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Transport mechanism in chemically reactive hybrid nanofluid flow containing gyrotactic micro-organisms over a curved oscillatory surface

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Applied Mathematics and Mechanics(English Edition) 2025年第1期46卷 177-192页

作者： M.NAVEED M.IMRAN T.ASGHAR z.abbas Department of Mathematics Division of Science and TechnologyUniversity of Education Department of Mathematics The Islamia University of Bahawalpur

This paper examines the transport analysis, including both heat transfer and mass transfer, in hybrid nanofluid flow containing gyrotactic microorganisms towards a curved oscillatory surface. The influence of magnetic fields is also inspected in terms of their physical characteristics. To depict the phenomena of transport, modified versions of both Fick's and Fourier's laws are used. Additionally, the characteristics of both heterogeneous and homogeneous chemical reactions are also incorporated. Utilizing a curvilinear coordinate system, the flow problem is formulated as partial differential equations(PDEs)for momentum, concentration, microorganism field, and energy. An analytical solution to the obtained flow equations is achieved utilizing the homotopy analysis method(HAM).The effects of significant flow parameters on the pressure and microorganism fields, velocity, oscillation velocity, concentration, and temperature distributions are shown via graphs. Furthermore, the variations in skin friction, mass transfer rate, heat transfer rate, and local motile number due to different involved parameters are presented in tables and are analyzed in detail. Graphical results indicate that the curves of velocity and temperature fields are enhanced as the values of the solid volume fraction variables *** is also verified that the concentration rate field decreases as the values of the homogeneous reaction strength parameter and the radius of curvature parameter increase, and it increases with the Schmidt number and the heterogeneous reaction strength *** outcomes show a favorable response of the motile number to advanced values of the Peclet number, the Schmidt number, the microorganism difference parameter, and the bio-convective Lewis number.

关键词： Peclet number

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Flow of Eyring-Powell liquid due to oscillatory stretchable curved sheet with modified Fourier and Fick’s model

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Applied Mathematics and Mechanics(English Edition) 2021年第10期42卷 1461-1478页

作者： M.IMRAN z.abbas M.NAVEED Department of Mathematics The Islamia University of BahawalpurBahawalpur 63100Pakistan Department of Mathematics Khwaja Fareed University of Engineering&Information TechnologyRahim Yar Khan 64200Pakistan

This study deals with the features of the mass and heat transport mechanism by adopting a modified version of Fourier and Fick’s model known as the CattaneoChristov double diffusive *** time-dependent magnetohydrodynamic(MHD)flow of the Eyring-Powell liquid across an oscillatory stretchable curved sheet in the presence of Fourier and Fick’s model is *** acquired set of flow equations is transformed into the form of nonlinear partial differential equations(PDEs)by applying appropriate similarity variables.A convergent series solution to the developed nonlinear equations is accomplished with the help of an analytical approach,i.e.,the homotopy analysis method(HAM).The consequences of diverse parameters,including the dimensionless EyringPowell liquid parameter,the radius of curvature,the Schmidt/Prandtl numbers,the ratio of the oscillatory frequency of the sheet to its stretchable rate constant,the mass and thermal relaxation variables involved in the flow,and the heat and mass properties,are displayed through graphs and *** is noted from this study that the amplitude of the pressure distribution rises for the high parametric values of the Eyring-Powell parameter.

关键词： oscillatory stretchable curved surface magnetohydrodynamic(MHD) Eyring-Powell liquid Cattaneo-Christov double diffusion analytical technique

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Axisymmetric Stagnation-Point Flow with a General Slip Boundary Condition over a Lubricated Surface

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Chinese Physics Letters 2012年第2期29卷 126-129页

作者： M.Sajid K.Mahmood z.abbas The Abdus Salam International Centre for Theoretical Physics Strada Costiera 1134014TriesteItaly Department of Mathematics Riphah International UniversityIslamabad 44000Pakistan Department of Mathematics The Islamia University of BahawalpurBahawalpurPakistan

