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This paper aims to analyze the mathematical and theoretical scrutiny of non-Newtonian Williamson liquid on an asymmetry tapered channel with thermal and mass transportation. No slip boundary conditions for velocity, heat and concentration are kept on channel walls. Buongiorno model for thermal transport of nano-fluid is also incorporated. Flow in permeable surface is categorized via modified Darcy law. Current problem is formulated by incorporating distinct effects such as modified Darcy law, electro osmosis, heat generation and chemical reaction. RK-4 based shooting method has been utilized to evaluate the nonlinear equations. Graphical results are formulated to visualize the prominence of distinct parameters. [ABSTRACT FROM AUTHOR]

In this article, the physical impact on thermal performance of unsteady incompressible hybrid nanofluid C u − G O / (H 2 O) − C 2 H 6 O 2 (50:50 vol%) has been presented by using the implicit finite difference procedure. A rigid circular object is taken for instance at time t = 0 , a free stream flow hits the outer surface of the circular object. The fluid crosses the boundary of the circular object at different positions. A highly non-linear complex partial differential system is achieved which is solved numerically. The infiltration of various parameters for instance: nanoparticle shapes (cylinders, bricks and Platelets) and volume fraction parameters on velocity profile, skin friction, temperature profile and Nusselt number are demonstrated qualitatively through illustrations. Outputs specify that: mono nanofluid and hybrid nanofluid created by extending volume fractions causes diminution in the velocity profile. Furthermore, solid hydrogen bonding of hybrid nanofluid reasons a sharp growth in thermal conductivity and, thus, rise in temperature profile is noticed. Moreover, the heat transfer rate and temperature profile has always been influenced by different shape factor, so the cylindrical shape particles lead this category afterwards, bricks and platelets. It is noticed that rise in volume fraction parameters show reduction in velocity profile, but opposite impact is noticed in temperature distribution. Moreover, the thermal performance of hybrid nanoparticles is better than the mono nanoparticles. • GO- Cu/H2O– C2H6O2 (50:50 vol%) hybrid nanofluid has been presented. • A rigid circular object is taken. • The different shapes of nanoparticles has been considered. • The fluid crosses the boundaries of the circular object at different positions. • A highly non-linear complex partial differential system is achieved which is solved numerically. [ABSTRACT FROM AUTHOR]

Fluids like hybrid nanofluids have great potential that present exceptional thermal behavior and thermophysical properties as compare to ordinary nanofluids. Hybrid nanofluids are obtained by the mixture of two different nanoparticles in a base fluid. Many scholars stated that hybrid-nanofluids could be replaced by conventional coolants, especially fluids which work at high temperature. Therefore, these kinds of nanofluids are less damaging for environmental impact and also lead to save energy. The main idea of hybrid nanofluids is to develop performance of heat transfer and its advantages has directed to comparatively good hope for its applications. The objective of present article is to examine 3D stagnation point flow of hybrid nanofluid passes along a stretchable heated wavy cylinder under the impact of variable thickness and slip conditions. For this purpose we consider alloy particles of AA7075 + AA7072 and AA7072 which are suspended in methanol liquid. The alloy particles merged in this analysis are entirely manufactured materials as well as possessing higher heat transfer characteristics. Alloy AA7072 is a combination of zinc and aluminum in ratio 1:98 with addition of metals like silicon, copper and ferrous. Similarly, alloy AA7075 is a combination of zinc, aluminum, copper and magnesium in ratio −6, −9, −1 and −3 respectively with addition of metals like silicon, magnesium and ferrous. The scenario of this model is scrutinized mathematically by captivating induced magnetic field with in the domain of thermal boundary layer. Similarity transformations are deployed to change the governing equations into nonlinear ODEs and consequently solved this system through bvp4c solver. The impact of emerging parameters on velocity, induction and energy distributions are examined through graphical depiction. Furthermore, heat transfer rates and drag forces near the boundary are designed numerically in tabular form. [ABSTRACT FROM AUTHOR]

