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The purpose of this paper is to obtain semi-analytical solutions of similarity solutions for the nano boundary layer flows with Navier boundary condition. The similarity solutions of viscous flows over a two-dimensional stretching surface and an axisymmetric stretching surface are investigated.

In this work, the governing partial differential equations are transformed to a nonlinear ordinary differential equation by using some proper similarity transformations. Then an efficient semi-analytical method, the Laplace Adomian decomposition method (LADM) is applied to obtain semi-analytical solutions of the similarity solutions in both of viscous flows over a two-dimensional stretching surface and an axisymmetric stretching surface. To improve the accuracy and enlarges the convergence domain of the obtained results by the LADM, the study has combined it with Padé approximation.

Accuracy and efficiency of the presented method are illustrated and denoted through the tables and figures. Also the effects of the suction parameter λ and slip parameter K on the fluid velocity and on the tangential stress are investigated.

The similarity solutions of the governing partial differential equation are obtained analytically by using an efficient developed method, namely the Laplace Adomian decomposition-Padé method. The analytic solutions of nonlinear ordinary differential equation are constructed for both of viscous flows over a two-dimensional stretching surface and an axisymmetric stretching surface.

The purpose of this paper is to discuss the flow of Casson nanofluid past a nonlinear permeable stretching sheet in the presence of thermal radiation, chemical reaction, viscous dissipation, heat source, and magnetohydrodynamics.

Appropriate transformations are used to convert the boundary layer equations into nonlinear ODEs which are then solved numerically by using the Runge-Kutta-Fehlberg fourth-fifth order method along with shooting technique.

Solution of this systems is obtained for velocity, temperature, and concentration profiles. Graphical illustrations are added to discuss the effect of evolving parameters against above-mentioned distributions. Tabular values of local skin friction factor, local Nusselt number, and local Sherwood number are also added and studied accordingly.

A good agreement of the present results has been observed by comparing with the existing literature results. It is noted that skin friction coefficient, Nusselt number, and Sherwood number decrease with Casson parameter and increase with suction parameter.

The current determination is committed to characterize the boundary layer flow of Williamson nanofluid prompted by nonlinear strained superficial under heat and mass transport mechanisms. Buongiorno model is presented to view the influence of nanoparticles in fluid flow. Scrutiny has been conceded under the action of the transversely smeared magnetic field. Heat and mass relocation exploration are conducted in the companionship of radiation effects and actinic compensation.

Similarity variable is designated to transmute nonlinear partial differential equations of conservation laws of mass, momentum, energy and species into ordinary dimensional expressions. These constitutive and complicated ordinary differential expressions assessing the flow situation are handled efficaciously by manipulating Runge–Kutta–Fehlberg procedure (RK-5) with shooting routine.

The graphical demonstration is deliberated to scrutinize the variation in velocity, temperature and concentration profiles with respect to flow regulating parameters. Numerical data are displayed through tables in order to surmise variation in skin friction coefficient and Nusselt number. The augmenting values of fluid parameter and magnetic parameter reduces the horizontal fluid velocity, whereas normal velocity upsurges for mounting values of stretching ratio parameter. Moreover, mounting values of radiation parameter and thermophoresis parameter upsurges the temperature profile, whereas, growing values of Prandtl number lessen the temperature field.

The current exploration is used in many industrial and engineering applications in order to discuss the transport phenomenon.

Flow over a nonlinear stretched surface has numerous applications in the industry. The present attempt examines the combined influence of various physical characteristics for the flow of Williamson fluid and no such attempt exist in the available literature.

The purpose of this paper is to examine the interaction effects of a transverse magnetic field and slip effects of Casson fluid with suspended nanoparticles over a nonlinear stretching surface. Mathematical modeling for the law of conservation of mass, momentum, heat and concentration of nanoparticles is executed.

Governing nonlinear partial differential equations are reduced into nonlinear ordinary differential equations and then shooting method is employed for its solution. The slope of the linear regression line of the data points is calculated to measure the rate of increase/decrease in the reduced Nusselt number.

The effects of magnetic parameter (0=M=4), Casson parameter (0.1=β<8), nonlinear stretching parameter (0=n=3) and porosity parameter (0=P=6) on axial velocity are shown graphically. Numerical results were compared with another numerical approach and an excellent agreement was observed. This study reveals the fact that the Brownian motion parameter and boundary layer thickness have a direct relationship with temperature. Also, Brownian motion and thermophoresis contribute to an increase in the thermal boundary layer thickness.

