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| 1 | Boundary layer flow of third grade nanofluid with Newtonian heating and viscous dissipation显示文摘Two-dimensional boundary layer flow of an incompressible third grade nanofluid over a stretching surface is investigated.Influence of thermophoresis and Brownian motion is considered in the presence of Newtonian heating and viscous dissipation.Governing nonlinear problems of velocity, temperature and nanoparticle concentration are solved via homotopic procedure.Convergence is examined graphically and numerically. Results of temperature and nanoparticle concentration are plotted and discussed for various values of material parameters, Prandtl number, Lewis number, Newtonian heating parameter, Eckert number and thermophoresis and Brownian motion parameters. Numerical computations are performed. The results show that the change in temperature and nanoparticle concentration distribution functions is similar when we use higher values of material parameters β1 andβ2. It is seen that the temperature and thermal boundary layer thickness are increasing functions of Newtonian heating parameter γ.An increase in thermophoresis and Brownian motion parameters tends to an enhancement in the temperature. | S.A.Shehzad Tariq Hussain T.Hayat M.Ramzan A.Alsaedi | 2015 | Journal of Central South University2015，22，1： | 8 |
| 2 | Analysis of Heat Transfer Phenomenon in Magnetohydrodynamic Casson Fluid Flow Through Cattaneo–Christov Heat Diffusion Theory显示文摘Heat transport phenomenon of two-dimensional magnetohydrodynamic Casson fluid flow by employing Cattaneo–Christov heat diffusion theory is described in this work. The term of heat absorption/generation is incorporated in the mathematical modeling of present flow problem. The governing mathematical expressions are solved for velocity and temperature profiles using RKF 45 method along with shooting technique. The importance of arising nonlinear quantities namely velocity, temperature, skin-friction and temperature gradient are elaborated via plots. It is explored that the Casson parameter retarded the liquid velocity while it enhances the fluid temperature. Further, we noted that temperature and thickness of temperature boundary layer are weaker in case of Cattaneo–Christov heat diffusion model when matched with the profiles obtained for Fourier's theory of heat flux. | G.K.Ramesh B.J.Gireesha S.A.Shehzad F.M.Abbasi | 2017 | Communications in Theoretical Physics2017，67，7： | 7 |
| 3 | Convective heat and mass transfer in MHD mixed convection flow of Jeffrey nanofluid over a radially stretching surface with thermal radiation显示文摘Mixed convection flow of magnetohydrodynamic(MHD) Jeffrey nanofluid over a radially stretching surface with radiative surface is studied. Radial sheet is considered to be convectively heated. Convective boundary conditions through heat and mass are employed. The governing boundary layer equations are transformed into ordinary differential equations. Convergent series solutions of the resulting problems are derived. Emphasis has been focused on studying the effects of mixed convection, thermal radiation, magnetic field and nanoparticles on the velocity, temperature and concentration fields. Numerical values of the physical parameters involved in the problem are computed for the local Nusselt and Sherwood numbers are computed. | M.BILAL ASHRAF T.HAYAT A.ALSAEDI S.A.SHEHZAD | 2015 | Journal of Central South University2015，22，3： | 6 |
| 4 | MHD three-dimensional flow of Jeffrey fluid with Newtonian heating显示文摘The magnetohydrodynamic(MHD) three-dimensional flow of Jeffrey fluid in the presence of Newtonian heating is investigated. Flow is caused by a bidirectional stretching surface. Series solutions are constructed for the velocity and temperature fields. Convergence of series solutions is ensured graphically and numerically. The variations of key parameters on the physical quantities are shown and discussed in detail. Constructed series solutions are compared with the existing solutions in the limiting case and an excellent agreement is noticed. Nusselt numbers are computed with and without magnetic fields. It is observed that the Nusselt number decreases in the presence of magnetic field. | S.A.Shehzad T.Hayat M.S.Alhuthali S.Asghar | 2014 | Journal of Central South University2014，21，4： | 6 |
