Boundary layer flow of third grade nanofluid with Newtonian heating and viscous dissipation

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.

Convective heat and mass transfer in MHD mixed convection flow of Jeffrey nanofluid over a radially stretching surface with thermal radiation

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.

Mixed convective heat and mass transfer analysis for peristaltic transport in an asymmetric channel with Soret and Dufour effects

The present investigation addresses the simultaneous effects of heat and mass transfer in the mixed convection peristaltic flow of viscous fluid in an asymmetric channel. The channel walls exhibit the convective boundary conditions. In addition, the effects due to Soret and Dufour are taken into consideration. Resulting problems are solved for the series solutions. Numerical values of heat and mass transfer rates are displayed and studied. Results indicate that the concentration and temperature of the fluid increase whereas the mass transfer rate at the wall decreases with increase of the mass transfer Biot number. Furthermore, it is observed that the temperature decreases with the increase of the heat transfer Biot number.

Flow of Casson nanofluid with viscous dissipation and convective conditions: A mathematical model

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.

Heat transfer analysis in peristaltic flow of MHD Jeffrey fluid with variable thermal conductivity

The effect of an inclined magnetic field in the peristaltic flow of a Jeffrey fluid with variable thermal conductivity is discussed. The temperature dependent thermal conductivity of fluid in an asymmetric channel is taken into account. A dimensionless nonlinear system subject to a long wavelength and a low Reynolds number is solved. The explicit expressions of the stream function, the axial velocity, the pressure gradient, and the temperature are obtained. The effects of all physical parameters on peristaltic transport and heat transfer characteristics are observed from graphical illustrations. The behaviors of θ∈ [0, π/2] and θ∈ [π/2, π] on fluid flow and heat transfer are found to be opposite. Further, the size of trapped bolus is greater for the case of the inclined magnetic field （θ≠ π/2） than that for the case of the transverse magnetic field （θ = π/2）. The heat transfer coefficient decreases when the constant thermal conductivity （Newtonian） fluid is changed to the variable thermal conductivity （Jeffrey） fluid.

Mixed Convection Stagnation Point Flow of Casson Fluid with Convective Boundary Conditions

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.

MHD flow of nanofluids over an exponentially stretching sheet in a porous medium with convective boundary conditions

This article concentrates on the steady magnetohydrodynamic （MHD） flow of viscous nanofluid. The flow is caused by a permeable exponentially stretching surface. An incompressible fluid fills the porous space. A comparative study is made for the nanoparticles namely Copper （Cu）, Silver （Ag）, Alumina （A1203） and Titanium Oxide （TiO2）. Water is treated as a base fluid. Convective type boundary conditions are employed in modeling the heat transfer process. The non-linear partial differential equations governing the flow are reduced to an ordinary differential equation by similarity transformations. The obtained equations are then solved for the development of series solutions. Convergence of the obtained series solutions is explicitly discussed. The effects of different parameters on the velocity and temperature profiles are shown and analyzed through graphs.

Melting heat transfer in Cu-water and Ag-water nanofluids flow with homogeneous-heterogeneous reactions

This article addresses melting heat transfer in magnetohydrodynamics(MHD)nanofluid flows by a rotating disk. The analysis is performed in Cu-water and Ag-water nanofluids. Thermal radiation, viscous dissipation, and chemical reactions impacts are added in the nanofluid model. Appropriate transformations lead to the nondimensionalized boundary layer equations. Series solutions for the resulting equations are computed.The role of pertinent parameters on the velocity, temperature, and concentration is analyzed in the outputs. It is revealed that the larger melting parameter enhances the velocity profile while the temperature profile decreases. The surface drag force and heat transfer rate are computed under the influence of pertinent parameters. Furthermore, the homogeneous reaction parameter serves to decrease the surface concentration.

Stagnation-point flow of couple stress fluid with melting heat transfer

Melting heat transfer in the boundary layer flow of a couple stress fluid over a stretching surface is investigated. The developed differential equations are solved for homotopic solutions. It is observed that the velocity and the boundary layer thickness are decreasing functions of the couple stress fluid parameter. However, the temperature and surface heat transfer increase when the values of the couple stress fluid parameter increase. The velocity and temperature fields increase with an increase in the melting process of the stretching sheet.

Diffusion of chemically reactive species in third grade fluid flow over an exponentially stretching sheet considering magnetic field effects

This article addresses the magnetohydrodynamics(MHD) flow of a third grade fluid over an exponentially stretching sheet. Analysis is carried out in the presence of first order chemical reaction. Both cases of constructive and destructive chemical reactions are reported. Convergent solutions of the resulting differential systems are presented in series forms. Characteristics of various sundry parameters on the velocity, concentration, skin friction and local Sherwood number are analyzed and discussed.

Flow of Burgers' fluid over an inclined stretching sheet with heat and mass transfer

Effects of heat and mass transfer in the flow of Burgers fluid over an inclined sheet are discussed. Problems formulation and relevant analysis are given in the presence of thermal radiation and non-uniform heat source/sink. Thermal conductivity is taken temperature dependent. The nonlinear partial differential equations are simplified using boundary layer approximations. The resultant nonlinear ordinary differential equations are solved for the series solutions. The convergence of series solutions is obtained by plotting theη-curves for the velocity, temperature and concentration fields. Results of this work describe the role of different physical parameters involved in the problem. The Deborah numbers corresponding to relaxation time(β1 and β2) and angle of inclination(α) decrease the fluid velocity and concentration field. Concentration field decays as Deborah numbers corresponding to retardation time(β3) and mixed convection parameter(G) increase. Large values of heat generation/absorption parameters A/B, and the temperature distribution across the boundary layer increase. Numerical values of local Nusselt number,-θ′(0), and local Sherwood number,-f′(0), are computed and analyzed. It is found that θ′(0) increases with an increase in β3.