Despite the immense significance and repeated employment of non-Newtonian fluids in industry and science, no attempt has been made up till now to inspect the Casson nanofluid flow with a permeable nonlinear stretching surface.

This paper aims to deal with the study of heat and mass transfer on double-diffusive three-dimensional hydromagnetic boundary layer flow of an electrically conducting Casson nanofluid over a stretching surface. The combined effects of nonlinear thermal radiation, magnetic field, buoyancy forces, thermophoresis and Brownian motion are taken into consideration with convective boundary conditions.

Similarity transformations are used to reduce the governing partial differential equations into a set of nonlinear ordinary differential equations. The reduced equations were numerically solved using Runge–Kutta–Fehlberg fourth-fifth-order method along with shooting technique.

The impact of several existing physical parameters such as Casson parameter, mixed convection parameter, regular buoyancy ratio parameter, radiation parameter, Brownian motion parameter, thermophoresis parameter, temperature ratio parameter on velocity, temperature, solutal and nanofluid concentration profiles are analyzed through graphs and tables in detail. It is found that the solutal component increases for Dufour Lewis number, whereas it decreases for nanofluid Lewis number. Moreover, velocity profiles decrease for Casson parameter, while the Nusselt number increases for Biot number, radiation and temperature ratio parameter.

This paper is a new work related to three-dimensional double-diffusive flow of Casson nanofluid with buoyancy and nonlinear thermal radiation effect.

In this framework, the three dimensional (3D) flow of hydromagnetic Carreau nanofluid transport over a stretching sheet has been addressed by considering the impacts of nonlinear thermal radiation and convective conditions.

Infinite shear rate viscosity impacts are invoiced in the modeling. The heat and mass transport characteristics are explored by employing the effects of a magnetic field, thermal nonlinear radiation and buoyancy effects. Rudimentary governing partial differential equations (PDEs) are represented and are transformed into ordinary differential equations by the use of similarity transformation. The nonlinear ordinary differential equations (ODEs), along with the boundary conditions, are resolved with the aid of a Runge-Kutta-Fehlberg scheme (RKFS) based on the shooting technique.

The impact of sundry parameters like the viscosity ratio parameter (β*), nonlinear convection parameters due to temperature and concentration (β_T, β_C), mixed convection parameter (α), Hartmann number (M²), Weissenberg number (We), nonlinear radiation parameter (N_R), and the Prandtl number (Pr) on the velocity, temperature and the concentration distributions are examined. Furthermore, the impacts of important variables on the skin friction, Nusselt number and the Sherwood number have been scrutinized through tables and graphical plots.

The velocity distribution is suppressed by greater values of the Hartmann number. The velocity components in the tangential and axial directions of the fluid are raised with the viscosity ratio parameter and the tangential slip parameter, but these components are reduced with concentration to thermal buoyancy forces ratio and stretching sheet ratio.

This paper aims to assess the effectiveness of Hall currents and power-law slip condition on the hydromagnetic convective flow of an electrically conducting power-law fluid over an exponentially stretching sheet under the effect of a strong variable magnetic field and thermal radiation. Flow formation is developed using the rheological expression of a power-law fluid.

The nonlinear partial differential equations describing the flow are transformed into the nonlinear ordinary differential equations by employing the local similarity transformations and then solved numerically by an effective numerical approach, namely, fourth-order Runge–Kutta integration scheme, along with the shooting iteration technique. The numerical solution is computed for different parameters by using the computational software MATLAB bvp4c. The bvp4c function uses the finite difference code as the default. This method is a fourth-order collocation method. The impacts of thermophysical parameters on velocity and temperature distributions, skin friction coefficients and Nusselt number in the boundary layer regime are exhibited through graphs and tables and deliberated with proper physical justification.

Our investigation conveys that Hall current has an enhancing behavior on velocity profiles and reduces skin friction coefficients. An increase in the power-law index is observed to deplete velocity and temperature evolution. The temperature for the pseudo-plastic (shear-thinning) fluid is relatively higher than the corresponding temperature of the dilatant (shear-thickening) fluid. The streamlines are more distorted and have low intensity near the surface of the sheet for the dilatant fluid than the pseudo-plastic fluid.

