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This article documents the hydro-magnetic, incompressible Jeffery-Hamel flow in convergent/divergent (CD) channels with stretchable walls. Although there seem to be several works on the subject in the available literature, only a few attempts have been made to work into mass and heat transfer analysis. Consequently, novelty of present study is to investigate the significance of Soret/Dufour. Joule heating, and chemical reaction effects on Jeffery-Hamel flow. The governing coupled system of PDEs showing the mathematical framework of the current physical problems is converted into ODEs through proper transformations. The numerical solution of the obtained couple of ODEs is simulated with the assistance of Mathematica-11 solver NDSolve. The computed outcomes depict that Lorentz force developed due to the magnetic field decays the fluid motion for both convergent and divergent channels. Furthermore, incorporating the heat source and Dufour effects yields a sustainable increase in temperature distribution, whereas the Soret number has reverse features on concentration. Furthermore, the numerical outcomes reflect the significant variation in Nusselt number against magnetic, radiation parameter and Soret number. [ABSTRACT FROM AUTHOR]

The aim of the current analysis is to evaluate the significances of magnetic dipole and heat transmission through ternary hybrid Carreau Yasuda nanoliquid flow across a vertical stretching sheet. The ternary compositions of Al2O3, SiO2, and TiO2 nanoparticles (nps) in the Carreau Yasuda fluid are used to prepare the ternary hybrid nanofluid (Thnf). The heat transfer and velocity are observed in context of heat source/sink and Darcy Forchhemier effect. Mathematically, the flow scenario has been expressed in form of the nonlinear system of PDEs for fluid velocity and energy propagation. The obtained set of PDEs are transform into ODEs through suitable replacements. The obtained dimensionless equations are computationally solved with the help of the parametric continuation method. It has been observed that the accumulation of Al2O3, SiO2 and TiO2-nps to the engine oil, improves the energy and momentum profiles. Furthermore, as compared to nanofluid and hybrid nanofluid, ternary hybrid nanofluid have a greater tendency to boost the thermal energy transfer. The fluid velocity lowers with the outcome of the ferrohydrodynamic interaction term, while enhances with the inclusion of nano particulates (Al2O3, SiO2 and TiO2). [ABSTRACT FROM AUTHOR]

The hydrothermal features of unsteady, incompressible, and laminar hybrid nanofluid motion through a porous capillary are analytically studied in the magnetic field presence. The hybrid nanofluid (GO + ZnO + Blood) is synthesized by blending nanomaterials of graphene oxide and zinc oxide with blood acting as the host fluid. The mathematical model of the flow comprises of a coupled nonlinear set of partial differential equations (PDEs) satisfying appropriate boundary conditions. These equations are reduced to ordinary differential equations (ODEs) by using similarity transformations and then solved with homotopy analysis method (HAM). The impacts of various pertinent physical parameters over the hybrid nanofluid state functions are examined by displaying 2 D graphs. It has been observed that the fluid velocity mitigates with the varying strength of M, A0, N0, and N1. The enhancing buoyancy parameter ϵ augments the fluid velocity. The increasing Prandtl number causes to reduce, while the enhancing A0, B, and N2 augment the hybrid nanofluid temperature. The fluid concentration mitigates with the higher Schmidt number values and A0, and augments with the increasing Soret number strength. The augmenting magnetic field strength causes to enhance the fluid friction, whereas the convective heat transfer increases with the Prandtl number rising values. The rising Sherwood number drops the mass transfer rate of the fluid. The achieved results are validated due to the agreement with the published results. The results of this computation will find applications in biomedicine, nanotechnology, and fluid dynamics. [ABSTRACT FROM AUTHOR]

The hybrid nano-composite fluid transportation in Jaffery-Hemal flow (JHF) has important uses in various technologies, like converging dies, hydrology, automobiles, etc. Such significant applications motivated us to work on the current problem. Therefore, the purpose of the current work is to inspect the energy efficiency analysis of hybrid nanofluids via convergent/divergent channels using porous space. The hybrid nanofluid consists of polyethylene glycol water, nanoparticles Zr O 2 and MgO. To understand the porosity features, the Darcy-Forchheimer law is used. Solar radiation is considered for a more comprehensive analysis of the thermal field. The strong ODEs are obtained using a suitable similarity transformation. The NDSolve technique is used to simulate numerical results, which are then compared with previous published results. Plots and tables are used to report physical investigations of the related parameters. For higher solid volume fractions, the divergent channel's velocity drops. Whereas it increases for a convergent channel. In the presence of variables, Eckert number, and porosity parameter, skin friction increases in divergent channels and decreases in convergent channels for both nanofluids and hybrid nanofluids. Furthermore, it is noticed that hybrid nanocomposite has more dominant features than nanocomposite for both scenarios of narrowing/expanding channels. [ABSTRACT FROM AUTHOR]

