In this manuscript, a computational paradigm of technique shooting is exploited for investigation of the three-dimensional Eyring-Powell fluid with activation energy over a stretching sheet with slip arising in the field of fluid dynamics. The problem is modeled and resulting nonlinear system of PDEs is transformed into nonlinear system of ODEs using well-known similarity transformations. The strength of shooting based computing approach is employed to analyze the dynamics of the system. The proposed technique is well-designed for different scenarios of the system based on three-dimensional non-Newtonian fluid with activation energy over a stretching sheet. Slip condition is also incorporated to enhance the physical and dynamical analysis of the system. The proposed results are compared with the bvp4C method for the correctness of the solver. Graphical and numerical illustrations are used to envisage the behavior of different proficient physical parameters of interest including magnetic parameter, stretching rate parameter, velocity slip parameter, Biot number on velocity, and Lewis number on temperature and concentration.

This study investigates the transportation of mass and heat in the 3D flow of hybrid nanofluids over a rotating disk in the presence of uniform magnetic field acting along the transverse direction to the flow. Water is being used as a base fluid mixed with nanoparticles of aluminum oxide and copper. The mathematical model of the nano-fluidic problem in terms of partial differential equations (PDEs) is formulated by considering the velocity slip at the boundary and heat transport mechanism due to thermal convection and radiation effects. Suitable similarity transformations are being used to transform the governing system of PDEs into a system of nonlinear ordinary differential equations. The transformed model is then analyzed by employing the competency of the Lobatto IIIA technique. Numerical and graphical illustrations are presented for the analysis of different flow parameters by varying velocities and temperature profiles. The behavior of heat transfer rate and coefficient skin friction is also studied numerically for the presented flow model.

In this study, an attempt is made to explore the two‐phase Casson nanofluid passing through a stretching sheet along a permeable surface with the effects of chemical reactions and gyrotactic microorganisms. By utilizing the strength of similarity transforms the governing PDEs are transformed into set of ODEs. The resulting equations are handled by using a proficient numerical scheme known as the shooting technique. Authenticity of numerical outcomes is established by comparing the achieved results with the MATLAB built‐in solver bvp4c. The numerical outcomes for the reduced Nusselt number and Sherwood number are exhibited in the tabular form, while the variations of some crucial physical parameters on the velocity, temperature, and concentration profiles are demonstrated graphically. It is observed that Local Nusselt number rises with the enhancement in the magnetic field parameter, the porous media parameter, and the chemical reactions, while magnetic field parameter along with porous media parameter retards the velocity profile.

A theoretical investigation on heat transfer of nanofluid transport in a ciliated channel is presented. A mathematical model for cilia oriented nanofluid transport through the human male reproductive tract is exhibited. Considering the structure of tubules, the Reynolds number is considered very small. The concept of a long wavelength approximation is incorporated to model the nanofluid flow problem. The exact analytical expressions for the x-component of velocity, temperature, nanoparticle concentration, stream function, volume flow rate, and pressure gradient are calculated. The solution for the transverse component of velocity, pressure rise per wavelength, and friction force on the wall of the channel is explored numerically, while variations in crucial flow parameters are examined graphically.

In this study, the competency of numerical computational framework based on Lobatto IIIA technique is utilized for dynamical analysis of the Darcy‐Forchheimer flow of Sisko nanomaterial with nonlinear thermal radiation. The resultant PDEs of the Sisko fluid model expressions are transformed into system of nonlinear ODEs by exploiting the similarity variables. Graphical representations and numerical illustrations are used to envisage the characteristics of various physical parameters of interest on velocity profile, nanoparticles concentration, and temperature distribution of Sisko fluidic system. In addition, skin friction and Nusselt number are numerically examined with observation that the material parameter of Sisko fluid increases the velocity profile as well as Nusselt number while decreasing temperature, concentration profiles, and skin friction coefficient.