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An increment in energy efficiency by employing nanoparticles is a hot topic of research in present era due to its abundant implications in modern engineering and technological processes. Therefore, the current research analysis reported the viscoelastic nanofluid flow over porous oscillatory moving sheet in the presence of microorganisms. A rate-type fluid namely Maxwell fluid is employed with the addition of nanoparticles. The paper aims to discuss this issue.

First, acceptable dimensionless variables are defined to convert the system of dimensional form into the system of dimensionless forms. Later on, the self-similar solution of the boundary value problem is computed by using the homotopy analysis method. The obtained results of velocity, temperature, mass concentration and motile microorganism density profiles are interpreted through physical background.

The presence of both thermophoresis and Brownian motion parameters also improve the thermophysical features of non-Newtonian nanoparticles. It is also pointed out that the presence of porous medium and magnetic force enhances the nanoparticles concentration. Moreover, a weaker distribution of gyrotactic microorganism has been depicted with Peclet number and bioconvection Lewis parameter.

No such article exists in the literature yet.

This paper aims to explore the flow of nanofluid over bi-directional stretching sheet in the presence of magnetic field and linear thermal radiation.

In this study, water is taken as a base fluid, and copper is diluted in the base fluid. Further, four different shapes of nanoparticles are considered for the analysis. The governing nonlinear partial differential equations are transformed into the system of ordinary differential equations after using the feasible similarity transformations. Solution of the model is then performed by means of Runge–Kutta scheme.

Influence of the emerging dimensionless parameters on velocity, temperature, skin friction coefficient and local rate of heat transfer are studied with the help of graphs.

The study is presented in this paper is original and has not been submitted to any other journal for the publication purpose. The contents are original, and proper references have been provided wherever applicable.

The purpose of this paper is to examine the magneto hydrodynamic flow and heat transfer of nanofluids over a permeable wedge based on engine oil which is under the effects of thermal radiation and convective heating.

The equations governing the flow are transformed into differential equations by applying similarity transformations. Keller box method is used to bring out the numerical solution.

The discovery interprets that temperature as well as the velocity of Ag-engine oil nanofluids are more noticeable than Cu-engine oil nanofluids. Thermal boundary layer increases for radiation parameter as well as Biot number. Fluctuations of co-efficient of drag skin friction as well heat transfer rate at the wall are also tested.

Till now, no numerical studies are reported on the heat transfer enhancement of the permeable wedge under thermal radiation on engine oil nanofluid flow by considering convective heating.

The purpose of this paper is to explore the impact of thermal radiation, viscous dissipation and Joule heating effects on the flow of a magneto-nanofluid between two horizontally placed plates. Three distinct shapes of nanoparticles in a base fluid (water) are considered to compose the nanofluid.

Introducing feasible similarity variables, the flow model is transformed into a nonlinear and coupled system of ordinary differential equations. The consequent system is solved by using homotopy analysis method.

Furthermore, the influence of embedded parameters on velocity and temperature profiles is highlighted graphically. The same is done for showing the variations in skin friction coefficient and local rate of heat transfer. Under certain conditions, present results compared with already existing results in the literature. Some main findings are pinpointed in the last section before the bibliography. From presented work, it is analyzed that the velocity field along y-axis and x-axis are increasing and decreasing functions of suction/injection parameter. The velocity of the fluid starts increases for Reynolds number and declines for volumetric fraction of the nanoparticles. Significant variations in angular velocity are observed for volumetric fraction and Reynolds number, respectively. Thermal field increases rapidly for brick-shaped nanoparticles, and for platelet-shaped nanoparticles, it decreases rapidly. Local rate of heat transfer increases for radiation and Reynolds number and starts decreasing for Eckert number.

The study presented is original and has not been submitted to any other journal for the publication purpose. The contents are original and proper references have been provided wherever applicable.

The purpose of this paper is to address the thermo-physical impacts of unsteady magneto-hydrodynamic (MHD) boundary layer flow of non-Newtonian tangent hyperbolic nanofluid past a moving stretching wedge. To delineate the nanofluid, the boundary conditions for normal fluxes of the nanoparticle volume fraction are chosen to be vanish.

The local similarity transformation is implemented to reformulate the governing PDEs into coupled non-linear ODEs of higher order. Then, numerical solution is obtained for the simplified governing equations with the aid of finite difference technique.

Numerical calculations point out that pressure gradient parameter leads to improve all skin friction coefficient, rate of heat transfer and absolute value of rate of nanoparticle concentration. As well as, lager values of Weissenberg number tend to upgrade the skin friction coefficient, while power law index and velocity ratio parameter reduce the skin friction coefficient. Again, the horizontal velocity component enhances with upgrading power law index, unsteadiness parameter, velocity ratio parameter and Darcy number and it reduces with rising values of Weissenberg number.

A numerical treatment of unsteady MHD boundary layer flow of tangent hyperbolic nanofluid past a moving stretched wedge is obtained. The problem is original.

The purpose of this paper is to assess the flow of a nanofluid over a porous moving wedge. The passive control model along with the magnetohydrodynamic (MHD) effects is used to formulate the problem. Furthermore, in energy equation, the non-linear thermal radiation has also been incorporated. The equations governing the flow are transformed into a set of ordinary differential equations by using suitable similarity transforms. The reduced system of equations is then solved numerically using a well-known Runge–Kutta–Fehlberg method coupled with a shooting technique. The influence of parameters involved on velocity, temperature and concentration profiles is highlighted with the help of a graphical aid. Expressions for skin-friction coefficient, local Nusselt number and Sherwood number are obtained and presented graphically.

