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In this novel numerical investigation, the application of well-renowned numerical technique known as Galerkin finite element method on full form of Navier-Stokes equations presented peristaltic flow of non-Newtonian fluid confined by a uniformly saturated porous medium. The rheological aspects of non-Newtonian material are discussed by considering micropolar fluid. The flow model consists of system of nonlinear partial differential equations with mixed boundary condition. The flow also experienced an externally applied magnetic field. The effects of inertial forces and the results independent of wavelength are obtained by dropping the presumptions of lubrication theory in modelling the governing equations. The numerical solution for formulated problem in terms of partial differential expressions is worked out via Galerkin finite technique in view of six nodal triangular elements. The enhancement in the inertial forces gives impressive pressure enhancement against wavelength while opposed the fluid flow in the vicinity of peristaltic walls of the tube but supported the fluid flow in the central region of the tube. The present results are also compared with the available results after applying lubrication theory and found in reliable agreement.

Double diffusion flow of Jeffrey fluid in presence of nanoparticles is studied theoretically under time dependent thermal conductivity. The considered nanoparticles are evaporated over convectively heated surface which moves periodically in its own plane. The appropriate dimensionless variables are employed to obtain the dimensionless forms of governing equations. We computed the analytical solution of non-linear differential equations by utilizing homotopy analysis method. The present investigation reveals the features of various emerging parameters like Deborah number, combined parameter, oscillation frequency to stretching rate ratio, Prandtl number, Lewis number, thermophoresis parameter, Brownian motion parameter, nano Lewis number, modified Dufour parameter, and Dufour solutal Lewis number. A useful enhancement in movement of nanoparticles is observed by utilizing the combined magnetic and porosity effects. Unlike traditional studies, present analysis is confined with the unsteady transportation phenomenon from periodically moving surfaces. Such computation may be attributable in flow results from tensional vibrations due to stretching and elastic surfaces. The simulation presented here can be attractable significance in the bioengineered nanoparticles manufacturing. It is observed that the heat transportation of nanoparticles may efficiently enhance through the utilization of variable thermal conductivity. The solutal concentration decreases with increasing Deborah number and Lewis number. It is further noted that the nano Lewis number causes reduction of nanoparticles concentration.

The structure of needle is mostly similar as paraboloid of upset parallel to flow possesses and has huge applications in building and modern procedures including microstructure electronic gadgets and microscale cooling gadgets for thermal evacuation application. Based on these applications, an axisymmetric Darcy–Forchheimer flow and energy transport of hybrid nanoliquid over a slender moving needle is considered. Impact of heat sink/source and Newtonian heating is inspected. The dimensional nonlinear administering partial differential equations (PDEs) are modified to dimensionless nonlinear ordinary differential equations (ODEs) with assistance of similarity technique which is then explained numerically utilizing Runge–Kutta–Fehlberg scheme from Dsolve code MAPLE. It ought to be noticed that approval of results shows a decent concurrence with previously existing reports. It is noticed that the enhancing Forchheimer number and porosity parameter increase the temperature.

The basic idea of the present article is to model and study the aspects of curvature-dependent channel walls on peristalsis of laminar viscous material flow through a curved geometry. Mathematical modeling for such flow configuration is being presented for the first time. Lubrication theory assumptions are used for mathematical modeling of the problem. Moreover, the numerical method is used to solve the resulting system of equation. The impacts of different flow quantities on the heat transfer rate, velocity and temperature profiles are discussed via graphs. Results indicate that the curvature parameter considerably influences the mechanical and thermal aspects of the flow and hence must be included in the modeling of flows through curved a channel.

In current attempt, a numerical code was developed to model the nanofluid free convected magnetized flow by porous cavity. Non-Darcy formula is carried out to include the term of porosity in momentum expression. Radiative phenomenon is reported for distinct nanoparticle shapes. Aspects of radiative constraint, shape factor, Rayleigh number, magnetic force, and nanoparticles’ shape on nanofluid magneto-hydrodynamic natural convection are analyzed. Result demonstrated that application of external magnetic force deteriorates the convection and this reduction is more perceptible at the greater permeability. The conductive heat transport is the dominating form of heat transportation under the impact of higher magnetic force. For the constant values of Rayleigh, Hartmann’s and Darcy number, $${\text{Nu}}_{{{\text{avg}}}}$$ is independent of shape factor and observes a direct association with the radiation parameter.