Present attempt inspects the entropy analysis and melting effect in flow of hybrid nanomaterials consisting of CNTs nanoparticles and engine oil Flow is by a stretching cylinder. Formulation is accountable to the viscous dissipation, velocity slip and thermal radiation impacts. In order to estimate the disorder within the thermo-physical frame, second-order analysis has been used. The governing system with the imposed boundary condition is dimensionless via proper variables. Numerical outcomes are expressed graphically and analyzed. Comparison of hybrid nanomaterial, nanomaterials and regular liquid is expressed graphically. Outcomes indicate that the hybrid nanomaterials have great impact throughout the inspection than the ordinary nanomaterials. [ABSTRACT FROM AUTHOR]

This communication explores the MHD flow of third grade fluid bounded by a stretching surface with homogeneous-heterogeneous reactions. Incompressible fluid is electrically conducting in the presence of constant magnetic field. Heat transfer is performed through exponential based space internal heat source, non-linear thermal radiation and convective boundary condition. Non-linear differential systems are computed by homotopic technique. Intervals of convergence through numerical data and plots are explicitly determined. The dimensionless velocity, temperature, and concentration distributions manifesting the characteristics of various influential parameters are addressed. The skin friction coefficient and local Nusselt number are also addressed. Clearly temperature is enhanced by radiation, temperature ratio, and magnetic parameters. [ABSTRACT FROM AUTHOR]

Current work focuses on stagnation point flow of MHD Carreau fluid with heterogeneous-homogeneous reactions. Non-linear stretched sheet of variable thickness is the main agent for flow induction. Liquid is assumed an electrically conducted. Nonlinear thermal radiation and heat generation/absorption aspects are addressed. Proper transformations lead to dimensionless the governing problem. Resultant systems are tackled numerically via NDSolve based Shooting scheme. Importance of emerging variables is addressed through graphical illustrations. Tables regarding the estimations of skin friction and rate of heat transfer are computed and examined for various physical variables. It is found that convective and radiation variables improve the liquid temperature. Obtained outcomes are also compared in limiting way and found an excellent agreement. [ABSTRACT FROM AUTHOR]

In the present study we aim to model and examine the impact of melting and double stratification on MHD flow of Carreau liquid over a stretching sheet. Incompressible non-Newtonian liquid is electrically conducting and exposed to a constant magnetic field. The exponential space dependent internal heat source effect is incorporated in the energy expression. Mass transfer is characterized in terms of activation energy and a binary chemical reaction. In addition, Soret and Dufour phenomena are included. The boundary layer concept is utilized to simplify the governing equations. A system of ordinary differential equations is obtained through proper transformations. The coupled non-linear system is then computed by the NDSolve technique. Plots and tabulated values are arranged for interpretation of different variables. The obtained results show that the flow field is influenced appreciably by melting, the heat source, the reaction rate and the activation energy. Moreover, Nusselt and Sherwood numbers are increased by the activation energy. [ABSTRACT FROM AUTHOR]

This research is exhibited to visualize the squeezed flow of magneto-nanoliquid between two parallel disks. Transportations of heat and mass are characterized through thermal radiation and chemical reaction. Suitable similarity variables lead to dimensionless problem. The homotopic technique is adopted to find out the solutions. Behavior of sundry variables is declared graphically. Physical quantities of curiosity such as skin friction and Nusselt number at both disks are estimated and elaborated. Our investigation depicts that thermal field is augmented via radiation and Brownian diffusion variables. Besides, comparative table is also designed to validate our present outcomes with previous limiting study. [ABSTRACT FROM AUTHOR]

Abstract Double stratification in stagnation point flow of magneto Williamson nanoliquid towards nonlinear stretching sheet of variable thickness is explored. Flow is stretched in non-linear way since the sheet is assumed not flat. Aspects of viscous dissipation and radiation are accounted. First order chemical reaction is also present. Proper transformations lead to dimensionless the problems. Resultant problems is analytically solved via homotopic technique. Convergent solutions are obtained. Graphs and table are arranged to manifest the behavior of various influential variables. Our analysis pointed out that stratification variables diminishes the temperature and concentration. Moreover skin friction is decayed for larger magnetic parameter. Finally, conclusion of current investigations are listed in the last section. Highlights • Effects of double stratification in MHD stagnation point flow of Williamson nanoliquid are investigated. • Stretching velocity is considered nonlinear with variable thickness. • Novel features of thermophoresis, Brownian diffusion and zero mass flux conditions are addressed. • Heat transfer characteristics with variable thermal conductivity and viscous dissipation feature are considered. [ABSTRACT FROM AUTHOR]

This paper addresses nonlinear mixed convection flow due to Riga plate with double stratification. Heat transfer analysis is reported for heat generation/absorption and nonlinear thermal radiation. Physical problem is mathematically modeled and nonlinear system of partial differential equations is achieved. Transformations are then utilized to obtain nonlinear system of ordinary differential equations. Homotopic technique is utilized for the solution procedure. Graphical descriptions for velocity, temperature, and concentration distributions are captured and argued for several set of physical variables. Features of skin friction and Nusselt and Sherwood numbers are also illustrated. Our computed results indicate that the attributes of radiation and temperature ratio variables enhance the temperature distribution. Moreover, the influence of buoyancy ratio and modified Hartmann number has revers effects on rate of heat transfer. [ABSTRACT FROM AUTHOR]