Numerical solution of the problem is obtained using the well-known Runge–Kutta–Fehlberg method.

The analysis provided gives a clear description that the increase in m and magnetic parameter M results in an increased velocity profile. Both these parameters normalize the velocity field. Radiation parameter, Rd, increases the temperature and concentration of the system so does the temperature ratio θ_ω reduces the heat transfer rate at the wall for both stretching and shrinking wedge.

In the study presented, the flow of nanofluid over a moving permeable wedge is considered. The solution of the equations governing the flow is presented numerically. For the validity of results obtained, a comparison is also presented with already existing results. To the best of the authors’ knowledge, this investigation is the first of its kind on the said topic.

The purpose of this study is to analyze thermo-diffusion and diffusion-thermo effects, combined with first-order chemical reaction, in the flow of a micropolar fluid through an asymmetric channel with porous boundaries. Suction/injection velocities of upper and lower walls are taken to be different from each other. The channel exhibits a parting or embracing motion and the fluid enters, or leaves, the channel because of suction/injection through the permeable walls.

The solution of the problem is obtained by using the fourth-order Runge-Kutta method combined with the shooting technique.

The asymmetric nature of the channel that is caused by the different permeabilities of the walls deeply influences the flow. The temperature of the fluid rises significantly by increasing the absolute value of A for both Case I and Case II. While, for the concentration profile, the concentration drops near the lower vicinity of the center in Case I, and, it falls near the lower wall of the channel in Case II. Stronger Dufour effects increase the temperature of the fluid except for Case 1 at the center of the channel and for Case II in lower quarter of the channel.

It is confirmed that the presented work is original and is not under consideration by any other journal.

In this communication, a theoretical simulation is aimed to characterize the Darcy–Forchheimer flow of a magneto-couple stress fluid over an inclined exponentially stretching sheet. Stokes’ couple stress model is deployed to simulate non-Newtonian microstructural characteristics. Two different kinds of thermal boundary conditions, namely, the prescribed exponential order surface temperature (PEST) and prescribed exponential order heat flux, are considered in the heat transfer analysis. Joule heating (Ohmic dissipation), viscous dissipation and heat source/sink impacts are also included in the energy equation because these phenomena arise frequently in magnetic materials processing.

The governing partial differential equations are transformed into nonlinear ordinary differential equations (ODEs) by adopting suitable similar transformations. The resulting system of nonlinear ODEs is tackled numerically by using the Runge–Kutta fourth (RK4)-order numerical integration scheme based on the shooting technique. The impacts of sundry parameters on stream function, velocity and temperature profiles are viewed with the help of graphical illustrations. For engineering interests, the physical implication of the said parameters on skin friction coefficient, Nussult number and surface temperature are discussed numerically through tables.

As a key outcome, it is noted that the augmented Chandrasekhar number, porosity parameter and Forchhemeir parameter diminish the stream function as well as the velocity profile. The behavior of the Darcian drag force is similar to the magnetic field on fluid flow. Temperature profiles are generally upsurged with the greater magnetic field, couple stress parameter and porosity parameter, and are consistently higher for the PEST case.

The findings obtained from this analysis can be applied in magnetic material processing, metallurgy, casting, filtration of liquid metals, gas-cleaning filtration, cooling of metallic sheets, petroleum industries, geothermal operations, boundary layer resistors in aerodynamics, etc.

From the literature review, it has been found that the Darcy–Forchheimer flow of a magneto-couple stress fluid over an inclined exponentially stretching surface with heat flux conditions is still scarce. The numerical data of the present results are validated with the already existing studies under limited cases and inferred to have good concord.

The aim of this manuscript is to study the flow of a nanofluid through a porous channel under the influence of a transverse magnetic field. Permeability of the walls is considered to be different, which results in an asymmetric nature of the flow. The height of the channel is variable, and it dilates or squeezes at a uniform rate.

A numerical solution (Runge–Kutta–Fehlberg) has been obtained after reducing the governing equations to a system of nonlinear ordinary differential equations using some suitable similarity transforms, both in time and space.

An increase in absolute values of the permeability parameter results in an enhanced mass transfer rate at both the walls, while the rate of heat transfer also increases at the lower wall. Few graphs are also dedicated to see the behavior of Nusselt and Sherwood numbers following the variations in flow parameters.

A pictorial description of the flow and effects of emerging parameters on the temperature and nanoparticle concentration profiles is presented to analyze the flow behavior. It is established that the asymmetry of the channel affects the flow quite significantly.

The evaluation of high thermal efficiency has actively highlighted the unique behaviour of hybrid nanofluid. Thus, the purpose of this paper is to emphasize the hybrid nanofluid’s stagnation point in three-dimensional flow with magnetic field.

The defined ordinary differential equations systems are addressed using the bvp4c solver.

The results indicate that using dual solutions is possible as long as the physical parameters remain within their specified ranges. Hybrid nanofluid flow has been recognised for its superior heat transfer capabilities in comparison to both viscous flow and nanofluid flow. Furthermore, it has been demonstrated in the current study that augmenting the volume concentration of nanoparticles leads to a corresponding enhancement in the rate of heat transfer. When the velocity gradients ratio is augmented, there is a corresponding reduction in the thermal performance. The separation value grows as the magnetic parameter rises, which signifies the expansion of the boundary layer.

The originality of the paper highlights the general mathematical hybrid model of the three-dimensional problem with the magnetohydrodynamics (MHD) effect in the stagnation point flow. The comprehensive examination of the suggested model has not yet been thoroughly addressed in prior research.