The peristaltic transport of Carreau-Yasuda fluid model over a sinusoidal medium of non-Newtonian nano flow is examined. In this analysis, the channel walls are considered as ciliated with the higher and lower walls. The formulation of the 2D fluid model depends on the nonlinear (PDEs) that are transformed into simple ordinary (ODEs) by applying the dimensionless parameters and long-wavelength approximation. The numerical solution of the 2D system is taken out by applying the MATHEMATICA solver NDSolve function. The impact of various parameters, such as, flow rate parameter F , wave-length number δ , Brownian motion number N b , thermophoresis number N t , and account of eccentricity α on the velocity profile, temperature distribution, and concentration distribution and stream function are addressed with graphs. [ABSTRACT FROM AUTHOR]

Current analysis is devoted to explore the computational aspects of variable viscosity on Williamson nanofluid over a non-linear stretching sheet. Viscosity of the fluid is assumed to be depend on temperature and due to thermal stratification, viscosity of the fluid also depends upon thermal diffusion. The basic mathematical problem (system of PDEs) is converted into non-linear ODEs via applying suitable transformations. Computational solutions of the problem is achieved by efficient numerical approach (shooting method). Characteristics of controlling parameters i.e. Lewis number, thermophoresis parameter, Hartmann number, plastic dynamic viscosity parameter, Weissenberg number, Prandtl number, stretching index, Brownian motion parameter, Prandtl number, thermal and solutal stratification parameters are plotted on concentration, velocity and temperature gradients. Furthermore friction factor coefficient, heat and mass diffusion rates are presented through graphs and tables. Conclusions are made on the basis of entire investigation and it is seen that velocity profile reduces for large values of variable viscosity and thermal stratification parameters while thermal stratification parameter shows opposite behavior for temperature profile. Moreover, concentration profile reduces for enhancing values of Lewis number and increases for large values of stretching velocity parameter. [ABSTRACT FROM AUTHOR]

This exploration deals with the interaction of inclined MHD peristaltic transport of lignin based hybrid nano-fluid flow in a wavy microfluidic inclined channel. The channel is filled with lignin based hybrid nano-fluid Mo S 2 - S i O 2. Both the left and right walls are kept at uniform temperature having wavy shape. Impact of zeta potentials at the left and right walls are examined. The governing equations are solved for hybrid nanofluid Mo S 2 - S i O 2 by utilizing RK-4 based shooting method. Influence of engrossed parameters on the flow characteristics has been discussed via graphs. Range of engrossed parameters are taken as M = 0.1 , 1 , 1.4. n = 10 , 10.5 , 11. ϕ 1 = ϕ 2 = 0.001 , 2.5 , 2.7. ξ 1 = ξ 2 = - 0.12 , - 0.13 , - 0.14. . Based on numerical experiments, it is concluded that the velocity profile is significantly affected by nanoparticle volume fraction parameter. Moreover, the inclined magnetic parameter retards the motion of lignin based hybrid nanoliquid. [ABSTRACT FROM AUTHOR]

The flow of 2-D cross fluid model with mass and heat transmission over a linearly stretched sheet is analyzed in this paper. Furthermore, we have expanded our study by considering the effects of MHD flow, stagnation point, double stratification, heat generation, radiation effect, nanofluid flow, activation energy and mass diffusion. This type of study has not being investigated previously in literature. The flow generating PDEs are altered into ODEs by deploying suitable transformations. The effects of the parameters involved, namely the Weissenberg number, magnetic field coefficient, Brownian motion coefficient, radiation parameter, Damkohler number, thermophoresis coefficient, Schmidt number, activation energy, heat generation parameter and temperature difference coefficient on the velocity, concentration and energy fields are thoroughly scrutinized. The problem is solved through numerical technique (BVP4c) on MATLAB. The outcomes reveal that the velocity curve upsurges for rising Weissenberg number and decreases due to magnetic parameter. The heat field improves for increasing behavior of the Brownian motion, thermophoresis, heat generation, thermal conductivity and radiation coefficient whereas reverse results are obtained due to Prandtl number and stratification parameter. The concentration improves due to thermophoresis parameter and diffusivity coefficient while reverse outcomes are noticed due to Schmidt number, Damkohler number, temperature difference parameter and Brownian motion parameter. [ABSTRACT FROM AUTHOR]

