In this study, a novel theoretical model for three‐dimensional (3D) laminar magnetohydrodynamic (MHD) flow of a non‐Newtonian second‐grade fluid along a plate of semi‐infinite length is developed based on slightly sinusoidal transverse suction velocity. The suction velocity involves a steady distribution with a low superimposed perpendicularly varying dispersion. The strength of the uniform magnetic field is incorporated in the normal direction to the wall. The variable suction transforms the fluidic problem into a 3D flow problem because of variable suction velocity in the normal direction to the plane wall. The proposed mathematical modeling and its dynamical analysis are prescribed for the boundary layer flow keeping the magnetic effects without taking into consideration the induced magnetic field. An analytical perturbation technique is employed for the series solutions of the system of ordinary differential equations of velocity profile and pressure. Graphical illustrations are used to analyze the behavior of different proficient parameters of interest. The magnetic parameter is responsible for accelerating the main flow velocity, while controlling the cross flow velocities.

This article presents a mathematical model and theoretical analysis of coating of a thin film of non-Newtonian polymers as they travel through a small space between two reverse-rotating rolls. The dimensionless forms of the governing equations are simplified with the help of the lubrication approximation theory (LAT). By using the perturbation technique, the analytical solutions for velocity, flow rate and pressure gradient were obtained. From an engineering point of view, some significant results such as thickness of the coated web, pressure distribution, separation points, separation force and power input were computed numerically. The effect of velocities ratio $k$ and Weissenberg number $We$ on these physical quantities is presented graphically; others are shown in tabular form. It is noted that the involved material parameters provide a mechanism to control the flow rate, pressure distribution, the thickness of coating, separation force and power input. Moreover, the separation point is shifted toward the nip region by increasing velocities ratio $k$.

This article describes the development of a mathematical model of the reverse roll coating of a thin film for an incompressible non-isothermal magnetohydrodynamics $\left(MHD\right)$ viscoplastic fluid as it passes through a small gap between two rolls rotating reversely. The equations of motion required for the fluid added to the web are constructed and simplified using the lubrication approximation theory $\left(LAT\right)$. Analytical results are obtained for the velocity profile, pressure gradient, and temperature distribution. The pressure distributions and flow rate are calculated numerically using the trapezoidal rule and regular false position method, respectively. Some of these results are presented graphically, while others are shown in a tabular form. From the present analysis, it has been observed that the magnitude of pressure distributions increases by increasing the value of the involved parameters. It is worth mentioning that the velocities ratio and Brickman’s number are controlling parameters for the temperature distributions. The results indicate the strong effectiveness of the viscoplastic parameter and velocities ratio for the velocity and pressure distributions. It is also concluded that the coating of Casson material has been remarkably affected by the magnetohydrodynamics effects.

In present study we have considered oblique stagnation point flow of a viscous fluid with heat transfer towards a stretching cylinder. This is presumed that fluid impinges obliquely on the surface of the cylinder. Mathematical model assuming axisymmetric nature of the flow in the cylindrical coordinates is developed. Similarity transformations are employed, and the obtained system of ordinary differential equations is then solved using a hybrid homotopy analysis method. The obtained results are validated by applying Keller-box method. The temperature and velocity profiles are given graphically and are then examined for the effect of related parameters. The results obtained are attuned with existing relevant literature.