In this paper, stagnation point region (suspended with nanofluid and microorganisms) is examined subjected to velocity and thermal slips. The flow is assumed to be flowing across an exponentially stretching flat surface under magnetic field environment. Governing transport equations (framed under Buongiorno's model) are converted into self-similar form through suitable unsteady exponential similarity transformations which are then solved by employing implicit finite difference scheme (IFDS) known as Keller-box method (KBM). A parametric analysis is performed along with limited details of KBM. Influence of pertinent constraints on local skin friction, local Nusselt number, local Sherwood number and local density number of micro-organisms are also uncovered through graphs. A significant decrease in skin-friction coefficients has been detected with respect to thermal slip in comparison to velocity slip. Keywords: Unsteady flow, Stagnation point region, Mixed convection, Microorganisms, Nanoparticles, Slip regime, Keller-box scheme

The main aim of the current paper is to investigate the mass and heat transportation of a Casson nanomaterial generated by the inclination of the surface. The magnetic field effect along with suction or injection are considered. The working nanomaterial is taken into consideration based on the concept of the Buongiorno nanofluid theory, which explores the thermal efficiencies of liquid flows under movement of Brownian and thermophoretic phenomena. The emergent system of differential expressions is converted to dimensionless form with the help of the appropriate transformations. This system is numerically executed by the implementation of Keller–Box and Newton’s schemes. A good agreement of results can be found with the previous data in a limiting approach. The behavior of the physical quantities under concern, including energy exchange, Sherwood number, and wall shear stress are portrayed through graphs and in tabular form. The Nusselt number and Sherwood number are found to diminish against the altered magnitudes of Brownian motion and the inclination parameter. Moreover, the velocity profile decreases with the growth of the inclination effect. In the same vein, the buoyancy force and solutal buoyancy effects show a direct relation with the velocity field. The outcomes have promising technological uses in liquid‐based systems related to stretchable constituents.

The main focus in this work is to explore the features of laminar Blasius and Rayleigh–Stokes flow with ohmic heating under suspension of hybrid nanofluids. The mathematical model is converted into pair of self-similarity equations by applying appropriate transformations. The reduced similarity equivalences are then exploited numerically by Runge–Kutta–Fehlberg fourth–fifth-order scheme. To know the better description of problem, the flow and energy transport features are explored for distinct values of different factors. The present study concludes that the thermal conductivity of hybrid nanofluid is higher than that of a regular nanofluid in the presence of specified factors.

This article executes MHD heat transport augmentation in aqueous based nanoparticles fluid flow over convergent/divergent channel. Joule heating, magnetic field and Darcy-Forchheimer effects are explained for concentration and temperature distributions. Darcy-Forchheimer theory is utilized to explore the impact of porous medium. The system of partial differential expressions is transformed into ordinary ones and evaluated numerically by implementing RKF-45 scheme. Expressions for velocity and temperature profile are derived and plotted under the assumption of flow parameter. Influence of various parameters on heat transfer rates and surface drag force are discussed with the help of table and plots.

The influences of Al2O3 nanoparticles with various shapes on thermal characteristics of nanofluid within a permeable space concerning magnetic force have been simulated by means of CVFEM. To form the final PDEs, radiation term has been incorporated. Impacts of magnetic force, radiation constraint, Rayleigh number and shape factor on nanomaterial behaviour have been analysed. Results demonstrate that the higher values of shape factor lead to augmented convective heat transfer. By augmenting the magnetic strength, conductive heat transfer can be predominant than that of the convection.

Magnetohydrodynamics (MHD) boundary layer slip Casson fluid flow over a dissipated moving cylinder is explored. Casson fluid model is employed as a non-Newtonian material that demonstrates the phenomenon of yield stress. Blood material is considered to be an example of Casson liquid. The non-linear partial differential quantities are transformed into expressions of ordinary derivatives through transformation of similarity variables. These equations are computed for numeric solutions by using Runge-Kutta method along with shooting scheme. The impact of pertinent constraints on the fluid velocity and temperature are examined through graphs. The coefficient of the skin friction and the rate of heat transfer are found numerically. Comparing of the present study with the earlier results is also presented. We observed that the coefficient of skin friction increases for higher values of Hartmann number.

A numerical study of unsteady hydromagnetic flow of Casson liquid passed through the oscillatory moving surface is presented. The interaction of radiation term is reported in the energy equation. The flow is generated by the rapid move?ment of elastic surface that stretched back and forth periodically. The number of variables is reduced by introducing dimensionless variables. An implicit technique developed on finite difference algorithm is implemented to the system of PDE. The impact of various parameters like Casson liquid parameter, the oscillation frequency and stretching rate ratio, Hartmann number and effective Prandtl number are shown through various graphs. The observation indicates that the amplitude of the velocity declines by enhancing Casson liquid parameter, oscillation frequency and stretching rate ratio and Hartmann number. The temperature declines by increasing Casson fluid parameter and effective Prandtl number. The results also indicate that the time-series of local Nusselt number increases by enhancing effective Prandtl number.

