A numerical study is performed to examine the magnetohydrodynamic effects on the transient three-dimensional stagnation point flow of a Casson fluid along a bi-directional stretching sheet. The physical model of the flow includes a sheet which is stretched in both the tangential directions and is thus called "bi-directional stretching". The heat transfer mechanism includes the influences of space- and time-dependent non-uniform heat generation/absorption, as well as dissipation due to viscosity. The mathematical modeling of the problem involves the constitution of a set of coupled nonlinear boundary layer equations, together with suitable boundary conditions. The mathematical model thus developed is then subjected to suitable similarity transformations to arrive at a set of ordinary differential equations, which were then treated with the successive linearization method (SLM) to obtain approximate solutions for the velocity and temperature fields. A parametric study is carried out, and the results are discussed and presented graphically to analyze the behavior of the primary and secondary velocity distributions, as well as fluid temperature, along with significant physical quantities such as skin friction and Nusselt number for various values of the nondimensional parameters. Multiple quadratic regression analysis is also carried out to investigate the significance of parameters and to estimate the skin-friction and heat transfer coefficients.

In this research paper, the authors wish to examine the effects of couple stress on hybrid nanofluid considering magnetohydrodynamic three-dimensional transient flow between two parallel plates. Stretching of the lower plate causes fluid flow in the channel. The fluid flow model is shown in mathematical form using a set of coupled nonlinear partial differential equations, which are then translated into coupled nonlinear ordinary differential equations using the proper transformation. The authors used the spectral quasi linearization method (SQLM), an effective numerical technique, to solve the updated equations and study the effects of various flow parameters on fluid temperature and velocity. The Nusselt number and skin friction coefficients were also investigated from an engineering standpoint. The generated solutions are verified using the residual analysis. Statistical analysis is performed on the skin-friction coefficients and the Nusselt number using quadratic regression models.

The goal of the research presented in this paper is to examine how a magnetic field affects the unsteady flow of an incompressible nanofluid over a spinning disc that is inclined and stretched while the flow is embedded in a non-Darcy porous medium. Furthermore, the heat transmission mechanism takes into account Joule heating and viscous dissipation. By imposing thermal radiation to enhance the heat transmission system under the effects of convection, the current article becomes more realistic. A set of nonlinear partial differential equations and associated boundary conditions defines the mathematical problem. Using an appropriate similarity transformation, the mathematical model is converted into a set of nonlinear ordinary differential equations with boundary conditions, which are then solved numerically by the Spectral Quasi Linearization Method (SQLM). Graphs and tables for various flow parameters illustrate the complete results for the exploration of dimensionless velocity and temperature. Regression analysis is used to statistically estimate the local Nusselt number and the skin friction coefficients. From the numerical results, it is found that when the magnetic parameter is increased, the flow velocity in the radial and tangential directions decreases due to the Lorentz force. With the variation of the Forchheimer number, the fluid flow in both directions decreases with increasing inertia coefficient. By increasing the magnetic parameter and Eckart number, the temperature of the fluid increases. The performed quadratic regression analysis reveals that the permeability of the medium and the generated Lorentz force are significant for the skin friction coefficient in the radial direction, whereas the stretching parameter and Forchheimer number are significant for the skin friction coefficient in the tangential direction. Thermal radiation and convective heating are found to significantly affect the heat transfer coefficient.

The current study investigates the three-dimensional radiative and convective Casson hybrid nanofluid flow and heat transfer with the Cattaneo–Christov heat flux model over an inclined spinning and extending disk subjected to an applied magnetic field. Additionally, the study considers the impacts of Joule’s heating and viscous dissipation. Mathematical modelling of the nanofluid flow problem containing Ag and multiwalled carbon nanotubes (MWCNT) nanoparticles with water as the base fluid in a Darcy medium is done using a cylindrical coordinate system. The simplified system of equations is subjected to the spectral quasilinearisation method (SQLM) approach for the graphical and tabular representations. Examining key parameters, such as magnetic field, Bejan number, angle of inclination, disk movement parameter and disk rotation reveals interesting results on velocity and temperature profiles. The research concludes that the Bejan number increases with higher values of temperature ratio, radiation and magnetic parameters, while it decreases with increasing Casson parameter and Brinkman number. Radial wall friction decreases with improved magnetic field, temperature ratio, stretching and porosity parameters, but tangential wall friction increases. The present results are compared with the one already existing in literature to validate the numerical scheme and the results are found to agree well with the previously published work. The application of hybrid nanofluid flow over rotating and stretching disks is widespread in various fields, including rotating machinery, electronic devices, patient treatment instruments, crystal growth method, etc.

