1313-1328页

作者： O.U.MEHMOOD N.MUSTAPHA S.SHAFIE Department of Mathematics Faculty of ScienceUniversiti Teknologi Malaysia81310 UTM JohorJohor BharuMalaysia

In this paper, the effects of slip and heat transfer are studied on the peristaltic transport of a magnetohydrodynamic （MHD） fourth grade fluid. The governing equations are modeled and solved under the long wavelength approximation by using a regular perturbation method. Explicit expressions of solutions for the stream function, the velocity, the pressure gradient, the temperature, and the heat transfer coefficient are presented. Pumping and trapping phenomena are analyzed for increasing the slip parameter. Further, the temperature profiles and the heat transfer coefficient are observed for various increasing parameters. It is found that these parameters considerably affect the considered flow characteristics. Comparisons with published results for the no-slip case are found in close agreement.

关键词： peristaltic flow fourth grade fluid heat transfer slip condition inclinedchannel

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Hybrid Effects of Thermal and Concentration Convection on peristaltic flow of Fourth Grade Nanofluids in an Inclined Tapered Channel: Applications of Double-Diffusivity

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Computer Modeling in Engineering & Sciences 2021年第6期127卷 901-922页

作者： Safia Akram Alia Razia MCS National University of Sciences and TechnologyIslamabadPakistan

This article brings into focus the hybrid effects of thermal and concentration convection on peristaltic pumping of fourth grade nanofluids in an inclined tapered channel.First,the brief mathematical modelling of the fourth grade nanofluids is provided along with thermal and concentration convection.The Lubrication method is used to simplify the partial differential equations which are tremendously nonlinear.Further,analytical technique is applied to solve the differential equations that are strongly nonlinear in nature,and exact solutions of temperature,volume fraction of nanoparticles,and concentration are studied.Numerical and graphical findings manifest the influence of various physical flow-quantity parameters.It is observed that the nanoparticle fraction decreases because of the increasing values of Brownian motion parameter and Dufour parameter,whereas the behaviour of nanoparticle fraction is quite opposite for thermophoresis parameter.It is also noted that the temperature profile decreases with increasing Brownian motion parameter values and rises with Dufour parameter values.Moreover,the concentration profile ascends with increasing thermophoresis parameter and Soret parameter values.

关键词： Nanofluids thermal and concentration convection peristaltic flow inclined tapered channel fourth grade fluid

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