We investigate the axisymmetric stagnation-point flow of a viscous fluid over a lubricated surface by imposing a generalized slip condition at the fluid-fluid *** power law non-Newtonian fluid is considered as a *** lubrication layer is thin and assumed to have a variable *** transformed nonlinear ordinary differential equation governing the flow is linearized using *** method of superposi-tion is adopted to convert the boundary value problem into an initial value problem and the solution is obtained numerically by using the fourth-order Runge-Kutta *** results are discussed to see the influence of pertinent *** limiting cases of Navier and no-slip boundary conditions are obtained as the special cases and found to be in excellent agreement with the existing results in the literature.

关键词： boundary ordinary assumed

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Unsteady three-dimensional MHD flow of the micropolar fluid over an oscillatory disk with Cattaneo-Christov double diffusion

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Applied Mathematics and Mechanics(English Edition) 2019年第10期40卷 1471-1486页

作者： A.RAUF S.A.SHEHzAD z.abbas T.HAYAT Department of Mathematics COMSATS University Islamabad Sahiwal 57000 Pakistan Department of Mathematics The Islamia University of Bahawalpur Bahawalpur 63100 Pakistan Department of Mathematics Quiad-i-Azam University Islamabad 44000 Pakistan

Cattaneo-Christov heat and mass flux models are considered rather than Fourier and Fick laws due to the presence of thermal and concentration transport hyperbolic phenomena. The generalized form of the Navier-Stokes model is considered in hydromagnetic flow. Three-dimensional (3D) unsteady fluid motion is generated by the periodic oscillations of a rotating disk. Similarity transformations are used to obtain the normalized fluid flow model. The successive over relaxation (SOR) method with finite difference schemes are accomplished for the numerical solution of the obtained partial differential non-linear system. The flow features of the velocity, microrotation, temperature, and concentration fields are discussed in pictorial forms for various physical flow parameters. The couple stresses and heat and mass transfer rates for different physical quantities are explained via tabular forms. For better insight of the physical fluid model, 3D fluid phenomena and two-dimensional (2D) contours are also plotted. The results show that the micropolar fluids contain microstructure having non-symmetric stress tensor and are useful in lubrication theory. Moreover, the thermal and concentration waves in Cattaneo-Christov models have a significance role in the laser heating and enhancement in thermal conductivity.

关键词： three-dimensional (3D) flow micropolar fluid magnetohydrodynamics (MHD) Cattaneo-Christov theory oscillatory disk

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A revised Cattaneo-Christov micropolar viscoelastic nanofluid model with combined porosity and magnetic effects

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Applied Mathematics and Mechanics(English Edition) 2020年第3期41卷 521-532页

作者： S.A.SHEHzAD S.U.KHAN z.abbas A.RAUF Department of Mathematics COMSATS University IslamabadSahiwal 57000Pakistan Department of Mathematics The Islamia University of BahawalpurBahawalpur 63100Pakistan

The dynamics of non-Newtonian fluids along with nanoparticles is quite interesting with numerous industrial applications. The current predominately predictive modeling deals with the flow of the viscoelastic micropolar fluid in the presence of nanoparticles. A progressive amendment in the heat and concentration equations is made by exploiting the Cattaneo-Christov(C-C) heat and mass flux expressions. Besides, the thermal radiation effects are contributed in the energy equation and aspect of the radiation parameter, and the Prandtl number is specified by the one-parameter *** formulated expressions are converted to the dimensionless forms by relevant similarity functions. The analytical solutions to these expressions have been erected by the homotopy analysis method. The variations in physical quantities, including the velocity,the temperature, the effective local Nusselt number, the concentration of nanoparticles,and the local Sherwood number, have been observed under the influence of emerging parameters. The results have shown good accuracy compared with those of the existing literature.