The study is pertinent to the expulsion of polymer sheet and photographic films, hydrometallurgical industry, electrically conducting polymer dynamics, magnetic material processing, solutions and melts of polymer processing, purification of molten metals from nonmetallic. The results obtained in this work can be relevant in fluid mechanics and heat transfer applications.

The present problem has, to the authors' knowledge, not communicated thus far in the scientific literature. A comparative study with the published works is conducted to verify the accuracy of the present study. The results obtained in this analysis are significant in providing the standards for validating the accuracies of some numerical or empirical methods.

The purpose of the current flow configurations is to bring to attention the thermophysical aspects of magnetohydrodynamics (MHD) Williamson nanofluid flow under the effects of Joule heating, nonlinear thermal radiation, variable thermal coefficient and activation energy past a rotating stretchable surface.

A mathematical model is examined to study the heat and mass transport analysis of steady MHD Williamson fluid flow past a rotating stretchable surface. Impact of activation energy with newly introduced variable diffusion coefficient at the mass equation is considered. The transport phenomenon is modeled by using highly nonlinear PDEs which are then reduced into dimensionless form by using similarity transformation. The resulting equations are then solved with the aid of fifth-order Fehlberg method.

The rotating fluid, heat and mass transport effects are analyzed for different values of parameters on velocity, energy and diffusion distributions. Parameters like the rotation parameter, Hartmann number and Weissenberg number control the flow field. In addition, the solar radiation, Joule heating, Prandtl number, thermal conductivity, concentration diffusion coefficient and activation energy control the temperature and concentration profiles inside the stretching surface. It can be analyzed that for higher values of thermal conductivity, Eckret number and solar radiation parameter the temperature profile increases, whereas opposite behavior is noticed for Prandtl number. Moreover, for increasing values of temperature difference parameter and thermal diffusion coefficient, the concentration profile shows reducing behavior.

This paper is useful for researchers working in mathematical and theoretical physics. Moreover, numerical results are very useful in industry and daily-use processes.

This paper aims to explore the study of magnetohydrodynamic viscous fluid flow past on a stretching cylinder with nonlinear thermal radiation having gyrotactic microorganisms.

Appropriate transformations reduce the nonlinear partial differential equation to ordinary ones. Subsequent nonlinear equations are calculated to get convergent series solutions.

Fluid velocity declines for elevating values of magnetic field parameter. For larger values of curvature parameter near the cylinder temperature reduces.

To the best of the authors’ knowledge, magnetohydrodynamic boundary layer flow of viscous fluid by nonlinear stretching cylinder with nonlinear thermal radiation having gyrotatic microorganisms is not studied yet. The purpose is to study this.

The purpose of this study is to provide a numerical investigation of Casson nanofluid along a vertical nonlinear stretching sheet with variable thermal conductivity and viscosity.

The boundary-layer equations are presented in the dimensionless form using proper non-similar transformations. The subsequent non-dimensional nonlinear partial differential equations are solved using the implicit finite difference technique. To linearize the nonlinear terms present in these equations, the quasilinearization technique is used.

The investigation showed graphically the temperature, velocity and nanoparticle volume fraction for particular included physical parameters. It is observed that the velocity profile decreases with an increase in the values of Casson fluid parameter while increases with an increase in the viscosity variation parameter. The temperature profile enhances for large values of velocity variation parameter and thermal conductivity parameter while it reduces for large values of thermal buoyancy parameter. Further, the Nusselt number and skin-friction coefficient are introduced which are helpful in determining the physical aspects of Casson nanofluid flow.

The immediate control of heat transfer in the industrial system is crucial because of increasing energy prices. Recently, nanotechnology is proposed to control the heat transfer phenomenon. Ongoing research in complex nanofluid has been fruitful in various applications such as solar thermal collectors, nuclear reactors, electronic equipment and diesel–electric conductor. A reasonable amount of nanoparticle when added to the base fluid in solar thermal collectors serves to deeper absorption of incident radiation, and hence it upgrades the efficiency of the solar thermal collectors.

The non-similar solution of Casson nanofluid due to a vertical nonlinear stretching sheet with variable viscosity and thermal conductivity is discussed in this work.