Axisymmetric Stagnation-Point Flow of Nanofluid over a Stretching Surface

This paper investigates the laminar boundary layer flow of nanofluid induced by a radially stretching sheet. Nanofluid model exhibiting Brownian motion and thermophoresis is used. Series solutions for a reduced system of nonlinear ordinary differential equations are obtained by homotopy analysis method (HAM). Comparative study between the HAM solutions and previously published numerical results shows an excellent agreement. Velocity, temperature and mass fraction are displayed for various values of parameters. The local skin friction coefficient, the local Nusselt number and the local Sherwood number are computed. It is observed that the presence of nanoparticles enhances the thermal conductivity of base fluid. It is found that the convective heat transfer coefficient (Nusselt number) is decreased with an increase in concentration of nanoparticles whereas Sherwood number increases when concentration of nanoparticles in the base fluid is increased.     

Heat transfer analysis in the flow of Walters' B fluid with a convective boundary condition

Radiative heat transfer in the steady two-dimensional flow of Walters' B fluid with a non-uniform heat source/sink is investigated. An incompressible fluid is bounded by a stretching porous surface. The convective boundary condition is used for the thermal boundary layer problem. The relevant equations are first simplified under usual boundary layer assumptions and then transformed into a similar form by suitable transformations. Explicit series solutions of velocity and temperature are derived by the homotopy analysis method(HAM). The dimensionless velocity and temperature gradients at the wall are calculated and discussed.     

Heat and mass transfer analysis on the flow of a second grade fluid in the presence of chemical reaction

The laminar flow problem of convective heat transfer for a second grade fluid over a semi-infinite plate in the presence of species concentration and chemical reaction is investigated. The governing equations are transformed into a dimensionless system of three non-linear coupled partial differential equations. These equations have been solved analytically subject to the relevant boundary conditions by employing a homotopy analysis method (HAM). It is noted that for the arising system, the HAM performs extremely well in terms of efficiency and simplicity. The influence of dimensionless pertinent parameters on the velocity, temperature and concentration fields has been examined carefully.     

Convective Heat and Mass Transfer in Magneto Jeffrey Fluid Flow on a Rotating Cone with Heat Source and Chemical Reaction

The present paper addresses the megnetohydrodynamic Jeffrey fluid flow with heat and mass transfer on an infinitely rotating upright cone. Inquiry is carried out with heat source/sink and chemical reaction effects. Further, constant thermal and concentration flux situations are imposed. Optimal homotopy analysis method (OHAM) is employed to achieve series solutions of the concerned differential equations. Important results of the flow phenomena are explored and deliberated by means of graphs and numerical tables. It is perceived that thermal boundary layer thickness possess contrast variations for the heat source and heat sink, respectively. The chemical reaction enhances the heat transfer rate but decline the mass transfer rate. Moreover, the precision of the existing findings is verified by associating them with the previously available work.     

Numerical study of magneto-convective heat and mass transfer from inclined surface with Soret diffusion and heat generation effects: A model for ocean magnetic energy generator fluid dynamics

A mathematical model is developed for steady state magnetohydrodynamic (MHD) heat and mass transfer flow along an inclined surface in an ocean MHD energy generator device with heat generation and thermo-diffusive (Soret) effects. The governing equations are transformed into nonlinear ordinary differential equations with appropriate similarity variables. The emerging two-point boundary value problem is shown to depend on six dimensionless thermophysical parameters - magnetic parameter, Grashof number, Prandtl number, modified Prandtl number, heat source parameter and Soret number in addition to plate inclination. Numerical solutions are obtained for the nonlinear coupled ordinary differential equations for momentum, energy and salinity (species) conservation, numerically, using the Nachtsheim–Swigert shooting iteration technique in conjunction with the Runge–Kutta sixth order iteration scheme. Validation is achieved with Nakamura's implicit finite difference method. Further verification is obtained via the semi-numerical Homotopy analysis method (HAM). With an increase in magnetic parameter, skin friction is depressed whereas it generally increases with heat source parameter. Salinity magnitudes are significantly reduced with increasing heat source parameter. Temperature gradient is decreased with Prandtl number and salinity gradient (mass transfer rate) is also reduced with modified Prandtl number. Furthermore, the flow is decelerated with increasing plate inclinations and temperature also depressed with increasing thermal Grashof number.     