关键词： micropolar viscoelastic fluid nanoparticle thermal radiation Cattaneo-Christov(C-C)theory porous medium

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Thermally Radiative Viscous Fluid Flow Over Curved Moving Surface in Darcy-Forchheimer Porous Space

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Communications in Theoretical Physics 2019年第3期71卷 259-266页

作者： A.Rauf z.abbas S.A.Shehzad T.Mushtaq Department of Mathematics The Islamia University of Bahawalpur Department of Mathematics COMSATS University Islamabad

A numerical analysis is developed for incompressible hydromagnetic viscous fluid passed through a curved stretching surface. Fluid saturated by porous space is bounded by curved surface. Term of porous medium is characterized by implementation of Darcy-Forchheimer theory. Adequate similarity variables are implemented to develop a system of non-linear ordinary differential system of equations, which govern the flow behavior. The impact of radiation constraint and Eckert number is incorporated in the energy equation. Numerical scheme based on RKF45 technique is implemented to solve the derived flow model. Prescribed heat flux(PHF) and prescribed surface temperature(PST) boundary conditions are utilized on temperature with Prescribed Surface Concentration(PSC) and Prescribed Mass Flux(PMF)on concentration. Flow behavior is discussed for both the slip and no-slip conditions. Dimensionless physical quantities are presented through graphs and tables.

关键词： viscous fluid porous medium curved stretching sheet radiation Joule heating

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Numerical simulation of chemically reactive Powell-Eyring liquid flow with double diffusive Cattaneo-Christov heat and mass flux theories

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Applied Mathematics and Mechanics(English Edition) 2018年第4期39卷 467-476页

作者： A.RAUF z.abbas S.A.SHEHzAD A.ALSAEDI T.HAYAT Department of Mathematics The Islamia University of Bahawalpur Department of Mathematics COMSATS Institute of Information Technology Department of Mathematics Faculty of Science King Abdulaziz University Department of Mathematics Quaid-i-Azam University

A numerical study is reported for two-dimensional flow of an incompressible Powell-Eyring fluid by stretching the surface with the Cattaneo-Christov model of heat diffusion. Impacts of heat generation/absorption and destructive/generative chemical reactions are considered. Use of proper variables leads to a system of non-linear dimensionless expressions. Velocity, temperature and concentration profiles are achieved through a finite difference based algorithm with a successive over-relaxation(SOR) method. Emerging dimensionless quantities are described with graphs and tables. The temperature and concentration profiles decay due to enhancement in fluid parameters and Deborah numbers.

关键词： Powell-Eyring fluid Cattaneo-Christov model chemical reaction finite difference

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Numerical and statistical approach for Casson-Maxwell nanofluid flow with Cattaneo-Christov theory

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Applied Mathematics and Mechanics(English Edition) 2021年第7期42卷 1063-1076页

作者： T.MUSHTAQ A.RAUF S.A.SHEHzAD F.MUSTAFA M.HANIF z.abbas Department of Mathematics COMSATS University IslamabadVehari CampusVehari 61100Pakistan Department of Mathematics COMSATS University IslamabadSahiwal CampusSahiwal 57000Pakistan Department of Mathematics The Islamia University of BahawalpurBahawalpur 63100Pakistan

The rheological features of an incompressible axi-symmetric Casson-Maxwell nanofluid flow between two stationary disks are *** lower permeable disk is located at z=-a,while the upper disk is placed at z=*** the disks are porous and subjected to uniform *** fluid properties such as thermal conductivity vary with *** Cattaneo-Christov thermal expression is implemented along with the Buongiorno nanofluid *** operating the similarity functions,the reduced form of the fluid model in terms of ordinary differential equations is obtained and solved by the bvp4 c numerical *** physical quantities are demonstrated graphically on the velocity and temperature ***-dimensional flow arrangements and twodimensional contour patterns against several dimensionless variables are also *** numerical values of the local Nusselt and Sherwood numbers for various quantities are presented in tabular *** intensity of the linear relationship between the Nusselt and Sherwood numbers is assessed through Pearson’s product-moment correlation *** statistical implication of the linear association between variables is also examined by the t-test statistic approach.

