Hall and ion-slip effects on mixed convection flow of Williamson nanofluid over a nonlinear porous stretching sheet with variable thermal conductivity

The intent of this investigation is to analyze the Williamson nanofluid stream past a nonlinearly broadening surface through a leaky medium in the existence of mixed convection, Hall, ion-slip, thermal radiation, and viscous dissipation impacts. Suitable similitude changes give joined nonlinear differential schemes, which were numerically explained via spectral relaxation method. Effectiveness of various physical parameters on velocity ingredients, temperature, and nanoparticle concentration distributions alongside the physical quantities of interests was uncovered graphically. It is found that both velocity profiles increment with an expansion in the Hall parameter. Also, the opposite behavior is noticed for the primary and auxiliary velocity profiles as the ion-slip parameter rises. Moreover, it is observed that the primary velocity and concentration profiles expand with an expansion in the velocity power index parameter, however, the secondary velocity profile reduces. Further, it was showed that the fluid velocities decay while temperature distribution advances by the superior values of the Williamson fluid parameter. Finally, the authenticity of the outcomes was confirmed by contrasting them with prior outcomes under some limited presumptions and discovered to be in terrific understanding.     

Entropy analysis of unsteady MHD three-dimensional flow of Williamson nanofluid over a convectively heated stretching sheet

This article addresses an investigation of the entropy analysis of Williamson nanofluid flow in the presence of gyrotactic microorganisms by considering variable viscosity and thermal conductivity over a convectively heated bidirectionally stretchable surface. Heat and mass transfer phenomena have been incorporated by taking into account the thermal radiation, heat source or sink, viscous dissipation, Brownian motion, and thermophoretic effects. The representing equations are nonlinear coupled partial differential equations and these equations are shaped into a set of ordinary differential equations via a suitable similarity transformation. The arising set of ordinary differential equations was then worked out by adopting a well-known scheme, namely the shooting method along with the Runge-Kutta-Felberge integration technique. The effects of flow and heat transfer controlling parameters on the solution variables are depicted and analyzed through the graphical presentation. The survey finds that magnifying viscosity parameter, Weissenberg number representing the non-Newtonian Williamson parameter cause to retard the velocity field in both the directions and thermal conductivity parameter causes to reduce fluid temperature. The study also recognizes that enhancing magnetic parameters and thermal conductivity parameters slow down the heat transfer rate. The entropy production of the system is estimated through the Bejan number. It is noticeable that the Bejan number is eminently dependent on the heat generation parameter, thermal radiation parameter, viscosity parameter, thermal conductivity parameter, and Biot number. The skillful accomplishment of the present heat and mass transfer system is achieved through the exteriorized choice of the pertinent parameters.     

Unsteady 3D mixed convection flow of a chemically reactive Oldroyd-B nanofluid configured by a periodically accelerated surface

Fundamental developments in nanotechnology have attracted the attention of scientists towards the interaction of nanoparticles due to their fascinating applications in thermal engineering and solar energy systems. Convinced by such motivating applications, the current research project addresses the utilization of nanoparticles in the unsteady three-dimensional chemically reactive flow of an Oldroyd-B fluid induced by a bidirectional oscillatory stretching surface. The effects of mixed convection are also considered here. The prime features of the nanofluid namely thermophoresis and Brownian motion characteristics are explored by introducing the famous Buongiorno's nanofluid model. The relevant equations for the formulated theoretical model have been reduced by the appropriate transformations for which the analytic solution is deliberated via the homotopic technique. Later on, a complete graphical analysis for distinct flow parameters is deliberated for dimensionless velocities, concentration, and temperature distributions with the relevant physical implications. Moreover, stimulating physical quantities like local Nusselt and Sherwood numbers are numerically calculated and discussed. The study emphasizes that decreasing variation in both components of velocities has been reported with an increment of relaxation time, while the impact of the retardation time constant is quite opposite. It is further claimed that the velocity distribution has an increasing tendency in the horizontal direction for a higher buoyancy ratio and mixed convection parameters. Moreover, an increment in thermophoresis parameter enhances both temperature and concentration distributions.     