Analysis for flow of Jeffrey fluid with nanoparticles

An analysis of the boundary layer flow and heat transfer in a Jeffrey fluid containing nanoparticles is presented in this paper. Here, fluid motion is due to a stretchable cylinder. The thermal conductivity of the fluid is taken to be temperature-dependent. The partial differential equations of velocity, temperature, and concentration fields are transformed to a dimensionless system of ordinary differential equations. Nonlinear governing analysis is computed for the homotopy solutions. The behaviors of Brownian motion and thermophoresis diffusion of nanoparticles have been examined graphically. Numerical values of the local Nusselt number are computed and analyzed.     

Exact solutions for the flow of Casson fluid over a stretching surface with transpiration and heat transfer effects

The effects of transpiration on forced convection boundary layer non-Newtonian fluid flow and heat transfer toward a linearly stretching surface are reported.The flow is caused solely by the stretching of the sheet in its own plane with a velocity varying linearly with the distance from a fixed point.The constitutive relationship for the Casson fluid is used.The governing partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations by using similarity transformations.Exact solutions of the resulting ordinary differential equations are obtained.The effect of increasing Casson parameter,i.e.,with decreasing yield stress(the fluid behaves as a Newtonian fluid as the Casson parameter becomes large),is to suppress the velocity field.However,the temperature is enhanced as the Casson parameter increases.It is observed that the effect of transpiration is to decrease the fluid velocity as well as the temperature.The skin-friction coefficient is found to increase as the transpiration parameter increases.     

Dual solutions in boundary layer flow of a moving fluid over a moving permeable surface in presence of prescribed surface temperature and thermal radiation

An analysis of the heat transfer for a boundary layer forced convective flow past a moving permeable flat surface parallel to a moving fluid is presented. Prescribed surface temperature at the boundary is considered. A thermal radiation term in the energy equation is considered. The similarity solutions for the problem are obtained and the reduced ordinary differential equations are solved numerically. To support the validity of the numerical results, a comparison is made with the available results for some particular cases of this study. Dual solutions exist when the surface and the fluid move in the opposite directions.     

Variable fluid properties and variable heat flux effects on the flow and heat transfer in a non-Newtonian Maxwell fluid over an unsteady stretching sheet with slip velocity

The effects of variable fluid properties and variable heat flux on the flow and heat transfer of a non-Newtonian Maxwell fluid over an unsteady stretching sheet in the presence of slip velocity have been studied. The governing differential equations are transformed into a set of coupled non-linear ordinary differential equations and then solved with a numerical technique using appropriate boundary conditions for various physical parameters. The numerical solution for the governing non-linear boundary value problem is based on applying the fourth-order Runge-Kutta method coupled with the shooting technique over the entire range of physical parameters. The effects of various parameters like the viscosity parameter, thermal conductivity parameter, unsteadiness parameter, slip velocity parameter, the Deborah number, and the Prandtl number on the flow and temperature profiles as well as on the local skin-friction coefficient and the local Nusselt number are presented and discussed. Comparison of numerical results is made with the earlier published results under limiting cases.     

MHD flow and mass transfer of a upper-convected Maxwell fluid past a porous shrinking sheet with chemical reaction species

This article looks at the mass transfer of the steady two-dimensional magnetohydrodynamic (MHD) boundary layer flow of an upper-convected Maxwell (UCM) fluid past a porous shrinking sheet in the presence of chemical reaction. The resulting nonlinear partial differential equations are reduced to the system of nonlinear ordinary differential equations by means of similarity transformations. Expressions of velocity and the concentration fields are obtained using the homotopy analysis method (HAM). The convergence of the obtained series solutions is explicitly discussed. The influences of sundry parameters on the velocity and the concentration fields are made and discussed in detail. The values of the skin friction coefficient and the surface mass transfer for various interesting parameters are also tabulated.     