This study deals with the investigation of boundary layer nanofluid flow on a slender paraboloid surface. The front tip of bullet, airplane, missiles and rockets are some examples of this surface. The thermal conductivity and viscosity of fluid has importance in many engineering applications such as auto mobile industries, solar power generation and heat exchangers, therefore the fluid property such as viscosity is considered to be temperature dependent. The thermophoretic motion, Brownian motion, heat generation and chemical reaction effects examines the behavior of heat and mass transport. The unsteady governing model includes momentum, heat and concentration equations which occur in the form of coupled PDEs. In order to solve numerically, a set of suitable transformations simplify the basic governing laws and convert these equations in the form of coupled ODEs. To show the graphical behavior, we simplify determine model of equations by using Matlab software via BVP4c method a built in command. At last, the discussion related to graphs for variation in different parameters are included. [ABSTRACT FROM AUTHOR]

When an object moves alongside a curved surface, it shows a curvilinear motion. The perception of curvilinear motion is majorly used in applications which are associated with centripetal and centrifugal forces. In this analysis, we studied the behaviour of nano-fluid and hybrid nano-fluid via curved surface with combined effects of heat generation and porous medium. For nano-fluid the combination of base fluid methanol and nano-particles AA7075 are assumed, while for hybrid nano-fluid base fluid methanol and nano-particles AA7075+AA7072 are used. AA7072 is mixture of zinc and alumina with some metals like copper, silicon and ferrous. Similarly AA7075 is mixture of magnesium, alumina and zinc with metals copper, silicon and ferrous. The partial differential equations are converted into ordinary differential equations by using similarity transformation. With the help of MATLAB software we used Bvp4c method to draw the graphs of the resulting equations and also we discuss the effect of solid volume fraction φ 1 , φ 2 , curvature parameter λ , Heat generation ω and porous medium ε for nano-fluid and hybrid nano-fluid. By enhancing the curvature parameter and volume fraction the temperature and velocity profile also enhances while the velocity profile reduces for porous medium and temperature profile increases for heat generation parameter. Nusselt number and skin friction effects are studied in the form of tables. An entropy generation analysis is also conducted. [ABSTRACT FROM AUTHOR]

• Carbon nanotubes are considered. • Flow is assumed in channel. • Heat transfer is considered. The current study aims to examine the peristaltic movement of carbon nanotubes (CNTs) flow in an electro-osmotic curved channel with variable viscosity. No-slip conditions near the channel walls are used. Poisson and Nernst–Planck equations are used to model the electro-osmotic phenomena. Using a curvilinear coordinate system, the equations for nanofluid flow along a curved pipe are formed. Firstly the problem is formulated and then un-dimensionalized. The approximation of long-wavelength along with a lesser Reynolds number has been applied to estimate the equations. The resulting mathematical relations are numerically solved by using the shooting method. To analyze the behavior graphically, we use MATLAB software. Graphical findings show the influence of parameters that affect the flow characteristics. It is noted that the velocity and temperature of the flow decrease by increasing the viscosity parameter. It is also observe that the heat absorption parameter helps to raise the temperature profile for CNTs. [ABSTRACT FROM AUTHOR]

Current discussion is to evaluate the influence of wall properties on thermal and flow performance, through a sinusoidal inclined wavy tube. To fulfill this phenomena we consider a sinusoidal tube having wavy walls, furthermore silicon-dioxide, ferrosoferric-oxide and zinc-oxide are treated as nano-particles and combination of 40% C 2 H 6 O 2 and 60% H 2 O as a base-fluid, but after the literature review we have seen that Iftikhar et al. (2018) presented the consequence of wall properties on copper–water nano-fluid through inclined tube. The out-coming arithmetical results are simplified with the assist of mathematica and perturbation method. Further-more, we graphically evaluate the thermal and flow performance of nanofluids at different rate of solid volume fractions (ϕ) , rigidity parameter (E 1) , Grashof number (G r) , slip parameter (γ) and heat generation parameter. we observed that Solid volume fraction (ϕ) of silicon dioxide, ferrosoferric oxide and zinc oxide causes the reduction of velocity profile. And velocity profile shows the opposite behavior corresponding to (E 1) and (G r). Temperature profile θ (r , t) decreases by developing the amount of (ϕ) for silicon dioxide, ferrosoferric oxide and zinc oxide, and temperature profile moves upward corresponding to heat parameter B. • Wall properties and thermal behavior of nano-fluids flow over an inclined sinusoidal wavy pipe is assumed. • Silicon-dioxide, ferrosoferric -oxide and zinc-oxide are treated as nano-particles and combination of 40% ethylene-glycol and 60% water as a base fluid. • We assume a sinusoidal wavy surface. • The problem is solved by using Mathematica. [ABSTRACT FROM AUTHOR]