Mathematical modeling and study of MHD flow of Williamson nanofluid over a nonlinear stretching plate with activation energy

This study investigates the Williamson nanofluid flow through a nonlinear stretching plate. It aims to analze the global influence of Williamson parameter (λ) rather than local, which is researched for a linear stretching case in the literature. In addition, the features of activation energy are also taken into account in the current review. The developed model with the consequent similarity transformation has still not been perceived. The transformed partial differential equations are solved analytically. The consequences of embedded parameters on the velocity, temperature, and concentration profiles are displayed through figures. Also, the consequences of embedded parameters on skin friction, heat transfer, and mass transfer are demonstrated through tables.     

Analytical approach on magnetohydrodynamic Casson fluid flow past a stretching sheet via Adomian decomposition method

Flow phenomena of three-dimensional conducting Casson fluid through a stretching sheet are proposed in the present investigation with the impact of the magnetic parameter in a permeable medium. The adaptation of particular transformations is useful to modify the governing equations into their nondimensional as well as the ordinary form. However, these transformed equations are nonlinear and approximate analytical methods for the solution of the complex form of governing equations. In particular, the Adomian decomposition method is proposed for the solution. The behavior of several variables, such as the magnetic and porous matrix, on the flow profile as well as the rate of shear stress, are discussed via graphs and tables. The conformity of the current result with the earlier study shows a road map for further investigation. The major concluding remarks are; the retardation in the velocity distribution is rendered due to an increase in the Casson parameter moreover, the Casson parameter favors in reducing the rate of shear stress coefficient in magnitude.     

Study of chemically reactive and thermally radiative Casson nanofluid flow past a stretching sheet with a heat source

Nanoparticle (NP) delivery is an exciting and rapidly developing field that adequately takes care of thermal radiation in blood flow and is likely to have bearing on the therapeutic procedure of hyperthermia, blood flow, and heat transfer in capillaries. The NP parameters such as size, shape, and surface characteristics can be regulated to improve nano-drug delivery efficiency in biological systems. The NPs outperform traditional drug delivery processes in drug carrying capacity and controlled release. The current article investigates the boundary layer flow and heat transfer of thermally radiative Casson nanofluid (NF) over a stretching sheet with chemical reaction and internal heat source. In our study, Cu and Al₂O₃ are taken as NPs in a suitable base fluid. The problem is analyzed by using similarity transformations and is solved with MATLAB's built-in solver bvp4c. The effects of pertinent parameters characterizing the flow model are presented through graphs and tables. The important findings of the investigation are noted as: the use of metallic oxide is more beneficial to attain higher temperature within a few layers close to the bounding surface; the appearance of convexity and concavity in the concentration profile attributed to flow instability, and the constructive and destructive heterogeneous reactions at the bounding surface have distinct roles to modify the NF flow in the boundary layer.     

Mixed convection flow of a Maxwell nanofluid with Hall and ion‐slip impacts employing the spectral relaxation method

This article investigates the Hall and ion‐slip impacts on the mixed convection flow of a Maxwell nanofluid over an expanding surface in a permeable medium. The impacts of Brownian movement and thermophoresis parameters, Soret, Dufour, viscous dissipation, chemical reaction, and suction parameters, are, moreover, considered. Using the similitude changes, the partial differential equations with regard to the momentum, energy, and concentration equations are transformed to an arrangement of nonlinear ordinary differential equations, which are handled numerically utilizing a spectral relaxation method (SRM). The impacts of noteworthy physical parameters on the velocities, thermal, and concentration distributions are investigated graphically. Moreover, the numerical values of skin‐friction coefficients, local Nusselt number, and Sherwood number for different values of the mixed convection parameter $\left(\gamma \right),$ Deborah number $\left(\lambda \right),$ Hall parameter $({\beta }_{\mathrm{H}}),$ ion‐slip parameter $({\beta }_{\mathrm{i}}),$ Dufour number (Du), and Soret number $\left(\mathit{Sr}\right)$ are computed and tabulated. It is discovered that ascent in Deborah number reduces both the stream and transverse velocity profiles, while the inverse pattern is seen with augmentation in the mixed convection parameter. In addition, inverse patterns of the stream and transverse velocity profiles are seen with expansion in magnetic, Hall, and ion‐slip parameters. Besides this, the temperature and concentration disseminations decline with augmentation in Dufour number and chemical reaction parameters, respectively. It is likewise seen that both the skin‐friction coefficients lessen with expansion in Deborah number, and they ascend with upgrade in blended convection and ion‐slip parameters, while the opposite condition is noticed with augmentation in Hall parameter. Furthermore, the reverse trends of local Nusselt and Sherwood numbers are discovered with expansion in the Dufour and Soret numbers.     