Heat transfer in a porous saturated wavy channel with asymmetric convective boundary conditions

The viscous flow in a wavy channel with convective boundary conditions is investigated. The channel is filled with a porous viscous fluid. Two cases of equal and different external convection coefficients on the walls are taken into account. Effect of viscous dissipation is also considered. The governing equations are derived employing long wavelength and low Reynolds number approximations. Exact closed form solutions are obtained for the simplified equations. Important physical features for peristaltic flow caused by the wavy wave are pumping, trapping and heat transfer rate at the channel walls. These are discussed one by one in depth and detail through graphical illustrations. Special attention has been given to the effects of convective boundary conditions. The results show that for Bi1≠Bi2, there exists a critical value of Brinkman number Brc at which the temperatures of both the walls become equal. And, for Bi1>Bi2 and Br>Brc, the temperature of the cold wall exceeds the temperature of hot wall.

MHD stagnation point flow by a permeable stretching cylinder with Soret-Dufour effects

Combined effects of Soret(thermal-diffusion) and Dufour(diffusion-thermo) in MHD stagnation point flow by a permeable stretching cylinder were studied. Analysis was examined in the presence of heat generation/absorption and chemical reaction. The laws of conservation of mass, momentum, energy and concentration are found to lead to the mathematical development of the problem. Suitable transformations were used to convert the nonlinear partial differential equations into the ordinary differential equations. The series solutions of boundary layer equations through momentum, energy and concentration equations were obtained.Convergence of the developed series solutions was discussed via plots and numerical values. The behaviors of different physical parameters on the velocity components, temperature and concentration were obtained. Numerical values of Nusselt number, skin friction and Sherwood number with different parameters were computed and analyzed. It is found that Dufour and Soret numbers result in the enhancement of temperature and concentration distributions, respectively.

霍尔效应和欧姆热效应下纳米流体通过弯曲通道时的蠕动（英文）

纳米流体以其优异的热物理性质吸引了许多科学家。在常规流体中加入少量的纳米粒子会显著地增强传热特性。纳米材料的可持续性和效率对纳米技术的进步具有关键作用。本文分析了霍尔效应、欧姆热效应和速度滑移对纳米流体蠕动的影响。考虑了对流边界条件和热的产生/吸收,以促进传热特性。在曲线坐标下导出了弯曲通道中蠕动的控制方程。在长波长和小雷诺数的假设条件下,对方程进行了数值求解。研究表明,纳米流体提高了传热速率,降低了流体温度。Hartman数和Hall参数在流体运动和传热特性上表现出相反的行为。在存在速度滑移的情况下,压力梯度迅速减小,在通道的狭小区域表现出主导作用。

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

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.

Peristaltic flow of couple stress fluid through uniform porous medium

Investigation concerning peristaltic motion of couple stress fluid is made. An incompressible couple stress fluid occupies the porous medium. Mathematical anal- ysis is presented through large wavelength and low Reynolds number. Exact analytical expressions of axial velocity, volume flow rate, pressure gradient, and stream function are calculated as a function of couple stress parameter. The essential feature of the analysis is a full description of influence of couple stress parameter and permeability parameter on the pressure, frictional force, mechanical efficiency, and trapping.

Convective heat and mass transfer effects in three-dimensional flow of Maxwell fluid over a stretching surface with heat source

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.

Effects of homogeneous-heterogeneous reactions in flow of Powell-Eyring fluid

The steady two-dimensional flow of Powell-Eyring fluid is investigated. The flow is caused by a stretching surface with homogeneous-heterogeneous reactions. The governing nonlinear differential equations are reduced to the ordinary differential equations by similarity transformations. The analytic solutions are presented in series forms by homotopy analysis method(HAM). Convergence of the obtained series solutions is explicitly discussed. The physical significance of different parameters on the velocity and concentration profiles is discussed through graphical illustrations. It is noticed that the boundary layer thickness increases by increasing the Powell-Eyring fluid material parameter(ε) whereas it decreases by increasing the fluid material parameter(δ). Further, the concentration profile increases when Powell-Eyring fluid material parameters increase. The concentration is also an increasing function of Schmidt number and decreasing function of strength of homogeneous reaction. Also mass transfer rate increases for larger rate of heterogeneous reaction.

Effectiveness of Darcy-Forchheimer and nonlinear mixed convection aspects in stratified Maxwell nanomaterial flow induced by convectively heated surface

The effect of nonlinear mixed convection in stretched flows of rate-type nonNewtonian materials is described. The formulation is based upon the Maxwell liquid which elaborates thermal relation time characteristics. Nanofluid properties are studied considering thermophoresis and Brownian movement. Thermal radiation, double stratification, convective conditions, and heat generation are incorporated in energy and nanoparticle concentration expressions. A boundary-layer concept is implemented for the simplification of mathematical expressions. The modeled nonlinear problems are computed with an optimal homotopy scheme. Moreover, the Nusselt and Sherwood numbers as well as the velocity, nanoparticle concentration, and temperature are emphasized. The results show opposite impacts of the Deborah number and the porosity factor on the velocity distribution.

Darcy-Forchheimer flow by rotating disk with partial slip

The viscous dissipation and heat transfer in the Darcy-Forchheimer flow by a rotating disk are examined. The partial slip conditions are invoked. The optimal series solutions are computed via the optimal homotopic analysis method(OHAM). The thermophoresis and Brownian motions are studied. The Darcy-Forchheimer relation characterizes the porous space. The roles of influential variables on the physical quantities are graphically examined. A reduction in the local Nusselt number is observed through thermophoresis and thermal slip parameters. The local Sherwood number depicts an increasing trend for the higher Brownian motion and concentration slip parameters.