| 5 | Flow of Casson nanofluid with viscous dissipation and convective conditions: A mathematical model显示文摘The magnetohydrodynamic(MHD) boundary layer flow of Casson fluid in the presence of nanoparticles is investigated.Convective conditions of temperature and nanoparticle concentration are employed in the formulation. The flow is generated due to exponentially stretching surface. The governing boundary layer equations are reduced into the ordinary differential equations. Series solutions are presented to analyze the velocity, temperature and nanoparticle concentration fields. Temperature and nanoparticle concentration fields decrease when the values of Casson parameter enhance. It is found that the Biot numbers arising due to thermal and concentration convective conditions yield an enhancement in the temperature and concentration fields. Further, we observed that both the thermal and nanoparticle concentration boundary layer thicknesses are higher for the larger values of thermophoresis parameter. The effects of Brownian motion parameter on the temperature and nanoparticle concentration are reverse. | T.HUSSAIN S.A.SHEHZAD A.ALSAEDI T.HAYAT M.RAMZAN | 2015 | Journal of Central South University2015，22，3： | 4 |
| 6 | Natural Convection of Fe_3O_4-Ethylene Glycol Nanofluid under the Impact of Electric Field in a Porous Enclosure显示文摘Free convection of Fe_3O_4-Ethylene glycol nanofluid in existence of Coulomb forces is studied. Effect of thermal radiation is taken into account. Properties of nanofluid are varied with supplied voltage and shape of nanoparticles. The bottom wall is considered as positive electrode. Control Volume based Finite Element Method is used to obtain the results, which are the roles of Darcy number(Da), radiation parameter(Rd), Rayleigh number(Ra), nanofluid volume fraction(φ), and supplied voltage(?φ). Results indicate that Nusselt number is an enhancing function of supplied voltage and Darcy number. Maximum values for temperature gradient are occurred for platelet shape nanoparticles. | M.Sheikholeslami S.A.Shehzad R.Kumar | 2018 | Communications in Theoretical Physics2018，69，6： | 3 |
| 7 | Mixed Convection Stagnation Point Flow of Casson Fluid with Convective Boundary Conditions显示文摘The mixed convection stagnation-point flow of an incompressible non-Newtonian fluid over a stretching sheet under convective boundary conditions is investigated.Mathematical formulation is presented for a Casson fluid.The resulting partial differential equations are converted into the ordinary differential equations by the suitable transformations.The velocity and temperature profiles are computed by employing the homotopy analysis method.The plotted graphs illustrate the flow and heat transfer characteristics and their dependence upon the embedded parameters.Numerical values of skin-friction coefficient and Nusselt number are given and examined.Comparison of the present results with the existing solution is also given. | T.Hayat S.A.Shehzad A.Alsaedi M.S.Alhothuali | 2012 | Chinese Physics Letters2012，29，11： | 3 |
| 8 | A revised Cattaneo-Christov micropolar viscoelastic nanofluid model with combined porosity and magnetic effects显示文摘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 approach.The 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. | S.A.SHEHZAD S.U.KHAN Z.ABBAS A.RAUF | 2020 | Applied Mathematics and Mechanics(English Edition)2020，41，3： | 3 |
| 9 | Optimal treatment of stratified Carreau and Casson nanofluids flows in Darcy-Forchheimer porous space over porous matrix显示文摘A comparative three-dimensional(3D)analysis for Casson-nanofluid and Carreau-nanofluid flows due to a flat body in a magnetohydrodynamic(MHD)stratified environment is presented.Flow is estimated to be suspended in a Darcy-Forchheimer medium.Soret and Dufour responses are also accommodated in the flow field.A moving(rotating)coordinate system is exercised to examine the bidirectionally stretched flow fields(flow,heat transfer,and mass transfer).Nanofluid is compounded by taking ethylene glycol/sodium alginate as base fluid and ferric-oxide(Fe3O4)as nanoparticles.Governing equations are handled by the application of optimal homotopy asymptotic method(OHAM),where convergence parameters are optimized through the classical least square procedure.The novel mechanism(hidden physics)due to appearing parameters is explored with the assistance of tabular and graphical expositions.Outcomes reveal the double behavior state for temperature field with thermal stratification/Dufour number,and for concentration field with Soret number due to the presence of turning points. | R.KUMAR R.KUMAR S.A.SHEHZAD A.J.CHAMKHA | 2020 | Applied Mathematics and Mechanics(English Edition)2020，41，11： | 2 |