Numerical simulation of Dufour and Soret impacts on MHD Williamson nanofluid flow through an inclined surface

The carry-outs of Dufour and Soret, as well as radiation, and chemical response on a non-Newtonian MHD Williamson nanofluid flow through an inclined extended plane are discussed in this article. Keller-box analysis is being used to explore the influence of the Williamson factor here on the fluid domain quantitatively. Ordinary differential equations (ODEs) are recovered from boundary flow equations using appropriate similarity transformations. These ODEs are numerically addressed. Graphs and comparisons are used to simulate and study the features of flow characteristics such as velocity, temperature, and concentration of Williamson nanofluids distributions in response to various emerging parameters. The numerical computations show that our results are in reasonable harmony with previous studies. The numerical computations revealed that for the time being, the density of the momentum fluid layers is diminishing for the values of $ᴦ$, Le, $\Omega$, M, and increasing for Gc, Gr. The thickness of the thermal boundary layer is decreasing for Sr, Df, Pr, Gc, and Gr. M, $ᴦ$, $\Omega$, R, N, and Le are all on the rise. The concentration profile for R, Le, Nb, Nt, Gr, Gc, and N is decreasing, while Pr, Df, Sr, M, $ᴦ$, and $\Omega$ are increasing.     

Entropy generation in MHD Williamson nanofluid over a convectively heated stretching plate with chemical reaction

This investigation focuses on the influence of thermal radiation on the magnetohydrodynamic flow of a Williamson nanofluid over a stretching sheet with chemical reaction. The phenomena at the stretching wall assume convective heat and mass exchange. The novelty of the present study is the thermodynamic analysis in the nonlinear convective flow of a Williamson nanofluid. The resulting set of the differential equations are solved by the homotopy analysis method. We explored the impacts of the emerging parameters on flow, heat, and mass characteristics, including the rate of entropy generation and the Bejan number through graphs, and extensive discussions are provided. The expressions for skin friction, Nusselt and the Sherwood numbers are also analyzed and explored through tables. It is concluded that the rate of mass transfer may be maximized with the variation of the Williamson and chemical reaction parameters. Moreover, the entropy generation rate and the Bejan number are augmented via increasing the Williamson parameter.     

Viscous dissipation effect on mixed convective heat transfer of MHD flow of Williamson nanofluid over a stretching cylinder in the presence of variable thermal conductivity and chemical reaction

The effect of viscous dissipation and thermal radiation on mixed convective heat transfer of an MHD Williamson nanofluid past a stretching cylinder in the existence of chemical reaction is analyzed in this study. When energy equation is formulated, the variable thermal conductivity is deliberated. By proposing applicable similarity transformations, nonlinear ordinary differential equations (ODEs) are attained from partial differential equations. These nondimensional ODEs are computed through Runge-Kutta method integrated with shooting method using MATLAB software. The results found numerically are in agreement with that of the published works of similar nature in a limiting case. The results of the local Nusselt number, skin friction coefficient, and Sherwood numbers are organized in tables. The influence of protuberant parameters on temperature, velocity, and concentration is presented by graphs. From the results, it is seen that for higher values of variable thermal conductivity parameter, the local Sherwood number and skin friction coefficient upsurge, whereas the local Nusselt number diminishes.     