In present analysis, we investigate the flow behavior of SiO 2 / H 2 O / C 2 H 6 O 2 nanofluid along with magnetic field and heat generation influence on permeable channel having squeezing/dilating walls. The modeled partial differential system including mass balance, momentum and temperature equations are transformed into ordinary differential system by using similarity transformations and achieved the coupled of nonlinear ordinary differential equations. The numerical solution of coupled system of equations is interpreted for velocity and temperature by using Bvp4c method. The graphical behavior of different parameters such as deforming rate L (for velocity we have taken L = ± 0. 1 , ± 0. 7 and ± 1. 2 , wheres for temperature L = − 0. 1 , − 0. 7 and − 0. 9 has been taken), permeating Reynolds number H (for velocity H = 0. 1 , 0. 4 and 0.7 and for temperature H = − 0. 6 , − 0. 7 and − 0. 8 has been taken), Hartman number M (for velocity M = 0. 1 , 1. 3 and 2.5 is taken), heat generation β (for temperature β = 0. 1 , 0. 5 and 0.9 is taken) and solid fraction volume R (for velocity R = 0. 1 , 0. 9 and 1.2 is taken, for temperature R = 0. 7 , 0. 8 and 0.9 is assumed) for temperature and velocity have been plotted using Matlab software. The observation of case I; L > 0 , H > 0 , shows the velocity of both base ( H 2 O and C 2 H 6 O 2 ) fluids increases at middle portion of channel due to increase in L and M. On the other hands the velocity profiles show increasing behavior for H and decreasing behavior for R at the edges of channel. Temperature distribution observation of case I; L > 0 , H > 0 , it is cleared that the temperature of SiO 2 / H 2 O / C 2 H 6 O 2 nanofluid increases due to increase of β. The temperature profile of SiO 2 / H 2 O nanofluid decreases by increase of R, on other hands the temperature profile of SiO 2 / C 2 H 6 O 2 nanofluid decreases on interval (− 1 < h < 0) and increases on interval (0 < h < 1) with increase of R. The observation of case II; L < 0 , H < 0 , deduces that the temperature of SiO 2 / H 2 O / C 2 H 6 O 2 nanofluid increases by increase of H. The graphical results show that temperature profile reveals batter performance for base fluid H 2 O as compared to base fluid C 2 H 6 O 2 . We compared the present results with previous results and found that present results are similar to previous results. • SiO 2 / H 2 O / C 2 H 6 O 2 nanofluid in squeezing/dilating wall are investigated. • Heat generation is considered. • Low Reynolds number and long wavelength approximation is used. • The equations are solved by using perturbation technique. • Relationship between kinematic viscosity and intermolecular forces are described. [ABSTRACT FROM AUTHOR]

The study of 2D non-Newtonian Sutterby nanofluid flow under the effects of magneto-hydro-dynamics (MHD) over the paraboloid surface is investigated here. The upper part of aircraft, submarine, bullet, and car's bonnet are some samples of the paraboloid surface. The movement of these things depends in boundary layer which is formed within the space on it. The reaction between catalyst at the surface and Sutterby nanofluid yields substantial temperature differences consequently made buoyancy-driven flow in the boundary layer region. First-order activation energy is assumed to model the reaction on the catalyst surface that is sited on the paraboloid surface which starts the free convection. The main prevailing equations are reduced by using appropriate dimensionless variables. The numerical solutions of the dimensionless determining equations are achieved by adopting the Runge-Kutta Fehlberg ("RKF") method. The graphical outcomes of the velocity field depend on the dimensionless quantities such as the Deborah number De ,Hartmann number Ha , temperature and concentration-dependent buoyancy parameters i.e. (G t , G s). The contribution of the thermophoresis coefficient Nt , Prandtl number Pr and Brownian motion parameter Nb is examined for the temperature field. Also the effects of Schmidt number Sc are analyzed for the concentration field. We found that both Deborah number and Hartmann number (De , Ha) provide a decrease in the velocity field. The extreme velocity of the fluid is calculated when the fluid flow is categorized as Newtonian fluid i.e. (De = 0). The numerical outcomes of skin friction, local mass transfer rate and local heat transfer rate are also calculated. A detailed comparison with the numerical method is also given to validate the current results. [ABSTRACT FROM AUTHOR]