In this article, the flow of an incompressible nanoliquid induced due to unsteady contracting cylinder is investigated. Analysis of heat transport phenomenon is reported under uniform heat absorption/generation and convective type boundary condition. A set of transformations is implemented to reduce PDEs to ODEs. The obtained coupled nonlinear equations are treated numerically through the help of RKF 45 technique. Physical evaluation of convective condition and heat absorption/generation on thermal analysis is discussed through graphs. Output shows that both the parameters of convective condition and heat absorption/generation give an increment in liquid temperature and its related thickness of boundary layer. Keywords: Unsteadiness, MHD, Contracting cylinder, Nanoliquid, Uniform heat generation, Numerical solutions

CVFEM is employed in this article to model alumina nanofluid magnetohydrodynamic flow through a permeable enclosure. Influences of Hartmann number, buoyancy, radiation parameters on nanofluid treatment were displayed. Viscosity and thermal conductivity of alumina are predicted considering Brownian motion and shape factor impacts. Results are displayed that Lorentz forces boosts the conduction mechanism. Nu ave enhances with reduce of Ha . Augmenting radiation parameter makes thermal boundary layer to be thinner.

The objective of this research is to study the combined influences of applied electric and magnetic fields on the two-phase peristaltic motion of nanofluid through a curved channel. A two-phase model of a nanofluid, Maxwell’s model of thermal conductivity [1], and no-slip velocity and thermal boundary conditions have been used in this study. Hall effects, Joule heating (due to magnetic and electric fields), and viscous heating aspects are under consideration. Governing equations for the present flow configuration have been modeled and simplified by enforcing the lubrication scheme. Debye-Huckel approximation is used to obtain the analytical solution of the electric potential function (Poisson-Boltzmann equation). Resulting expressions are solved numerically through the NDSolve command in Mathematica and plotted in order to understand the effects of different dimensionless parameters on the temperature, stress, heat transmission rate, and fluid’s velocity. Graphical results demonstrated that the thermal transmission rate is augmented by increasing the Hartmann number, Brinkman number, and Debye-Huckel parameter while decreases for zeta potential ratio, Joule dissipation parameter, and electro-osmotic velocity. A decrease in axial velocity is noted near the lower wall for higher values of $${m}^{\ast}$$ .

The consequences of thermally radiative magneto-nano Casson fluid towards thin needle is executed in this investigation. The problem has been modeled mathematically under the Navier slip effect. The Prandtl boundary-layer expressions are framed and treated numerically after the application of similarity variables. Employing shooting method together with Runge–Kutta (R–K) method, the dimensionless equations are solved. The influence of various pertinent controlled dimensionless variables on momentum and temperature along with quantities related to engineering values specifically shear stress and rate of energy transfer are scrutinized through graphical plots. Multi-wall carbon nanotubes (MWCNTs) act as friction reducing factor. Needle surface transfers heat more from the fluid compared to parabolic revolution. Multi-wall carbon nanotubes transfers more heat from the fluid rather than the single-wall carbon nanotubes (SWCNTs). The heat transfer is more in parabolic surface compared to cylindrical surface and SWCNTs have superior values than MWCNTs. Numerical solutions are matched with the published material and perceived to be in a good agreement.

The combined effects of nonlinear thermal convection and radiation in 3D boundary layer flow of non-Newtonian nanofluid are scrutinized numerically. The flow is induced by the stretching of a flat plate in two lateral directions. The mechanism of heat and mass transport under thermophoretic and Brownian motion is elaborated via implementation of the thermal convective condition. The prevailing two-point nonlinear boundary value problem is reduced to a two-point ordinary differential problem by employing suitable similarity transformations. The solutions are computed by the implementation of homotopic scheme. At the end, a comprehensive parametric study has been conducted to analyze the typical trend of the solutions. It is found that the nanoparticle volume fraction and temperature profiles are stronger for the case of solar radiation in comparison with problem without radiation. Keywords: Non-linear convection, Nonlinear density temperature (NDT), Nonlinear thermal radiation, Three dimensional flow, Maxwell fluid, Nanoparticles

In this article, Control volume based finite element method (CVFEM) is employed to simulate magnetohydrodynamic (MHD) nanofluid convective heat transfer through a porous cavity by means of thermal non-equilibrium model. Nanofluid properties are estimated by means of Koo–Kleinstreuer–Li (KKL) model and Darcy–Boussinesq approximation is employed for momentum equation. Numerical simulations are provided to find the effects of Rayleigh number R a , solid–nanofluid interface heat transfer parameter N h s , Hartmann number H a and porosity e . Outputs depict that velocity augments with increase of N h s while it increases with augment of Rayleigh number. Temperature gradient reduces with augment of porosity.