MHD Williamson nanofluid across a permeable medium past an extended sheet with constant and irregular thickness

The main resource of this paper is to establish over fluid flows sheet using mathematical modeling for constant and variable thickness by including magnetic fields, electric fields, porous medium, heat propagation/immersion, and radiative heat relocation. The Implicit Finite Difference Method (IFDM) is applied to simplify using similarity conversions to implicate partial differential equations to convert into ordinary differential equations. IFDM has been implemented in MATLAB to tabulate numerical observations of the local parameters. Nusselt and Sherwood numbers are analyzed and measured for different parameters in different constant and variable thickness conditions of fluid properties. The influence of various parameters is explained through temperature, velocity, concentration, and nanoparticle volume fraction graphical representations. The coefficient of the skin friction for irregular fluid properties is shown to have a greater influence than that compared for constant fluid properties. Nevertheless, there is a reverse case in the local Nusselt number that is lower for the fluctuating fluid properties than with constant fluid properties. The results showed high-exactness computational outcomes are attained from the IFDM.     

MHD nonlinear natural convection flow of a micropolar nanofluid past a nonisothermal rotating disk

The aim of this analysis is to examine the steady, laminar boundary layer flow of a micropolar nanofluid owing to a rotating disk in the presence of a magnetic field and thermal and solutal nonlinear convection and nonisothermal parameters. The governing joined partial differential equations are converted into nonlinear ordinary differential equations by means of available transformations. The equations are calculated using the method bvp4c from Matlab software. The convergence test has been maintained; for the number of spots greater than the appropriate mesh number of points, the precision is not influenced, but the set time is boosted. Moreover, various quantities of the main parameters on skin friction coefficients, wall couple stress coefficients, Nusselt number, Sherwood number, velocities, temperature, and concentration of nanofluid are analyzed by means of tables and graphs. The results indicate that the presence of the nonisothermal parameter boosts the radial skin friction, temperature, and Sherwood number but causes decaying concentration distributions, the azimuthal skin friction coefficient, and Nusselt number that indicate the diffusion of momentum occurs more around the surface of the rotating disk.     

Thermophoresis and Brownian motion effects on Williamson nanofluid flow past a stretching surface with thermal radiation and chemical reaction

The heat transfer mechanism of nanofluids has numerous industrial applications owing to the non-Newtonian behavior and has been exercised as a thermophysical phenomena in presence of thermal radiation. The present paper deals with the thermal transfer characteristics of time-independent magnetohydrodynamics Williamson fluid past a stretching surface in presence of the reaction of chemical equilibrium is dealt. The flow constitutive nonlinear partial differential coupled equations are transmitted into ordinary differential equalities by employing relevant similarity transmutations. These deduced equations are determined by using the Runge–Kutta numerical technique with a shooting approach with the aid of MATLAB software. Influences of distinct pertinent flow parameters like an inclined uniform magnetic field, Soret number, heat generation/absorption, and Schmidt number constrained to convective boundary condition is displayed through graphs with relevant physical interpretations. Computed numerical values for the friction factor coefficient, local Nusselt parameter, and Sherwood number are tabulated.      

Finite element analysis of couple stress micropolar nanofluid flow by non‐Fourier's law heat flux model past stretching surface

Numerical analysis has been done to investigate magnetohydrodynamics nonlinear convective flow of couple stress micropolar nanofluid with Catteneo‐Christov heat flux model past stretching surface with the effects of heat generation/absorption term, chemical reaction rate, first‐order slip, and convective boundary conditions. The coupled highly nonlinear differential equation governing the steady incompressible laminar flow has been solved by a powerful numerical technique called finite element method. The impacts of diverse parameters on linear velocity, angular velocity (microrotation), temperature, concentration profile, local skin friction coefficient, local wall couple stress, local Nusselt number, and Sherwood number are presented in graphical and tabular form. The result pointed out that the enhancement in material parameter β increases the velocity of the fluid while the couple stress parameter K has quite opposite effect. Heat and mass transfer rate of the fluid are enhanced by increasing material parameter while couple stress parameter shows the opposite influence. Moreover, heat and mass transfer rate are higher with the Catteneo‐Christov heat flux model than Fourier's law of heat conduction. The accuracy of the present method has been confirmed by comparing with previously published works.     

