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Heat Transfer of casson fluid over a Vertical Plate with Arbitrary Shear Stress and Exponential Heating

Computers, Materials & Continua 2022年第4期71卷 1025-1034页

作者： Dolat Khan Gohar Ali Arshad Khan Ilyas Khan Department of Mathematics City University of Science and Information TechnologyPeshawar25000Pakistan Institute of Computer Sciences and Information Technology The University of AgriculturePeshawarPakistan Faculty of Mathematics and Statistics Ton Duc Thang UniversityHo Chi Minh City72915Vietnam

The basic objective of this work is to study the heat transfer of casson fluid of non-Newtonian nature.The fluid is considered over a vertical plate such that the plate exhibits arbitrary wall shear stress at the boundary.Heat transfers due to exponential plate heating and natural convection are due to buoyancy force.Magnetohydrodynamic(MHD)analysis in the occurrence of a uniform magnetic field is also considered.The medium over the plate is porous and hence Darcy’s law is applied.The governing equations are established for the velocity and temperature fields by the usual Boussinesq approximation.The problem is first written in dimensionless form using some useful non-dimensional quantities and then solved.The exact analysis is performed and hence solutions via integral transform are established.The analysis of various pertinent parameters on temperature distribution and velocity field are reported graphically.It is found that pours medium permeability parameter retards the fluid motion whereas,velocity decreases with increasing magnetic parameter.Velocity and temperature decrease with increasing Prandtl number whereas the Grashof number enhances the fluid motion.Further,it is concluded from this study that the results obtained here are more general and in a limiting sense several other solutions can be recovered.The Newtonian fluid results can be easily established by taking the casson parameter infinitely large i.e.,whenβ→∞.

关键词： Heat transfer casson fluid shear stress natural convection

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Importance of induced magnetic field and exponential heat source on convective flow of casson fluid in a micro-channel via AGM

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Theoretical & Applied Mechanics Letters 2022年第3期12卷 156-164页

作者： A.Hasibi A.Gholami Z.Asadi D.D.Ganji Department of Mechanical Engineering Babol University of TechnologyP.O.Box 484BabolIran Department of Mechanical Engineering Islamic Azad UniversitySariIran

The study of the natural convective flow of a fluid in the presence of an induced magnetic field has always been of considerable importance due to its many applications in various areas of science,technology,and industry,such as the operation of magnetohydrodynamic generators.This study addresses an analysis of exponential heat source and induced magnetic field on the second-class convection of casson fluid in a microchannel.The flow is in a vertical microchannel organized by two vertical plates.The answer to governing equations has been grabbed for temperature field,induced magnetic field,and velocity via Akbari-Ganji’s method(AGM).Nusselt number,skin friction coefficient,and current density are approximated.Graphs that describe the conclusion of influential physical variables on velocity,temperature,current density,induced magnetic field,and skin friction coefficient distributions are shown.Comparison of results with numerical method(Runge-Kutta-Fehlberg,RKF-45),homotopy perturbation method,and AGM confirms the accuracy of answers obtained with AGM.

关键词： AGM method casson fluid Microchannel Exponential heat source

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casson fluid flow and heat transfer over a nonlinearly stretching surface

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Chinese Physics B 2013年第7期22卷 298-302页

作者： Swati Mukhopadhyay Department of Mathematics the University of Burdwan

A boundary layer analysis is presented for non-Newtonian fluid flow and heat transfer over a nonlinearly stretching surface. The casson fluid model is used to characterize the non-Newtonian fluid behavior. By using suitable transformations, the governing partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations. Numerical solutions of these equations are obtained with the shooting method. The effect of increasing casson parameter is to suppress the velocity field. However the temperature is enhanced with the increasing casson parameter.

关键词： nonlinear stretching casson fluid heat transfer similarity transformations

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A Fractal-Fractional Model for the MHD Flow of casson fluid in a Channel

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Computers, Materials & Continua 2021年第5期67卷 1385-1398页

作者： Nadeem Ahmad Sheikh Dennis Ling Chuan Ching Thabet Abdeljawad Ilyas Khan Muhammad Jamil Kottakkaran Sooppy Nisar Fundamental and Applied Science Department Universiti Teknologi PETRONASPerak32610Malaysia Department of Mathematics City University of Science and Information TechnologyPeshawar25000Pakistan Department of Mathematics and General Sciences Prince Sultan University11586RiyadhSaudi Arabia Department of Medical Research China Medical University40402TaichungTaiwanChina Department of Computer Science and Information Engineering Asia UniversityTaichungTaiwanChina Faculty of Mathematics and Statistics Ton Duc Thang UniversityHo Chi Minh City72915Vietnam Department of Geosciences Universiti Teknologi PETRONASPerak32610Malaysia Department of Earth Sciences COMSATS University IslamabadAbbottabad CampusAbbottabad22010Pakistan Department of Mathematics College of Arts and SciencesPrince Sattam bin Abdulaziz UniversityWadi Aldawaser11991Saudi Arabia