Numerical study of three dimensional Carreau liquid flow with heat and mass transport features over a variable thickness sheet filled with microorganisms is analyzed. We considered the non-uniform heat sink or source and multiple slip effects. The governing non-linear partially differential expressions are developed into ordinary differential systems by using variable transformations. These expressions are solved numerically by using Runge-Kutta fourth order method connected with shooting methodology. A Parametric study is implemented to demonstrate the effects of Hartmann number, Prandtl number, Weissenberg number, Peclet number, chemical reaction and heat sink/source parameters on liquid velocity, temperature and concentration profiles. The quantities of physical interest are described within the boundary layer. From this analysis, we found that the magnetic parameter decrease the local Sherwood and local Nusselt numbers for both and cases. The constraint of chemical reaction enhances the mass transfer rate and decelerates the density of motile mass transfer rate. The space dependent and temperature dependent heat source/sink suppress the local Nusselt number.

Lattice Boltzmann Method (LBM) is utilized to simulate the magnetohydrodynamic (MHD) nanofluid forced convective heat transfer inside a porous three dimensional enclosure with hot cubic obstacle. Impact of Hartmann number H a , Darcy number D a and Reynolds number Re on nanofluid treatment were depicted. Al2O3- H 2 O nanofluid has been utilized considering single phase model. Results are demonstrated in forms of isokinetic, isotherms , streamlines, Nusselt number and velocity contours. Results show that temperature boundary layer becomes thinner with augment of D a and Re . Convective heat transfer reduces with rise of Hartmann number while it improves with rise of Darcy number.

In this simulation, CuO-H2O nanofluid flow due to Lorentz forces in a permeable channel has been reported via Lattice Boltzmann method. Homogeneous model is considered for nanofluid in which Brownian motion influence is taken into account. Isotherms and streamlines are depicted for various values of effective parameters such as CuO nanoparticles volume fraction, Reynolds number, Darcy number and Hartmann number. Results indicate that heat transfer rate enhances with increase of permeability of porous medium. Similar behavior is reported for Reynolds number. Temperature boundary layer thickness increases in existence of magnetic field.

A numerical study of hydromagnetic radiative stagnation point flow of micropolar nanofluid passed through a shrinking sheet is reported. Magnetic field is utilized in transverse direction. Nonlinear system of partial differential equations is converted into system of nonlinear ordinary ones by applying similarity transformations. Convective types of boundary conditions are applied on temperature and concentration. RKF45 technique is applied to investigate the numerical results of different dimensionless physical parameters in graphical and tabular forms. It is visualized that the increasing values of Biot numbers correspond to enhancement in temperature and nanoparticle volume distributions. Further, we observed that the increasing values of thermophoretic and Brownian motion parameters have reverse effects on nanoparticle volume fraction. Keywords: Micropolar nanofluid, MHD, Shrinking sheet, Brownian motion, Thermophoresis

An investigation is exhibited to analyze the presence of heat source and sink in doubly stratified MHD incompressible tangent hyperbolic fluid due to stretching of cylinder embedded in porous space under nanoparticles. To develop the mathematical model of tangent hyperbolic nanofluid, movement of Brownian and thermophoretic are accounted. The established equations of continuity, momentum, thermal and solutal boundary layers are reassembled into sets of non-linear expressions. These assembled expressions are executed with the help of Runge-Kutta scheme with MATLAB. The impacts of sundry parameters are illustrated graphically and the engineering interest physical quantities like skin friction, Nusselt and Sherwood number are examined by computing numerical values. It is clear that the power-law index parameter and curvature parameter shows favorable effect on momentum boundary layer thickness whereas Weissennberg number reveals inimical influence. Keywords: MHD, Tangent hyperbolic fluid, Heat source/sink, Nanoparticles

We investigated the role of vibrational rotations and slip conditions at liquid-sheet interface in maintaining the three dimensional flow of ferro-nanoliquid (water-Fe3O4) over a bi-directionally stretchable surface under the influence of magnetic field. It is assumed that chemical reactions prevail between two species A and B whose diffusion coefficients are unequal. Also, mass transfer is considered in the presence of homogeneous and heterogeneous reactions for species A and B . Influences of nonlinear thermal radiation along with viscous dissipation and Joule heating are also invoked into the analysis due to their predominance in the control of heat and mass transfer mechanism. Stability and convergence limitations are verified to ensure the accuracy of results. The outcome due to proposed explicit finite difference scheme is exhibited in the form of figures and tables to illustrate the influence of emerging parameters for two cases namely slip nanofluid (SNF) and no slip nanofluid (NSNF). Results reveal that vibrational rotations and slip at the surface of sheet substantially control flow, and heat and mass transfer phenomena.

This article concentrates on the magnetohydrodynamic (MHD) stagnation point flow of tangent hyperbolic nanofluid in the presence of buoyancy forces. Flow analysis caused due to stretching surface. Characteristics of heat transfer are examined under the influence of thermal radiation and heat generation/absorption. Newtonian conditions for heat and mass transfer are employed. Nanofluid model includes Brownian motion and thermophoresis. The governing nonlinear partial differential systems of the problem are transformed into a systems of nonlinear ordinary differential equations through appropriate variables. Impact of embedded parameters on the velocity, temperature and nanoparticle concentration fields are presented graphically. Numerical computations are made to obtain the values of skin friction coefficient, local Nusselt and Sherwood numbers. It is concluded that velocity field enhances in the frame of mixed convection parameter while reverse situation is observed due to power law index. Effect of Brownian motion parameter on the temperature and heat transfer rate is quite reverse. Moreover impact of solutal conjugate parameter on the concentration and local Sherwood number is quite similar.