Influence of temperature-dependent thermal conductivity on MHD flow of Cross nanoliquid bounded by a stretched sheet is explored. The combined feature of Brownian motion and thermophoresis in nanoliquid modeling is retained. In addition, the attributes of zero mass flux at sheet are imposed. First-order chemical reaction is retained. The resulting problems are numerically computed. Plots and tabulated values are presented and examined. It is figured out that larger thermophoretic diffusion and thermal conductivity significantly rise the thermal field, whereas opposite situation is seen for heat transfer rate. [ABSTRACT FROM AUTHOR]

The main focus of present attempt is model a peristaltic phenomenon of Phan-Thien-Tanner (PTT) fluid with consideration of Joule heating, Hall and ion-slip and dissipation effects. The Lorentz force is further considered to investigate the fluid flow transport in a channel. Electrically conducted fluid is considered in a symmetric channel. Energy conservation principles is employed to inspect the heat transfer analysis. Explicit expressions of stream function, pressure gradient and temperature for small Weissenberg number are constructed. Solutions of modeled problem is computed by employing regular perturbation technique. Graphical views of significant variables on axial velocity, pressure gradient and temperature are interpreted. The phenomena for pumping and trapping are carefully analyzed. Outcomes disclose that velocity of the channel boosts up against Hall current and ion slip variables. Furthermore, the presence of Joule heating greatly effects the behavior of magnetic and Hall current variables on temperature. The outcomes of current model could be utilized in drug delivery and controlling the blood flow systems. [ABSTRACT FROM AUTHOR]

Present analysis is made to communicate the Marangoni convection flow of hybrid nanomaterials by an infinite porous disk. Hybrid nanomaterials comprise of γ − ALOOH and AA 7075 nanoparticles and gasoline oil is considered. Darcy-Forchheimer law is utilized. Thermal field is quadratically varies on disk surface. Irregular heat source, radiation, dissipation effects are further considered to investigate the thermal field. The modeled system is dimensionless by the application of Von Kamran variables. NDsolver scheme approximated the reduced system. For the analysis of surface temperature gradient, temperature and velocity various physical variables are designed through graphs and table. It has been found that hybrid nanomaterials have highest thermal conductivity when compared with traditional liquid and nanoliquid. [ABSTRACT FROM AUTHOR]

• The hybrid nanofluid flow over an inclined stretching disk is studied. • The effect of variation in thin film and inclined disc are considered. • The Cu and Al 2 O 3 nanoparticles are used in the preparation of hybrid nanofluid. • The analytical solution is obtained through the Homotopy Analysis Method. • The consequences of thermal radiation and a magnetic field are also elaborated. Hybrid nanofluids have drawn more attention recently due to their potential to improve heat transfer in solar water heaters. However, it is still difficult to accurately predict how these nanofluids will behave when they flow over inclined rotating disks. The present work thoroughly analyses thin-film's 3D steady hybrid nanoliquid flow across an inclined spinning disk. The hybrid nanoliquid is a combination of copper (Cu) and aluminium oxide (Al 2 O 3) tiny-size solid particles suspended in water. The flow is expressed in from of nonlinear partial differential equations (PDEs). Employing the proper similarity transformation, the mathematical model is renovated into a collection of a system of coupled ordinary differential equations. Utilising the Homotopy Analysis Method obtained equations are resolved. According to graphical results, adding a porous medium to a thin film flows over an inclined spinning disc considerably accelerates heat transfer and possibly improving thermal efficiency. The effective heat transfer characteristics can potentially improve the proficiency of solar water heaters, using a hybrid nanofluid made up of Al 2 O 3 and Cu nano-sized solid particles suspended in water. The increasing impact of the thin film thickness drops the velocity and energy transmission rate of the fluid. [ABSTRACT FROM AUTHOR]

This article discloses a comparative analysis for convective movement of Williamson liquid by a cylinder and sheet. Heat transport mechanism is employed for sheet and cylinder via extra heat factors, convective condition, viscous dissipation, Joule heating and heat source. Concentration is regulated through auto-catalyst and reactant species. Keller box method is used for numerical outcomes to the obtained ordinary differential equations. Impacts of relevant variables of interest are graphically discussed. The findings reflect that movement of liquid and concentration are prominent by cylinder than sheet. Interestingly the contrary trend is observed for temperature. Skin friction is comparatively larger for cylinder than flat sheet. Nusselt number also holds observation similar to skin friction. Skin friction is decreased for larger Weissenberg number. Prandtl, Biot and curvature variables boost the heat transfer rate whereas Eckert and heat source variables show opposite trend. [ABSTRACT FROM AUTHOR]