| 10 | Hybrid nanomaterial flow and heat transport in a stretchable convergent/divergent channel:a Darcy-Forchheimer model显示文摘The flow behavior in non-parallel walls is an important factor of any physical model including cavity flow and canals, which is applicable for diverging/converging channel. The present communication explains that the flow of the hybrid nanomaterial subjected to the convergent/divergent channel has non-parallel walls. It is assumed that the hybrid nanomaterial movement is in the porous region. A Darcy-Forchheimer medium of porosity is considered to interpret the porosity features. A useful similarity function is adopted to get the strong ordinary coupled equations. Numerical solutions are achieved through the Runge-Kutta-Fehlberg(RKF) fourth-fifth order method, and they are validated with the existing results. Physical nature of the involving constraints is reported with the help of plots. It is explored that the velocity of divergent channel decreases, and convergent channel enhances for the higher solid volume faction. Further, the presence of inertia coefficient and porosity parameter amplifies the velocity at the wall. | G.K.RAMESH S.A.SHEHZAD I.TLILI | 2020 | Applied Mathematics and Mechanics(English Edition)2020，41，5： | 2 |
| 11 | Mixed convection flow of jeffrey nanofluid with thermal radiation and double stratification显示文摘This article addresses the two-dimensional laminar boundary layer flow of magnetohydrodynamic(MHD) Jeffrey nanofluid with mixed convection. Effects of thermal radiation, thermophoresis, Brownian motion and double stratifications are taken into account. Rosseland's approximation is utilized for the thermal radiation phenomenon. Convergent series solutions of velocity, temperature and nanoparticle concentration are developed. Graphs of dimensionless temperature and nanoparticle concentration are presented to investigate the influences of different emerging parameters. The values of skin-friction coefficient, local Nusselt and Sherwood numbers are computed and discussed for both Jeffrey and viscous fluids cases. We have observed that the temperature profile retarded for the larger values of Deborah number while an enhancement is noticed with the increasing values of ratio of relaxation to retardation times. Increasing values of thermal and nanoparticle concentration stratifications lead to a reduction in the temperature and nanoparticle concentration. The values of local Nusselt and Sherwood numbers are larger for the viscous fluid case when compared with Jeffrey fluid. | F.M.ABBASI S.A.SHEHZAD T.HAYAT M.S.ALHUTHALI | 2016 | Journal of Hydrodynamics2016，28，5： | 2 |
| 12 | Transient flows of Maxwell fluid with slip conditions显示文摘Two fundamental flows, namely, the Stokes and Couette flows in a Maxwell fluid are considered. The exact analytic solutions are derived in the presence of the slip condition. The Laplace transform method is employed for the development of such solutions. Limiting cases of no-slip and viscous fluids can be easily recovered from the present analysis. The behaviors of embedded flow parameters are discussed through graphs. | T.HAYAT S.ZAIB S.ASGHAR K.BHATTACHARYYA S.A.SHEHZAD | 2013 | Applied Mathematics and Mechanics(English Edition)2013，34，2： | 1 |