Dual solutions and stability analysis of flow and heat transfer of Casson fluid over a stretching sheet

The aim of the current study is to find out the dual solutions of the two-dimensional magnetohydrodynamic (MHD) flow of Casson fluid and heat transfer over the stretching sheet. The focus of the study is to examine the linear thermal radiation effects on dual solutions for both the steady and unsteady flow of Casson fluid over the stretching sheet under the influence of uniform magnetic field. The governing equations are formed as system of partial differential equations (PDEs). Using suitable transformations, the system of PDEs are converted into favorable nonlinear system of ordinary differential equations (ODEs). Simulations are performed in Maple 2015 to form the dual solutions in order to achieve the velocity, temperature, skin friction and heat transfer profiles of the Casson fluid over the stretching sheet. It is concluded that the dual solutions for the corresponding model are numerically stable. Furthermore, the upper branch solutions of the Casson fluid profiles are numerically stable as compared to the lower branch solutions. Results indicate that positive Eigen values of the MHD flow of Casson fluid provide stable profiles as compared to the negative Eigen values. It is believed that the current study would provide a base for the dual solution of the other types of the non-Newtonian fluid flows over various categories of surfaces.     

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(Al2O3) 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.     

Magnetohydrodynamic and radiation effects on the heat transfer of a continuously stretching/shrinking sheet with mass transpiration of the horizontal boundary

The aim of this paper is the investigation of heat transfer regarding the cases of both stretching and shrinking sheets with a sponge-like horizontal wall that allows for mass transpiration. The effects of Prandtl number, radiation and external magnetic field are extensively examined. The Navier-Stokes equations are reduced to partial differential equations, which are eventually become ordinary differential equations and solved analytically. Furthermore, the power-law wall temperature and heat flux boundary conditions are imposed on the boundary layer energy equation for obtaining exact analytical solutions. The results revealed that in both the stretching and shrinking sheet scenarios the thickness of the thermal boundary layer decreases with either increasing of transpiration as well as the Chandrasekhar and Prandtl number numbers or decreasing radiation number. Additionally, the characteristics of the heat transfer regarding a shrinking sheet and those of a stretching sheet are found not to be similar. In fact, a new solution branch appeared which indicates that multiple solutions may emerge under certain circumstances. Finally, by using the present analytical relationships, theoretical guidelines can be given for regulating the procedure.     

Casson fluid flow and heat transfer over a nonlinearly stretching surface

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.     

Upshot of Chemical Species and Nonlinear Thermal Radiation on Oldroyd-B Nanofluid Flow Past a Bi-directional Stretched Surface with Heat Generation/Absorption in a Porous Media

A three-dimensional mathematical model is developed to examine the flow of nonlinear thermal radiation Oldroyd-B nanofluid past a bidirectional linearly stretched surface in a porous medium. The flow is induced by temperature dependent thermal conductivity, chemical reaction and convective heat and mass conditions. Novel characteristics of Brownian motion and thermophoresis are accompanied by magnetohydrodynamic and heat generation/absorption.Self-similar transformations are employed to convert the system of nonlinear partial differential equations to a system of ordinary differential equations with high nonlinearity and are solved by strong analytic technique named as Homotopy Analysis method(HAM). Effects of varied arising parameters on involved distributions are reflected through graphical illustrations. From this study, it is perceived that strong magnetic field hinders the fluid's motion and leads to rise in temperature that eventually lowers heat transfer rate from the surface. Further, decrease in heat transfer rate is also observed for enhanced values of thermal radiation parameter. To validate our results, a comparison with already published paper in limiting case is also given and results are found in excellent oncurrence; hence reliable results are being presented.     

MHD Flow and Heat Transfer Characteristics in a Casson Liquid Film Towards an Unsteady Stretching Sheet with Temperature-Dependent Thermal Conductivity

Theoretical and numerical outcomes of the non-Newtonian Casson liquid thin film fluid flow owing to an unsteady stretching sheet which exposed to a magnetic field, Ohmic heating and slip velocity phenomena is reported here. The non-Newtonian thermal conductivity is imposed and treated as it vary with temperature. The nonlinear partial differential equations governing the non-Newtonian Casson thin film fluid are simplified into a group of highly nonlinear ordinary differential equations by using an adequate dimensionless transformations. With this in mind, the numerical solutions for the ordinary conservation equations are found using an accurate shooting iteration technique together with the Runge-Kutta algorithm. The lineaments of the thin film flow and the heat transfer characteristics for the pertinent parameters are discussed through graphs. The results obtained here detect many concern for the local Nusselt number and the local skin-friction coefficient in which they may be beneficial for the material processing industries. Furthermore, in some special conditions, the present problem has an excellent agreement with previously published work.     