关键词： Casson-Maxwell fluid porous disk Buongiorno theory variable thermal conductivity Cattaneo-Christov model uniform injection

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Entropy generation for mixed convection flow in vertical annulus with two regions hydromagnetic viscous and Cu-Ag water hybrid nanofluid through porous zone: a comparative numerical study

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Propulsion and Power Research 2022年第3期11卷 401-415页

作者： T.Rahim J.Hasnain N.Abid z.abbas Department of Mathematics The Islamia University of BahawalpurBahawalpur63100Pakistan Department of Computer Sciences Bahria UniversityIslamabad44000Pakistan

The primary determination of this study is a numerical investigation of the entropygeneration (EG) in the steady two-region flow of viscous fluid and hybrid nanofluid (NF) in along-infinite vertical annulus having a clear region as well as porous media. Stoke’s and single-phase NF models are used to study the viscous fluid and hybrid nanofluid (HNF) heat transferdevelopments, respectively. Two types of nanoparticles are taken, such as copper (Cu) and sil-ver (Ag) within base fluid water to make it a HNF. Darcy-Brinkman law is also used to examinethe flow through the porous zone in the annulus. Necessary quantities have been used in thesystem of equations to transfer them into non-dimensional forms. For momentum and energytransport, the numerical results are evaluated for various model parameters and are examinedvia the shooting method in MATHEMATICA. It is noted that the momentum and energy trans-port are more significant when two immiscible fluids in a clear vertical annulus are taken. Thefindings also indicate that two-phase momentum and heat flow are greater when a NF is used in Region-II and lower when a HNF is used. The temperature (in Region-II) falls with a high na-nomaterials volume fraction (see Figure 4) while it is increased when the Hartman number isincreased. Moreover, velocity declines with increment in nanomaterials volume fraction. Thus,higher thermal conductivity can be accomplished by using a magnetic field.

关键词： Two-phase flow Hybrid nanofluid Viscous fluid Porous zone Vertical annulus Entropy generation

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Dynamics of bioconvection flow of micropolar nanoparticles with Cattaneo-Christov expressions

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Applied Mathematics and Mechanics(English Edition) 2020年第9期41卷 1333-1344页

作者： S.A.SHEHzAD T.MUSHTAQ z.abbas A.RAUF S.U.KHAN I.TLILI Department of Mathematics COMSATS University IslamabadSahiwal 57000Pakistan Department of Mathematics COMSATS University IslamabadVehari 61100Pakistan Department of Mathematics The Islamia University of BahawalpurBahawalpur 63100Pakistan Institute of Research and Development Duy Tan UniversityDa Nang 550000Vietnam Faculty of Civil Engineering Duy Tan UniversityDa Nang 550000Vietnam

A numerical analysis is performed to analyze the bioconvective double diffusive micropolar non-Newtonian nanofluid flow caused by stationary porous *** consequences of the current flow problem are further extended by incorporating the Brownian and thermophoresis *** energy and mass species equations are developed by utilizing the Cattaneo and Christov model of heat-mass *** flow equations are converted into an ordinary differential model by employing the appropriate *** numerical solution is reported by using the MATLAB builtin bvp4c *** consequences of engineering parameters on the flow velocity,the concentration,the microorganisms,and the temperature profiles are evaluated *** numerical data for fascinating physical quantities,namely,the motile density number,the local Sherwood number,and the local Nusselt number,are calculated and executed against various parametric *** microrotation magnitude reduces for increasing magnetic *** intensity of the applied magnetic field may be utilized to reduce the angular rotation which occurs in the lubrication processes,especially in the suspension of *** the account of industrial applications,the constituted output can be useful to enhance the energy transport efficacy and microbial fuel cells.

关键词： bioconvection flow micropolar fluid nanoparticle Cattaneo-Christov theory porous disk

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