• The boundary-flows over a parabolic surface is computed for viscous fluid. • For large Reynolds number the basic flow may be determined numerically in terms of a similarity variable. • Resulting in enhanced heat transfer properties of the fluid. • Relationship between kinematic viscosity and intermolecular force is described. This article presents a study of nanofluid and hybrid nanofluid near a parabolic surface under the influence of heat generation and MHD. AA7072 and AA7075 are treated as nano particles while mathanol is used as a base fluid. We incorporated aluminum alloy of AA7072 in a base fluid for nanofluid and AA7072+AA7075 in base fluid for hybrid nanofluid. AA7072 and AA7075 manipulated in this study are uniquely manufactured to possess high heat transfer features. AA7072 alloy is a combined mixture of zinc and aluminium with some metallic elements such as copper, silicon, and ferrous. Similarly AA7075 is a compounded mixture of zinc, magnesium, ferrous, and silicon. By using similarity transformations, the PDEs are transmuted into ODEs. Furthermore, the transmuted equations are than interpreted numerically in MATLAB using Bvp4c. The graphical analysis is performed for different parameters to check the behaviour of velocity and temperature profiles. Velocity field attains increasing behaviour by an accretion in volume fraction ϕ 1 for both methanol+AA7072(nanofluid) and methanol+AA7072+AA7075(hybrid nanofluid). The velocity profile for methanol+AA7072 is higher than methanol+AA7072+AA7075. By increasing magnetic field parameter M, the velocity component f ′ (ψ) proceeds diminish trend for both methanol+AA7072 and methanol+AA7072+AA7075. But velocity field for methanol+AA7072 is moderate than methanol+AA7072+AA7075. The influence of heat generation parameter γ shows rising trend in temperature profile for both fluids. But heat generation parameter γ is more effective for hybrid nanofluid. Moreover, an entropy generation rate is also evaluated. [ABSTRACT FROM AUTHOR]

• A hybrid nanofluid study is examined in a sinusoidal wavy channel. • Heat generation effects are also analyzed. • Long wavelength and small Reynolds number approximation is assumed. • SiO 2 –TiO 2 /H 2 O Phenomena is taken. • Perturbation method is used to calculate the solution of the problem. The peristaltic transport of hybrid nanofluid (SiO 2 –TiO 2 /H 2 O) flow in a sinusoidal wavy channel under the heat generation effect is reported in present analysis. We have simplified two dimensional equations of hybrid nanofluid for peristaltic transport by using long wavelength (δ ≪ 1) and small Reynolds (Re) number assumptions. We also modeled temperature equation for hybrid nanofluid flow with the effect of heat generation. The two dimensional peristaltic flow equations of (SiO 2 –TiO 2 /H 2 O) are analytically solved by using perturbation method. The numerical integration and solutions of governing two dimensional equations are obtained in Mathematica software. The graphically behavior of solutions for temperature, pressure rise, streamlines and pressure gradient are elucidated with Matlab software. It is noticed that the pressure rise for hybrid nanofluid (SiO 2 –TiO 2 /H 2 O) increases for both amplitudes (a and b), solid fractional volume (ξ 1) and heat generation (β). We observe that higher pressure gradient requires to retain same flux in narrow part of sinusoidal channel, also due to increase of amplitudes (a and b) pressure gradient increases. Moreover size of trapping bolus decreases by increase of channel width d and increases due to increase of heat generation parameter β. [ABSTRACT FROM AUTHOR]

