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The purpose of this study is to conduct a comparative investigation for incompressible electrically conducting nanofluid fluid through wall jet. Single-walled carbon nanotubes (SWCNTs) and multiple-walled carbon nanotubes (MWCNTs) are considered as the nanoparticles. To record the effect of Lorentz forces, a magnetic field is applied normally with the assumption that the induced magnetic field is negligible.

Boundary layer approximation is used to convert governing equations into ordinary differential equations along with appropriate boundary conditions. To obtain the results, used homotopy analysis method (HAM) has been used as an analytical technique and to validate the obtained results a famous numerical Runge–Kutta–Fehlberg method is also exploited. It has been observed that the results obtained through both of the methods are in excellent agreement with exact solution.

The Hartmann number is used as controlling parameter for velocity and temperature profile. That can be recorded as its extended values help to normalize the velocity, whereas it controls the rapid increase in temperature. The temperature profile is boosted by increasing the value of the Biot number, a physical parameter. Similarly, it also increases for an increased percentage of volume fraction of particles (SWCNTs/MWCNTs). The Hartmann number plays an important role in decreasing local skin friction coefficient. The influence of the Biot number and volume fraction of nanoparticles caused similar increasing effects on the local Nusselt number. Nanoparticles of the form SWCNT provide better heat transfer as compared to MWCNTs. Influence of the Biot number and volume fraction of nanoparticles caused similar increasing effects on the local Nusselt number. Nanoparticles of the form SWCNT provide better heat transfer as compared to MWCNTs.

To gain insight into the problem, the effects of various emerging parameters and physical quantities such as Biot number, Nusselt number and skin friction coefficient, have been explored.

The purpose of this paper is to present investigation of the flow, heat and mass transfer of a nanofluid over a suddenly moved flat plate using Buongiorno’s model. This study is different from some of the previous studies as the effects of Brownian motion and thermophoresis on nanoparticle fraction are passively controlled on the boundary rather than actively.

The partial differential equations governing the flow are reduced to a system of non-linear ordinary differential equations. Viable similarity transforms are used for this purpose. A well-known numerical scheme called Runge-Kutta-Fehlberg method coupled with shooting procedure has been used to find the solution of resulting system of equations. Discussions on the effects of different emerging parameters are provided using graphical aid. A table is also given that provides the results of different parameters on local Nusselt and Sherwood numbers.

A revised model for Stokes’ first problem in nanofluids is presented in this paper. This model considers a zero flux condition at the boundary. Governing equations after implementing the similarity transforms get converted into a system of non-linear ordinary differential equations. Numerical solution using RK-Fehlberg method is also carried out. Emerging parameters are analyzed graphically. Figures indicate a quite significant change in concentration profile due to zero flux condition at the wall.

This work can be extended for other problems involving nanofluids for the better understanding of different properties of nanofluids.

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.

This paper aims to propose a method by merging Legendre wavelets method and quasilinearization technique to tackle with the nonlinearity and to get better and more accurate results.

To test the significance of the proposed scheme, the authors applied the method on the model representing magneto-hydrodynamic squeezing flow of a viscous fluid between two parallel infinite disks, where one disk is impermeable and the other is porous with either suction or injection of the fluid. For the sake of comparison, numerical solution by using RK-4 is also computed. From the graphs and tables, it is evident that the proposed method shows an excellent accordance with the numerical solution.

The solution converges to the numerical solution when the degree of Legendre polynomials m is increased. For m = 20 in all the three cases, for different values of S, M and A, the graphs of solutions obtained by Legendre wavelet quasilinearization technique show an excellent agreement with numerical solution. Also, it is evident from figures that suction and injection affects the velocity profile in opposite way. For suction, maximum velocity is seen to be at the center of the channel. Magnetic field can be used to regularize the flow and it stabilizes the flow behavior.

Magnetic field can be used to regularize the flow and it stabilizes the flow behavior.

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.

In this paper, the authors study the behavior of heat and mass transfer between parallel plates of a steady nanofluid flow in the presence of a uniform magnetic field. In the model of nanofluids, the essential effect of thermophoresis and Brownian motion has been encompassed.

The variation of parameters method has been exploited to solve the differential equations of nanofluid model. The legitimacy of the variation of parameters method has been corroborated by a comparison of foregoing works by many authors on viscous fluid.

An analysis of the model is performed for different parameters, namely, viscosity parameter, Brownian parameter, thermophoretic parameter and magnetic parameter.

The variation of parameters method proves to be very effective in solving nonlinear system of ordinary differential equations which frequently arise in fluid mechanics.

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 study is to investigate numerically the influence of nonlinear thermal radiation on the flow of a viscous fluid. The flow is confined in a channel with deformable porous walls.

Two numerical schemes, namely, Galerkin’s method (GM) and Runge–Kutta–Fehlberg (RKF) method have been used to obtain solutions after reducing the governing equations to a system of nonlinear ordinary differential equations.

Heat transfer rate falls at the upper wall owing to the decreasing values of the permeability parameter. However, at the lower wall, the same rate rises. Increment in θ_w increases the rate of heat transfer at both walls. Nusselt number also increases with the increasing values of Rd. Rd also uplifts the temperature distribution, except for the case where it falls near the lower wall owing to the contraction coupled with injection.

It is confirmed that the presented work is original.

In this current study, the authors aim to analyze non-linear radiative squeezed flow in a rotating frame of viscous fluid.

The Radioactive nature of the fluid is taken into consideration. The reduced form of equations governing the flow are developed by the implementation of similarity transformations. The coupled system thus obtained is solved by using the homotopy analysis method (HAM).

Augmentation in velocity and temperature profiles is discussed graphically by varying various involved parameters. The total error of the system is discussed in Table I. The cases of linear radiation and non-linear radiation are also discussed in Tables II and III.

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

The purpose of this study is to analyze the effects of carbon nanotubes (CNTs) in the Marangoni convection boundary layer viscous fluid flow. The analysis and formulation for both types of CNTs, namely, single-walled (SWCNTs) and multi-walled (MWCNTs), are described. The influence of thermal radiation effect assumed in the form of energy expression.

Appropriate transformations reduced the partial differential systems to a set of nonlinear ordinary differential equations (ODEs). The obtained nonlinear ODE set is solved via the least squares method. A detailed comparison between outcomes obtained by the least squares method, RK-4 and already published work is available.

Nusselt number was analyzed and found to be more effective for nanoparticle volume fraction and larger radiation parameters. Additionally, the error and convergence analysis for the least squares method was presented to show the efficiency of the said algorithm.

The results reveal that velocity is a decreasing function of suction for both CNTs. While enhancing the nanoparticle volume fraction, an increase for both thermal boundary layer thickness and temperature was attained. The radiation parameter has an increasing function as temperature. Velocity behavior is the same for nanoparticle volume fraction and suction. It was observed that velocity is less in SWCNTs as compared to MWCNTs.