| 13 | Convective heat and mass transfer effects in three-dimensional flow of Maxwell fluid over a stretching surface with heat source显示文摘Heat and mass transfer effects in three-dimensional flow of Maxwell fluid over a stretching surface were addressed.Analysis was performed in the presence of internal heat generation/absorption. Concentration and thermal buoyancy effects were accounted. Convective boundary conditions for heat and mass transfer analysis were explored. Series solutions of the resulting problem were developed. Effects of mixed convection, internal heat generation/absorption parameter and Biot numbers on the dimensionless velocity, temperature and concentration distributions were illustrated graphically. Numerical values of local Nusselt and Sherwood numbers were obtained and analyzed for all the physical parameters. It is found that both thermal and concentration boundary layer thicknesses are decreasing functions of stretching ratio. Variations of mixed convection parameter and concentration buoyancy parameter on the velocity profiles and associated boundary layer thicknesses are enhanced. Velocity profiles and temperature increase in the case of internal heat generation while they reduce for heat absorption. Heat transfer Biot number increases the thermal boundary layer thickness and temperature. Also concentration and its associated boundary layer are enhanced with an increase in mass transfer Biot number. The local Nusselt and Sherwood numbers have quite similar behaviors for increasing values of mixed convection parameter, concentration buoyancy parameter and Deborah number. | T.Hayat M.Bilal Ashraf A.Alsaedi S.A.Shehzad | 2015 | Journal of Central South University2015，22，2： | 1 |
| 14 | Bio-Marangoni convection flow of Casson nanoliquid through a porous medium in the presence of chemically reactive activation energy显示文摘Bioconvection research is primarily focused on the augmentation of energy and mass species,which has implications in the processes intensification,mechanical,civil,electronics,and chemical engineering branches.Advanced bioconvection technology sectors include cooling systems for electronic devices,building insulation,and geothermal nuclear waste disposal.Hence,the present investigation is mainly discoursing the impact of Marangoni convention Casson nanoliquid flow under gyrotactic microorganisms over the porous sheet.The partial differential equations(PDEs)are re-structured into ordinary differential equations(ODEs)via suitable similar variables.These ODEs are numerically solved with the help of the spectral relaxation method(SRM).The numerical outcomes are illustrated graphically for various parameters over velocity,temperature,concentration,and bioconvection profiles.Three-dimensional(3 D)views of important engineering parameters are illustrated for various parameters.The velocity of the Casson nanoliquid increases with increasing the Marangoni parameter but decreases against higher porosity parameter.The surface drag force enhances for enhancement in the Marangoni number.The rate of mass transmission is higher for reaction rate constraint but diminishes for activation energy parameter.The higher radiative values augment the rate of heat transmission. | J.K.MADHUKESH G.K.RAMESH B.C.PRASANNAKUMARA S.A.SHEHZAD F.M.ABBASI | 2021 | Applied Mathematics and Mechanics(English Edition)2021，42，8： | 1 |
| 15 | Dynamics of bioconvection flow of micropolar nanoparticles with Cattaneo-Christov expressions显示文摘A numerical analysis is performed to analyze the bioconvective double diffusive micropolar non-Newtonian nanofluid flow caused by stationary porous disks.The consequences of the current flow problem are further extended by incorporating the Brownian and thermophoresis aspects.The energy and mass species equations are developed by utilizing the Cattaneo and Christov model of heat-mass fluxes.The flow equations are converted into an ordinary differential model by employing the appropriate variables.The numerical solution is reported by using the MATLAB builtin bvp4c method.The consequences of engineering parameters on the flow velocity,the concentration,the microorganisms,and the temperature profiles are evaluated graphically.The 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 values.The microrotation magnitude reduces for increasing magnetic parameters.The 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 flows.On the account of industrial applications,the constituted output can be useful to enhance the energy transport efficacy and microbial fuel cells. | S.A.SHEHZAD T.MUSHTAQ Z.ABBAS A.RAUF S.U.KHAN I.TLILI | 2020 | Applied Mathematics and Mechanics(English Edition)2020，41，9： | 1 |