An emerging definition of the fractal-fractional operator has been used in this study for the modeling of casson fluid flow.The magnetohydrodynamics flow of casson fluid has cogent in a channel where the motion of the upper plate generates the flow while the lower plate is at a static position.The proposed model is non-dimensionalized using the Pi-Buckingham theorem to reduce the complexity in solving the model and computation time.The non-dimensional fractal-fractional model with the power-law kernel has been solved through the Laplace transform technique.The Mathcad software has been used for illustration of the influence of various parameters,i.e.,Hartman number,fractal,fractional,and casson fluid parameters on the velocity of fluid flow.Through graphs and tables,the results have been implemented and it is shown that the boundary conditions are fully satisfied.The results reveal that the flow velocity is decreasing with the increasing values of the Hartman number and is increasing with the increasing values of the casson fluid parameter.The findings of the fractal-fractional model have elucidated that the memory effect of the flow model has higher quality than the simple fractional and classical models.Furthermore,to show the validity of the obtained closed-form solutions,special cases have been obtained which are in agreement with the already published solutions.

关键词： Fractal-fractional derivative casson fluid MHD flow exact solutions

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Numerical Investigation of Micropolar casson fluid over a Stretching Sheet with Internal Heating

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Communications in Theoretical Physics 2017年第4期67卷 443-448页

作者： Zaffar Mehmood R.Mehmood Z.Iqbal Department of Mathematics HITEC UniversityTaxilaPakistan

This theoretical study investigates the microrotation effects on mixed convection flow induced by a stretching sheet. casson fluid model along with microrotation is considered to model the governing flow problem. The system is assumed to undergo internal heating phenomenon. The governing physical problem is transformed into system of nonlinear ordinary differential equations using scaling group of transformations. These equations are solved numerically using Runge Kutta Fehlberg scheme coupled with shooting technique. Influence of sundry parameters for the case of strong and weak concentration of microelements on velocity, temperature, skin friction and local heat flux at the surface are computed and discussed. Lower skin friction and heat flux is observed for the case of weak concentration(n = 0.5)compared to strong concentration of microelements(n = 0.0) near the wall.

关键词： micropolar casson fluid mixed convection internal heating numerical solution

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Thermal radiation and slip effects on magnetohydrodynamic(MHD)stagnation point flow of casson fluid over a convective stretching sheet

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Propulsion and Power Research 2019年第2期8卷 138-146页

作者： Jawad Raza School of Quantitative Sciences Universiti Utara MalaysiaMalaysia University of Lahore Pakpattan CampusPakistan

Current study examines the combined effect of thermal radiation and velocity slip along a convective heated stretching sheet.magnetohydrodynamic(MHD)effect near the stagnation point is also under consideration.The main structure of partial differential equations attained in the form of momentum,energy and concentration equations.For a self-similar solution,the system of governing PDEs assimilated into the set of nonlinear ordinary differential equations by applying suitable similarity transformation.Resulting nonlinear ODEs are successfully solved via Runge-Kutta-Fehlberg method.All obtained unknown functions are discussed in detail after plotting the numerical results against different arising physical parameters.The validations of numerical results have been taken into account with two different numerical approaches and it is found to be in excellent agreement with the numerical results.The study reveals that concentration boundary layer thickness decreases by increasing the values of Schmidt number and increases by increasing the chemical reaction parameter.

关键词： Magnetic field casson fluid Stretching sheet Thermal radiation Chemical reaction

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Effects of chemical reaction and heat generation/absorption on magnetohydrodynamic(MHD)casson fluid flow over an exponentially accelerated vertical plate embedded in porous medium with ramped wall temperature and ramped surface concentration

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Propulsion and Power Research 2019年第1期8卷 35-46页

作者： Hari R.Kataria Harshad R.Patel Department of Mathematics.Faculty of Science The M.S.University of Baroda.Vadodara 390002India Applied Science&Humanities Depariment Sardar Vallabhbhai Pael Institute of TechnologyVasad 388306India

This article studies effects of heat generation/absorption and chemical reaction on the unsteady magnetohydrodynamic(MHD)casson fluid flow past over exponentially accelerated vertical plate embedded in porous medium.It is assumed that the bounding plate has ramped temperature with ramped surface concentration and isothermal temperature with ramped surface concentration.This phenomenon is modeled in the form of system of partial differential equations with initial and boundary conditions.The goveming dimensionless equations are solved using Laplace transfom technique and expressions for velocity,temperature and concentration profiles are obtained.Expressions for skin friction,Nusselt number and Sherwood number are also derived and represented in tabular form.Effect of pertinent parameters on velocity,temperature and concentration profiles are presented through graphically.