The consequence of thermal radiation in laminar natural convective hydromagnetic flow of viscous incompressible fluid past a vertical cone with mass transfer under the influence of chemical reaction with heat source/sink is presented here. The surface of the cone is focused to a variable wall temperature (VWT) and wall concentration (VWC). The fluid considered here is a gray absorbing and emitting, but non-scattering medium. The boundary layer dimensionless equations governing the flow are solved by an implicit finite-difference scheme of Crank–Nicolson which has speedy convergence and stable. This method converts the dimensionless equations into a system of tri-diagonal equations and which are then solved by using well known Thomas algorithm. Numerical solutions are obtained for momentum, temperature, concentration, local and average shear stress, heat and mass transfer rates for various values of parameters Pr, Sc, λ, Δ, Rd are established with graphical representations. We observed that the liquid velocity decreased for higher values of Prandtl and Schmidt numbers. The temperature is boost up for decreasing values of Schimdt and Prandtl numbers. The enhancement in radiative parameter gives more heat to liquid due to which temperature is enhanced significantly. Keywords: Chemical reaction, Heat generation/absorption, MHD, Radiation, Vertical cone

The present research explores the three-dimensional stretched flow of viscous fluid in the presence of prescribed heat (PHF) and concentration (PCF) fluxes. Mathematical formulation is developed in the presence of chemical reaction, viscous dissipation and Joule heating effects. Fluid is electrically conducting in the presence of an applied magnetic field. Appropriate transformations yield the nonlinear ordinary differential systems. The resulting nonlinear system has been solved. Graphs are plotted to examine the impacts of physical parameters on the temperature and concentration distributions. Skin friction coefficients and local Nusselt and Sherwood numbers are computed and analyzed. Keywords: Three-dimensional flow, MHD, Flux conditions, Viscous dissipation, Joule heating, Exponentially stretching surface

The aim of this article is to highlight the unsteady mixed convective couple stress nanoliquid flow passed through stretching surface. The flow is generated due to periodic oscillations of sheet. An appropriate set of dimensionless variables are used to reduce the independent variables in governing equations arising from mathematical modeling. An analytical solution has been computed by employing the technique of homotopy method. The outcomes of various sundry parameters like couple stress parameter, the ratio of angular velocity to stretching rate, thermophoresis parameter, Hartmann number, Prandtl number, heat source/sink parameter, Schmidt number described graphically and in tabular form. It is observed that the velocity profile increases by increasing mixed convection parameter and concentration buoyancy parameter. The temperature enhances for larger values of Hartmann number and Brownian. The concentration profile increases by increasing thermophoresis parameter. Results show that wall shear stress increases by increasing couple stress parameter and ratio of oscillating frequency to stretching rate. Keywords: Oscillatory surface, Couple stress fluid, Nanoparticles, Heat absorption/generation

The nonlinear convective flow of kerosene-Alumina nanoliquid subjected to an exponential space dependent heat source and temperature dependent viscosity is investigated here. This study is focuses on augmentation of heat transport rate in liquid propellant rocket engine. The kerosene-Alumina nanoliquid is considered as the regenerative coolant. Aspects of radiation and viscous dissipation are also covered. Relevant nonlinear system is solved numerically via RK based shooting scheme. Diverse flow fields are computed and examined for distinct governing variables. We figured out that the nanoliquid’s temperature increased due to space dependent heat source and radiation aspects. The heat transfer rate is higher in case of changeable viscosity than constant viscosity.

Impact of gyrotactic microorganisms on two-dimensional (2D) stratified flow of an Oldroyd-B nanomaterial is highlighted. Applied magnetic field along with mixed convection is considered in the formulation. Theory of microorganisms is utilized just to stabilize the suspended nanoparticles through bioconvection induced by combined effects of buoyancy forces and magnetic field. Convergent series solutions for the obtained nonlinear differential systems are derived. Impacts of different emerging parameters on velocity, temperature, concentration, motile microorganisms density, density number of motile microorganisms and local Nusselt and Sherwood numbers are graphically addressed. It is observed that thermal, concentration and motile density stratification parameters result in reduction of temperature, concentration and motile microorganisms density distributions respectively.

The presence of dust particles is involved in many engineering and industrial processes like transport of petroleum, emission of smoke from vehicles, piping of power plants, treatment of wastewater, and corrosive particles in mining. Because of the importance of this phenomenon, we considered the Casson liquid flow past a stretching hollow cylinder with fluid–particle suspension and convective boundary condition aspects. Numerical solution is obtained via shooting techniques after the applying of similarity variables to the governing partial equations. Key parameters of the problem are discussed through graphs. It is noticed that the clean fluid temperature is always higher value than the dust fluid and also the presence of radiation enhanced the temperature at the surface.