| 16 | Thermally Radiative Viscous Fluid Flow Over Curved Moving Surface in Darcy-Forchheimer Porous Space显示文摘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. | A.Rauf Z.Abbas S.A.Shehzad T.Mushtaq | 2019 | Communications in Theoretical Physics2019，71，3： | 1 |
| 17 | 3D Casson nanofluid flow over slendering surface in a suspension of gyrotactic microorganisms with Cattaneo-Christov heat flux显示文摘A mathematical model is proposed to execute the features of the non-uniform heat source or sink in the chemically reacting magnetohydrodynamic(MHD) Casson fluid across a slendering sheet in the presence of microorganisms and Cattaneo-Christov heat flux. Multiple slips(diffusion, thermal, and momentum slips) are applied in the modeling of the heat and mass transport processes. The Runge-Kutta based shooting method is used to find the solutions. Numerical simulation is carried out for various values of the physical constraints when the Casson index parameter is positive, negative, or infinite with the aid of plots. The coefficients of the skin factors, the local Nusselt number, and the Sherwood number are estimated for different parameters, and discussed for engineering interest. It is found that the gyrotactic microorganisms are greatly encouraged when the dimensionless parameters increase, especially when the Casson fluid parameter is negative.It is worth mentioning that the velocity profiles when the Casson fluid parameter is positive are higher than those when the Casson fluid parameter is negative or infinite,whereas the temperature and concentration fields show exactly opposite phenomena. | V.NAGENDRAMMA C.S.K.RAJU B.MALLIKARJUNA S.A.SHEHZAD A.LEELARATHNAM | 2018 | Applied Mathematics and Mechanics(English Edition)2018，39，5： | 1 |
| 18 | Cattaneo-Christov heat and mass flux model for 3D hydrodynamic flow of chemically reactive Maxwell liquid显示文摘This research focuses on the Cattaneo-Christov theory of heat and mass flux for a three-dimensional Maxwell liquid towards a moving surface. An incompressible laminar flow with variable thermal conductivity is considered. The flow generation is due to the bidirectional stretching of sheet. The combined phenomenon of heat and mass transport is accounted. The Cattaneo-Christov model of heat and mass diffusion is used to develop the expressions of energy and mass species. The first-order chemical reaction term in the mass species equation is considered. The boundary layer assumptions lead to the governing mathematical model. The homotopic simulation is adopted to visualize the results of the dimensionless flow equations. The graphs of velocities, temperature, and concentration show the effects of different arising parameters. A numerical benchmark is presented to visualize the convergent values of the computed results. The results show that the concentration and temperature fields are decayed for the Cattaneo-Christov theory of heat and mass diffusion. | S.A.SHEHZAD T.HAYAT A.ALSAEDI M.A.MERAJ | 2017 | Applied Mathematics and Mechanics(English Edition)2017，38，10： | 1 |
| 19 | Numerical simulation of chemically reactive Powell-Eyring liquid flow with double diffusive Cattaneo-Christov heat and mass flux theories显示文摘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. | A.RAUF Z.ABBAS S.A.SHEHZAD A.ALSAEDI T.HAYAT | 2018 | Applied Mathematics and Mechanics(English Edition)2018，39，4： | 1 |
| 20 | Soret and Dufour effects on magnetohydrodynamic (MHD) flow of Casson fluid显示文摘This article studies the Soret and Dufour effects on the magnetohydrodynamic (MHD) flow of the Casson fluid over a stretched surface. The relevant equations are first derived, and the series solution is constructed by the homotopic procedure. The results for velocities, temperature, and concentration fields are displayed and discussed. Numerical values of the skin friction coefficient, the Nusselt number, and the Sherwood number for different values of physical parameters are constructed and analyzed. The convergence of the series solutions is examined. | T.HAYAT S.A.SHEHZAD A.ALSAEDI | 2012 | Applied Mathematics and Mechanics(English Edition)2012，33，10： | 1 |
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