关键词： Magneto hydrody-namics casson fluid Skin friction Nusselt number Sherwood number

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Heat and mass transfer in magnetohydrodynamic(MHD)casson fluid flow past over an oscillating vertical plate embedded in porous medium with ramped wall temperature

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Propulsion and Power Research 2018年第3期7卷 257-267页

作者： Hari R.Kataria Harshad R.Patel Department of Mathematics Faculty of ScienceThe M.S.University of BarodaVadodara 390002GujaratIndia Applied Science&Humanities Department Sardar Vallabhbhai Patel Institute of TechnologyVasad 388306India

The present paper is concerned with the study of flow,heat and mass transfer characteristics in the unsteady natural convective magneto hydrodynamics casson fluid flow past over an oscillating vertical plate.The governing partial differential equations are solved analytically using Laplace transform technique and numerically using Matlab software.Expressions of skin friction,Nusselt number and Sherwood number are obtained.The features of the fluid flow,heat and mass transfer characteristics are analyzed by plotting graphs and the physical aspects are discussed in detail.

关键词： Magneto hydrodynamics casson fluid Ramped temperature Skin friction Nusselt number Sherwood number

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Non-Aligned Stagnation Point Flow of a casson fluid Past a Stretching Sheet in a Doubly Stratified Medium

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fluid Dynamics & Materials Processing 2019年第3期15卷 233-251页

作者： N.Vijaya G.Venkata Ramana Reddy Y.Hara Krishna Koneru Lakshmaiah Education Foundation VaddeswaramGuntur522502India

This paper investigates the problem of oblique hydro magnetic stagnation point flow of an electrically conducting casson fluid over stretching sheet embedded in a doubly stratified medium in the presence of thermal radiation and heat source/absorption with first order chemical reaction.It is assumed that the fluid impinges on the wall obliquely.Similarity variables were used to convert the partial differential equations to ordinary differential equations.The transformed ordinary differential equations are solved numerically using Runge-Kutta-Fehlberg method with shooting technique.It is observed that a boundary layer is formed when the stretching velocity of the surface is less than the in viscid free stream velocity at a point decreases with increase in the non-Newtonian rheology parameter.The augmentation of the temperature is observed with the magnetic parameter,heat source parameter and thermal radiation parameter while a reverse effect with thermal stratification number,Prandtl number and the velocity ratio parameter.Influence of Skin friction coefficient,Nusselt number and Sherwood number on the flow configurations for different values of pertinent parameters are portrayed graphically and discussed.Numerical results are compared with the published results and are found to be in good agreement with previously published results as special cases of present problem.The mass concentration is seen to be decrease with Schmidt number,chemical reaction parameter and solutal stratification number.

关键词： Magnetic parameter heat source prandtl number chemical reaction casson fluid free stream stagnation flow parameters

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Flow of casson fluid with nanoparticles

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Applied Mathematics and Mechanics(English Edition) 2016年第4期37卷 459-470页

作者： T.HAYAT S.ASAD A.ALSAEDI Department of Mathematics Quaid-i-Azam University Nonlinear Analysis and Applied Mathematics (NAAM) Research Group Department of Mathematics Faculty of Science King Abdulaziz University Department of Mathematics COMSATS Institute of Information Technology

The boundary layer flow of a casson fluid due to a stretching cylinder is discussed in the presence of nanoparticles and thermal radiation. All physical properties of the casson fluid except the thermal conductivity are taken constant. Appropriate transformations yield the nonlinear ordinary differential systems. Convergent series solutions are developed and analyzed. The numerical results for the local Nusselt and Sherwood numbers are demonstrated. It is found that an increase in the strength of the Brownian motion decays the temperature noticeably. However, the rate of heat transfer and the concentration of the nanoparticles at the surface increase for larger Brownian motion parameters.

关键词： casson fluid stretching cylinder nanofluid

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