Peristalsis of fluids through curved geometries is widely encountered in several industrial and domestic pumping devices. Keeping this fact in mind, effects of variable magnetic field on peristalsis of Carreau-Yasuda (C-Y) fluid through a curved channel with velocity and thermal slip boundary conditions are studied. Heat transfer analysis has been carried out by considering the Joule heating and viscous dissipation effects. The long wavelength and small Reynolds number assumptions are adopted in mathematical modeling of the problem. Resulting non-linear system of differential equations has been solved numerically. Graphical results for axial velocity, temperature, heat transfer rate and stresses at the walls for the different flow parameters are discussed. It is reported that the radially varying magnetic field decreases velocity and increases the temperature of the fluid. Such magnetic field also enhances the heat transfer rate and stresses at the boundaries.

In this work, effects of nonlinear thermal radiation and first order chemical reaction on the boundary layer flow of Williamson nanofluid over a non-uniformly thicked stretchable Riga plate are examined. The analysis is subjected to the newly devised zero nanoparticles mass flux surface conditions and heat transfer due to convective boundary conditions. Governing boundary layer equations depicting mechanical properties of the considered plate and flow over it are made dimensionless using suitable transformations. Numerical results obtained through an implicit finite difference scheme (Keller-box method) reveal that flow inside the boundary layer is substantially influenced by radiation, chemical reaction, and a surface parallel Lorentz force.

This research is made to show the impact of external magnetic source on Fe3O4 – water nanofluid treatment in a permeable cavity. Shape factor effect on nanofluid properties are taken into account. Final equations are derived by means of vorticity stream function formulation. Control volume based finite element method is employed for solving final formulae. Figures are depicted for various values of radiation parameter, Darcy number, Fe3O4 –water volume fraction, Rayleigh number and Hartmann number. Results reveal that selecting Platelet shaped nanoparticles results the highest heat transfer rate. Nanofluid velocity and heat transfer rate decrease with augment of Hartmann number.

Entropy generation is one of the key features in the analysis as it exhibits irreversibility of the system. Therefore, present study investigates entropy generation rate in a mixed convective peristaltic motion of a reactive nanofluid through an asymmetrical divergent channel with heat and mass transfer characteristics. Endorsed nanofluid model holds thermophoresis and Brownian diffusions. Mathematical modeling is configured under the effects of mixed convection, heat generation/absorption and viscous dissipation. Chemical reaction is also introduced for the description of mass transportation. Resulting system of differential equations is numerically tackled by employing the Shooting method. Findings reveal that entropy generation rises by improving Brownian motion and thermophoresis parameters. Temperature of nanofluid decreases by rising buoyancy forces caused by concentration gradient. Concentration profile increases by increasing chemical reaction parameter. Velocity increases by enhancing Brownian motion parameter.

In this research, steady-state magnetized nanofluid flow under radiative wavy cavity is demonstarted. The porosity term is modeled by employing the non-Darcy’s theory of porosity. The working nanofluid is based on water-Al2O3 type nano-powder with the concnetration of 4%. The numerical modeling is estimated via control volume finite element (CVFE) technique. The results against the distinct emerging constraints namely magnetic force, Rayleigh number, porosity factor, shape factors, and shape of nanoparticles values on flow streamlines, average Nusselt number ( N u avg ) and isotherms are sketched and reported indetail. The sequence of radition on nanoraticles is discussed by considering distinct nanoparticles forms. The results show that the fluid advection decays with the enhancing trend of the media porosity and the phenomenon of conduction dominates over the process of convection. The nanoparticle shape insignificantly influences the N u avg for incrementing trend of magnetic and buoyancy forces.

In this manuscript, steady naturally convected nanofluid flow involving thermal radiation has been simulated by involving the inclined magnetic field. Aluminum-oxide nanoparticles are submerged into ordinary electrically conducting H2O. Radiative phenomenon along with distinct nanoparticles shapes is executed. The problem is formulated with the help of basic principles of fluid mechanics and the code is designed for achieving problem solutions. The nature of radiated constraint, Rayleigh number, nanoparticles' shape and magnetic field on nanofluid is labeled and discussed for distinct important quantities. Results revealed that the conduction process is significant mode of heat transportation for higher Darcy factor. The magnetic field utilization obstructs the flow circulation stimulated by the temperature gradient induced buoyancy force.