This paper investigates the unsteady magnetohydrodynamic flow of a couple stress Casson fluid between two parallel sheets where the heat transfer mechanism is incorporated with the influences of heat radiation, viscous dissipation, and Joule heating. The fluid flow is induced due to bi-directional stretching of the lower sheet of the channel. The mathematical model of the physical problem is governed by highly nonlinear coupled partial differential equations with boundary conditions that are then transformed into highly nonlinear ordinary differential equations with boundary conditions using well-defined similarity variables. The authors have used the well-known computational technique called the spectral successive linearization method (SLM) to solve the obtained ordinary differential equations subject to the boundary conditions. Graphs and tables show the effects of non-dimensional parameters on the important physical quantities such as the velocity and temperature profiles, and coefficients of skin-frictions and heat transfer. The quadratic regression method is used to perform statistical analysis of Nusselt number and skin friction coefficients. The present investigation has significant applications in different problems of biomedical engineering, clinical sciences, industrial manufacturing processes, and so forth.

The present analysis deals with the three-dimensional radiative, convective hybrid nanofluid flow over a rotating and stretching inclined disk under the action of the applied magnetic field, Joule's heating, and viscous dissipation effects. The mathematical model considers nanoparticles graphene oxide (GO) and molybdenum disulfide (MoS2) suspended in water as the base fluid within a Darcy medium. The cylindrical coordinate system is used to express continuity, momentum, and energy partial differential equations, out of which momentum and energy partial differential equations are transformed into ordinary differential equations using a suitable transformation method under the boundary-layer approximation. The transformed equations are further solved using the spectral quasi-linearization method. Graphical and numerical data are presented to investigate the behavior of velocity and temperature under various parameters and shape factors. The nature of fluid flow at the boundary wall is determined by tables of skin friction and the Nusselt number. Statistical analysis of the parameters for axial and tangential skin friction and the Nusselt number is performed using the quadratic regression model.

The phenomenon of heat transfer is prevalent in industries and has an extensive range of applications. However, mostly the discussion of heat transfer problems is limited to the study of the first law of thermodynamics, which deals with energy conservation. It is just restricted to the quantity of energy, not to its quality; i.e., there is no difference between the work (high-grade energy) and the heat (low-grade energy). A measurement of the degree of randomness of energy in a system is known as entropy. It is unavailable for doing useful work because work takes place only from ordered molecular motion. Even though many boundary layer models exist in the literature to investigate the flow and heat transfer of various fluids along a stretching surface, they have not yet been used at their maximum ability. The main motive of the current research is to discuss entropy generation or its minimization during heat transfer. This work presents an entropy generation analysis for the transient three-dimensional stagnation point flow of a hydromagnetic Casson fluid flowing over a stretching surface in the existence of Hall current, viscous dissipation, and nonlinear radiation. The physical configuration of the present work is described in terms of partial differential equations (PDEs) of nonlinear nature. Furthermore, these PDEs are converted into ordinary differential equations by using some relevant similarity transformations. An efficient numerical method named as the spectral quasilinearization method (SQLM) is used to solve this model. The expression of the Bejan number and volumetric entropy generation rate is also computed. A parametric analysis, including the essential physical parameters, is performed to examine the influences of distinct flow parameters on the velocity profile, temperature profile, Bejan number, entropy generation number, and the coefficients of skin friction and the Nusselt number. In order to further insight into the emerging physical quantities of engineering interest, multiple quadratic regression models are used to estimate the coefficients of skin friction and heat transfer.

This research investigates the three-dimensional magnetohydrodynamic flow of a Casson fluid between parallel plates, considering the influence of couple-stress and a magnetic field, along with the heat transfer influenced by a heat source. The fluid flow, driven by the stretching of the lower plate while keeping the upper plate stationary, has applications in various industries. The model involves nonlinear coupled partial differential equations with appropriate boundary conditions. The authors employed the Spectral Quasi Linearization Method (SQLM) to solve the transformed equations, examining the impact of different parameters on fluid temperature and velocities. Increasing the magnetic field strength, Casson parameter, and unsteadiness decreases velocities near the lower sheet but increases them near the upper sheet. Fluid temperature rises with higher Casson parameter and magnetic field strength but decreases with increased Prandtl number, couple stress parameter, unsteadiness, and stretching parameter. Nusselt number and skin-friction coefficients are analyzed numerically and statistically for engineering insights.