Characteristics of MHD three-dimensional flow of nanofluid over a permeable stretching porous sheet

The aim of the present work is to focus on heat and mass transfer characteristics of the magnetohydrodynamic three-dimensional flow of nanofluid over a permeable stretching porous sheet. The significance of this study is the consideration of copper-based and aluminum oxide-based nanofluids. The physical parameters like a chemical reaction, Soret effect, radiation, and heat generation, and radiation absorption being involved in this examination are novel. The nonlinear partial differential equations are transformed into ordinary differential equations by adopting suitable similarity transformations. The numerical solutions are obtained by applying the Runge–Kutta method of fourth-order with the Shooting technique using MATLAB. The results obtained are presented through graphs and tables for various parameters. A comparison with published results has been done to validate the methodology and found good coincidence. It is claimed that the increase in heat generation parameters results in increasing the temperature. With an increase in the Soret effect, the skin friction coefficient along x-axis increases and skin friction coefficient along the y-axis, Nusselt number and Sherwood number decrease.     

Second law analysis of pseudo-plastic nanofluid stream past a stretching sheet with a sliding consequence

The entropy generation (second law of thermodynamics) analysis of gyrotactic microorganism flow of power-law nanofluid with slip effects and combined effect of heat and mass transfer past a stretching sheet has been studied. The flow is maintained with Lorentz force and thermal radiation. The governing nonlinear partial differential equations are transformed into ordinary differential equations using similarity transformations. The impact of different physical parameters, such as convective bouncy parameter, power-law parameter, Brownian motion parameter, thermophoresis parameter, and slip parameter for velocity and temperature on the entropy generation number (Ns) are plotted graphically with the help of MATLAB built in bvp4c solver technique. Further, the uniqueness of this study is to find out the ratios of various irreversibilities due to thermal and mass diffusions, momentum diffusion, and microorganism over the total entropy generation rate. Our results showed that the power-law parameter and Brownian motion parameter influenced entropy generation positively. The slip parameter for velocity and temperature and the thermophoresis parameter helps to reduce the entropy production.     

Unsteady MHD mixed convection flow of a micropolar fluid along an inclined stretching plate

In this research, the unsteady magnetohydrodynamic mixed convection flow of a micropolar fluid over an inclined plate has been investigated. The problem is reduced to a system of non‐dimensional partial differential equations, which are solved numerically using the implicit finite‐difference scheme. Velocity profiles, temperature profiles, concentration profiles, the skin friction coefficient, the rate of heat transfer, and the rate of mass transfer are computed numerically for various values of different physical parameters. In this study, we consider both assisting and opposing flow. It is found that in the assisting flow case, a solution could be obtained for all positive values of the buoyancy parameter λ, while in the opposing flow case the solution terminated at $\lambda = {\lambda _c}(\lambda < 0)$ . © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21034     

Maxwell nanofluid heat and mass transfer analysis over a stretching sheet

The Buongiorno model Maxwell nanofluid flow, heat and mass transfer characteristics over a stretching sheet with a magnetic field, thermal radiation, and chemical reaction is numerically investigated in this analysis. This model incorporates the effects of Brownian motion and thermophoresis. The governing partial differential equations are transformed into a coupled nonlinear ordinary differential equation by using the similarity transformation technique. The resultant nonlinear differential equations are solved by using the Finite element method. The sketches of velocity, temperature and concentration with diverse values of magnetic field parameter (0.1 ≤ M ≤ 1.5), Deborah number (0.0 ≤ β ≤ 0.19), radiation parameter (0.1 ≤ R ≤ 0.7), Prandtl number (0.5 ≤ Pr ≤ 0.8), Brownian motion parameter (0.1 ≤ Nb ≤ 0.7), thermophoretic parameter (0.2 ≤ Nt ≤ 0.8), Chemical reaction parameter (1.0 ≤ Cr ≤ 2.5) and Lewis number (1.5 ≤ Le ≤ 3.0) have investigated and are depicted through plots. Moreover, the values of the Skin-friction coefficient, Nusselt number, and Sherwood numbers are also computed and are shown in tables. The sequels of this analysis reviewed that the values of Skin-friction coefficient and Sherwood number intensified with hiked values of Deborah number (β), whereas, the values of Nusselt number decelerate as values of (β) improves.