An investigation is made to examine the influence of chemically reactive species and mixed convection on the magneto-hydrodynamic (MHD) Williamson nanofluid induced by a nonisothermal cone and plate in porous medium. In the boundary layer region, nanoparticles deliver potentials in increasing the impact of convective heat transfer. Joule heating effect is also considered. Similarity transformations are used to convert the coupled partial differential equations into a set of nonlinear ordinary differential equations with variable coefficients. The transformed governing nonlinear boundary layer equations are solved numerically by using amended form of Fehlberg's method. It is adequate to discuss several physical mechanisms such as analytical velocity, temperature and concentration profiles and also closed-form skin friction/mass transfer/heat transfer coefficients, all as given in the present analysis. The numerical results acquired for several physical mechanisms are revealed through plots for two different cases (cone and plate). It is found that temperature profile increases for large values of thermophoresis parameter, Brownian motion and Eckert number, but reduces for large values of Prandtl number. Moreover, concentration profile reduces for large values of Lewis number and Brownian motion. [ABSTRACT FROM AUTHOR]

• Bingham nanofluid is considered in an inclined non uniform channel with chemically reactive species. • Effect of homogenious–heterogenious is depicted in the flow of Bingham nanofluid. • Walls are assumed to be flexible. • Convective boundary conditions for temperature and concentration equations are considered. Objective :The flow kinetics generated with a pulsatile wave that travel along the channel has prime relevance in various processes in physiology and industry. The aim here is to investigate such phenomenon with Bingham fluid with chemically reacting species in terms of their homogeneous and heterogeneous characteristics. Method: To formulate the mathematical descriptions Bingham fluid with heat and mass equations is accounted. Using the similarity solutions, the proposed leading partial differential equations of the flow phenomena transferred into the nonlinear ordinary differential equations and boundary conditions are solved analytically. Such considerations perceive prime importance in medicine and genetics where heterogeneity in a cell makes several diseases difficult to execute. Results : Further the physical aspect of human tabular organs i.e., porosity in a medium is retained in the analysis. The utility of magnetic field in reference to medicine is employed. The walls are considered flexible. The whole problem is set to lubrication approach for simplification of resulting system. The attained results are tested on physical grounds by plotting graphs. Conclusion: It is analyzed that the Hartman number and porosity parameter reduce the velocity and temperature profiles. The elastic wall parameters E 1 and E 2 enhances both the velocity and temperature fields while E 3 enrolls an adverse effect. [ABSTRACT FROM AUTHOR]

• Nanoparticle phenomena has been highlighted. • Electroosmotic flow is considered of Bingham fluid. • Mathematical peristaltic flow on Bingham Nanofluid. • Walls are assumed to be flexible. • Exact and analytical solutions are presented. The effects of slip condition and Joule heating on the peristaltic flow of Bingham nanofluid are investigated. The flow is taken in a porous channel with elastic walls. Mathematical formulation is presented under the assumption of long wavelength and small Reynolds number. The transformed equations for the flow are solved to seek values for the nanoparticles velocity, concentration and temperature along the channel length. Graphs are plotted to evaluate the behavior of various physical parameters on flow quantities in both slip and no-slip cases. The main features of the physical parameters are highlighted on the inclined non uniform channel. The results show an increment in velocity with rise in inclination and porosity while it reduces with magnetic field. Moreover, nanofluid favors the heat transfer and decline the concentration. [ABSTRACT FROM AUTHOR]

Recent study illustrates the systematic survey of boundary layer heat and mass diffusion (Cattaneo-Christov model) of Jeffery fluid passed by an inclined stretching surface in the occurrence of magnetic field. Prevailing non-linear PDEs are converted into non-linear ODEs and then the problem is solved via RK-4 technique (using coefficients of Cash and Craps). The related important physical parameters such as M magnetic parameter, λ T thermal buoyancy parameter, λ C concentration buoyancy parameter, γ inclined stretching sheet parameter, PrPrandtl number, N b Brownian motion parameter, N t thermophoresis parameter and Le Lewis number are plotted graphically for velocity, temperature and concentration distributions. In order to check the double diffusive phenomenon, the impact of fluid relaxation parameter δ m , thermal relaxation parameter δ e and nanoparticle concentration relaxation parameter δ c are reflected through tables and graphs. The main theme of present article is to explore its unique attempt towards the generalized version of conventional Fourier's law and Fick's law at nanostructure level. Assumption is drawn on the source of entire analysis and it is clear that the velocity and temperature profiles reduces for increasing values of fluid relaxation parameter, inclined sheet, magnetic field and Prandtl number. [ABSTRACT FROM AUTHOR]