This study demonstrated the effect of conical and fusiform turbulators placed in double-pipe heat exchanger (DPHE) on the heat transportation and turbulent flow designs. A total of 21 configurations including conical and fusiform turbulator inserts are simulated in a double-pipe heat exchanger with circular and rectangular tube configurations at four Reynolds number levels (Re = 4000, 7000, 10000, and 13000) on the tube side. Utilizing Fluent software, the finite-volume scheme is implemented to discretize the turbulence flow equations using the realizable k–e model. The results demonstrate that the maximum convective heat transfer coefficient is achieved when using a heat exchanger having a circular inner pipe. Further, the performance index of the heat exchanger (HE) is found to increase by modifying the shape of conical turbulators to fusiform. The DPHE with circular inner pipes and 12 mm fusiform turbulators is found to be the optimal configuration in-terms of thermal performance. At Re = 4000, the configuration with fusiform 9 mm inserts and a rectangular inner pipe with a 0.72 aspect ratio offered the highest coefficient of performance (approximately 27.74) with the overall heat transfer coefficient increased by 4.58% compared to the plain rectangular tube and by 4.68% compared to the circular tube without turbulators.

Present study addresses the Marangoni transport of dissipating SWCNT and MWCNT nanofluids under the influence of magnetic force and radiation. A novel exponential space dependent heat source is considered. The flow is generated due to a disk with surface tension created by thermal gradient. The partial differential equations system governing the flow of carbon-water nanoliquids and heat transfer through Marangoni convection is established. Subsequent system is reduced to nonlinear ordinary boundary value problem via generalized Karman transformations. Numerical solutions are developed of the arising nonlinear problem via Runge-Kutta based shooting approach. Impacts of embedded parameters are focused on Nusselt number , velocity and heat transport distributions through graphical illustrations. Our simulations figured out that the heat transfer rate increased via Marangoni convection; however it is decayed by applied magnetic force. The temperature of SWCNT-H 2O nanoliquid dominates MWCNT-H2O nanoliquid.

In this research, influence of Lorentz forces on nanofluid free convection inside a porous cavity is simulated. Simulations have been done via Lattice Boltzmann Method (LBM). Koo-Kleinstreuer-Li (KKL) model is applied in order to consider Brownian motion impact on nanofluid properties. Impacts of Darcy number ( Da ) , Rayleigh number ( Ra ) , nanofluid volume fraction ( ϕ ) and Hartmann number ( Ha ) on heat transfer treatment are illustrated. Outputs demonstrate that temperature gradient reduces with increase of Ha while it increases with augment of permeability of porous media and buoyancy forces.

This investigation looks at the effects of thermal radiation on the magnetohydrodynamic flow of Casson fluid over a stretched surface subject to power law heat flux and internal heat generation. Conservation of mass, linear momentum and energy are used in the development of relevant flow equations. Series solutions for velocity and temperature are derived. Effects of embedded physical parameters on the velocity and temperature profiles are analyzed. Numerical values of skin-friction coefficient and local Nusselt number are examined.

The present research focuses on three-dimensional nonlinear convective flow of viscoelastic nanofluid. Here, the flow is generated due to stretching of a impermeable surface. The phenomenon of heat transport is analyzed by considering thermal radiation and prescribed heat flux condition. Nanofluid model comprises of Brownian motion and thermophoresis. An electrically conducting fluid is accounted due to consideration of an applied magnetic field. The dimensionless variables are introduced for the conversion of partial differential equations into sets of ordinary differential systems. The transformed expressions are explored through homotopic algorithm. Behavior of different dimensionless parameters on the non-dimensional velocities, temperature and concentration are scrutinized graphically. The values of skin friction coefficients, Nusselt and Sherwood numbers are also calculated and elaborated. It is visualized that the heat transfer rate increases with Prandtl number and radiation parameter is higher.

Heat and mass transfer effects in the three-dimensional mixed convection flow of a viscoelastic fluid with internal heat source/sink and chemical reaction have been investigated in the present work. The flow generation is because of an exponentially stretching surface. Magnetic field normal to the direction of flow is considered. Convective conditions at the surface are also encountered. Appropriate similarity transformations are utilized to reduce the boundary layer partial differential equations into the ordinary differential equations. The homotopy analysis method is used to develop the solution expressions. Impacts of different controlling parameters such as ratio parameter, Hartman number, internal heat source/sink, chemical reaction, mixed convection, concentration buoyancy parameter and Biot numbers on the velocity, temperature and concentration profiles are analyzed. The local Nusselt and Sherwood numbers are sketched and examined.

This research article provides the magnetohydrodynamic (MHD) boundary-layer flow of Maxwell nanomaterial saturating a non-Darcy porous medium. Flow is generated due to a stretching surface. The flow in porous media is characterized by considering the Darcy–Forchheimer based model. Novel features of Brownian motion and thermophoresis are retained. A uniform applied magnetic field is employed. Small magnetic Reynolds number and boundary-layer assumptions are employed in the formulation. Simultaneous effects of convective heat and zero nanoparticles mass flux conditions are imposed. Transformation procedure is adopted to convert the partial differential system into the nonlinear ordinary differential system. The governing nonlinear ordinary differential system is solved for the convergent homotopic solutions. Convergence analysis is performed through the plot and numerical data. Graphs have been plotted in order to analyze the temperature and concentration profiles by distinct pertinent flow parameters. Local Nusselt number is also computed and examined.