Thermal radiation effects on Williamson fluid flow due to an expanding/contracting cylinder with nanomaterials: Dual solutions

The phenomena of heat and mass transfer during the flow of non-Newtonian transfer are amongst the core subjects in mechanical sciences. Recently, the nanomaterials are among the eminent tools for improving the low thermal conductivity of working fluids. Therefore, in view of the existing contributions, this article presents a two-dimensional numerical simulation for the transient flow of a non-Newtonian nanofluid generated by an expanding/contracting circular cylinder. This critical review further explores the impacts of variable magnetic field, thermal radiation, velocity slip and convective boundary conditions. The basic governing equations for Williamson fluid flow are formulated with the assistance of boundary layer approximations. The non-dimensional form of partially coupled ordinary differential equations has been tackled numerically by utilizing versatile Runge–Kutta integration scheme. The momentum, thermal and concentration characteristics are investigated with respect to several critical parameters, like, Weissenberg number, unsteadiness parameter, viscosity ratio parameter, slip parameter, suction parameter, magnetic parameter, thermophoresis parameter, Brownian motion parameter, Prandtl number, Lewis number and Biot number. The outcomes of the systematic reviews of these parameters and forest plots are illustrated. The study reveals that multiple solutions for the considered problem occurs for diverse values of involved physical parameters. The computed results indicate that the friction and heat transfer coefficients are significantly raised by the magnetic parameter for upper branch solutions.     

Chemical reaction effects on MHD rotating fluid over a vertical plate embedded in porous medium with heat source

Several boundary layer flowswith heat and mass transfer problems do arise from a pebble bed nuclear reactor system. In this study, we examine the combined effects of variable thermal conductivity, thermal diffusion, diffusion thermo, heat source, chemical reaction and fluid rotation on hydromagnetic mixed convective flow with heat and mass transfer over a vertical plate embedded in porous medium. The governing partial differential equations have been transformed into a system of ordinary differential equations by employing the similarity transformation and solved numerically using the Runge–Kutta–Fehlberg method with a shooting technique. Pertinent results obtained are presented graphically and in tabular form with respect to variation in various thermophysical parameters. A comparison of the special case of this study with the previously published work shows excellent agreement.     

Upshot of Chemical Species and Nonlinear Thermal Radiation on Oldroyd-B Nanofluid Flow Past a Bi-directional Stretched Surface with Heat Generation/Absorption ina Porous Media

A three-dimensional mathematical model is developed to examine the flow of nonlinear thermal radiation Oldroyd-B nanofluid past a bidirectional linearly stretched surface in a porous medium. The flow is induced by temperature dependent thermal conductivity, chemical reaction and convective heat and mass conditions. Novel characteristics of Brownian motion and thermophoresis are accompanied by magnetohydrodynamic and heat generation/absorption. Self-similar transformations are employed to convert the system of nonlinear partial differential equations to a system of ordinary differential equations with high nonlinearity and are solved by strong analytic technique named as Homotopy Analysis method (HAM). Effects of varied arising parameters on involved distributions are reflected through graphical illustrations. From this study, it is perceived that strong magnetic field hinders the fluid's motion and leads to rise in temperature that eventually lowers heat transfer rate from the surface. Further, decrease in heat transfer rate is also observed for enhanced values of thermal radiation parameter. To validate our results, a comparison with already published paper in limiting case is also given and results are found in excellent oncurrence; hence reliable results are being presented.     

Flow of a Jeffery-Six Constant Fluid Between Coaxial Cylinders withHeat Transfer Analysis

In the present investigation we have discussed the flow of a Jeffrey-six constant incompressible fluid between two infinite coaxial cylinders in the presence of heat transfer analysis. The governing equations of Jeffrey-six constant fluid along with energy equation have been derived in cylindrical coordinates. The highly nonlinear equations are simplified with the help of non-dimensional parameters and then solved analytically with the help of homotopy analysis method (HAM) for two fundamental flows namely Couette and Generalized Couette flow. The effects of emerging parameters are discussed through graphs. The convergence of the HAM solution has been discussed by plotting h-curves.