Influence of thermal radiation on nanofluid heat transfer in existence of Lorentz forces is investigated. Viscosity of Fe3O4 ferrofluid is considered as a function of magnetic field. CVFEM is selected to solve this problem. Effects of radiation parameter ( Rd ) , inclination angle ( ξ ) , Fe3O4-water volume fraction ( ϕ ) , Hartmann ( Ha ) and Rayleigh ( Ra ) numbers are demonstrated graphically. A correlation for average Nusselt number is extracted. Results demonstrate that rate of heat transfer enhances with augment of inclination angle. Nusselt number augments with rise of buoyancy forces and radiation parameter but it reduces with rise of Hartmann number.

Heat and mass transfer effects in three-dimensional mixed convection flow of viscoelastic fluid over a stretching surface with convective boundary conditions are investigated. The fluid is electrically conducting in the presence of constant applied magnetic field. Conservation laws of energy and concentration are based upon the Soret and Dufour effects. First order chemical reaction effects are also taken into account. By using the similarity transformations, the governing boundary layer equations are reduced into the ordinary differential equations. The transformed boundary layer equations are computed for the series solutions. Dimensionless velocity, temperature, and concentration distributions are shown graphically for different values of involved parameters. Numerical values of local Nusselt and Sherwood numbers are computed and analyzed. It is found that the behaviors of viscoelastic, mixed convection, and concentration buoyancy parameters on the Nusselt and Sherwood numbers are similar. However, the Nusselt and Sherwood numbers have qualitative opposite effects for Biot number, thermophoretic parameter, and Soret-Dufour parameters.

The main purpose of this research is to evaluate the impact of Darcy–Forchheimer flow in an incompressible third-grade liquid through Cattaneo–Christov heat flux approach. The Cattaneo–Christov heat flux theory is adopted to govern the mathematical expression of energy, which involves the heat flux relaxation time chracteristics. Time-dependent thermal conductivity is accounted. The steady problem is reduced to ordinary differential equations via suitable transformation. Numerical solutions for the resulting flow expressions have been computed with the help of Euler's explicit technique. Impact of influential variables on the velocity, temperature and skin-friction coefficient have been demonstrated and discussed through graphs. Copyright © 2017 John Wiley & Sons, Ltd.

The effect of non-linear convection in a laminar three-dimensional Oldroyd-B fluid flow is addressed. The heat transfer phenomenon is explored by considering the non-linear thermal radiation and heat generation/absorption. The boundary layer assumptions are taken into account to govern the mathematical model of the flow analysis. Some suitable similarity variables are introduced to transform the partial differential equations into ordinary differential systems. The Runge-Kutta-Fehlberg fourth- and fifth-order techniques with the shooting method are used to obtain the solutions of the dimensionless velocities and temperature. The effects of various physical parameters on the fluid velocities and temperature are plotted and examined. A comparison with the exact and homotopy perturbation solutions is made for the viscous fluid case, and an excellent match is noted. The numerical values of the wall shear stresses and the heat transfer rate at the wall are tabulated and investigated. The enhancement in the values of the Deborah number shows a reverse behavior on the liquid velocities. The results show that the temperature and the thermal boundary layer are reduced when the non-linear convection parameter increases. The values of the Nusselt number are higher in the non-linear radiation situation than those in the linear radiation situation.

Here, our aim is to address the mixed convective stagnation point flow of Carreau liquid over a moving permeable surface. Constitutive expression of an incompressible Carreau liquid is taken into account. The assumptions of boundary layer are implemented in the mathematical modeling of considered physical phenomenon. A well-known analytical technique homotopy analysis method is employed for the computations of governing equations. The numerical data of skin friction coefficient and local Nusselt number is obtained and explored. The velocity is enhanced for larger ratio of rate constants. The increasing values of suction parameter correspond to less velocity and temperature profiles. Further, a benchmark is presented to validate the solutions obtained here. It is noted that the computed analytical solutions have excellent match with previous published materials in a limiting manner.

Magnetohydrodynamic CuO-water nanofluid flow in a porous semi annulus with constant heat flux is studied by means of Control Volume based Finite Element Method. Koo-Kleinstreuer-Li correlation and Darcy model are applied for nanofluid and porous media, respectively. Effective parameters are radius of inner cylinder, CuO-water volume fraction, Hartmann and Rayleigh numbers for porous medium. A formula for Nuave is presented. Results revealed that heat transfer augmentation decreases with rise of buoyancy forces. Influence of adding nanoparticle augments with increase of Lorentz forces. Increasing Hartmann number leads to a reduction in temperature gradient.