Inclined relative magnetic field analysis of Brinkman type dusty fluid through fluctuating upright parallel plates.

Due to the widespread use of magnetohydrodynamic (MHD) in electromagnetic targeted therapy, malignant tumor therapy, magnetic microscopy, regulating blood circulation following operations, and fluid pumping in industrial and technical processes. The main goal of the article investigates the analysis of a dusty Brinkman fluid flowing through fluctuating parallel plates with an inclined relative magnetic field. The study aims to analyze the relative magnetic phenomena which is fixed relative to the fluid (MFFRF) or plate (MFFRP), and its impact on fluid and particle motion. The mathematical modelling of the fluid is established through a conventional partial differential equations, and Buckingham's pi theorem is utilized to obtain dimensionless variables. Poincare-Lighthill perturbation technique (PLPT) is employed to derive the solution, with the aid of the program Mathcad-15, the findings are displayed graphically for both velocities. The study indicates that the relative magnetic field significantly influences fluid and particle motion which can be utilized to control fluid pumping in industrial operations and blood flow during surgery.

Exact solutions via Prabhakar fractional approach to investigate heat transfer and flow features of hybrid nanofluid subject to shape and slip effects.

The core devotion of this study is to develop a generalized model by means of a recently proposed fractional technique in order to anticipate the enhancement in the thermal efficiency of engine oil because of the dispersion of graphene and magnesia nanoparticles. In addition to investigating the synergistic attributes of the foregoing particles, this work evaluates shape impacts for column, brick, tetrahedron, blade, and lamina-like shapes. In the primary model, the flow equation is coupled with concentration and energy functions. This classical system is transmuted into a fractional environment by generalizing mathematical expressions of thermal and diffusion fluxes by virtue of the Prabhakar fractional operator. In this study, ramped flow and temperature slip conditions are simultaneously applied for the first time to examine the behavior of a hybrid nanofluid. The mathematical analysis of this problem involves the incorporation of dimension-independent parameters into the model and the execution of the Laplace transform for the consequent equations. By doing so, exact solutions are derived in the form of Mittag-Leffler functions. Multiple illustrations are developed by dint of exact solutions to chew over all aspects of temperature variations and flow dynamics. For the preparation of these illustrations, the details of parametric ranges are as follows: [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]. The contribution of differently shaped nanoparticles, volume proportions, and fractional parameters in boosting the heat-transferring attributes of engine oil is also anticipated. In this regard, results for Nusselt number are provided in tabular form. Additionally, a brief analysis of shear stress is carried out for fractional parameters and various combinations of magnesia, graphene, and engine oil. This investigation anticipates that engine oil's hybridization with magnesia and graphene would result in a 33% increase in its thermal performance, which evidently improves its industrial significance. The enhancement in Schmidt number yields an improvement in the mass transfer rate. An increment in collective volume fraction leads to raising the profile of the thermal field. However, the velocity indicates a decreasing behavior. Nusselt number reaches its highest value ([Formula: see text]) for the lamina shape of considered particles. When the intensity of the buoyancy force augments, it causes the velocity to increase.

Biological interactions between micro swimmers and cross fluid with inclined MHD effects in a complex wavy canal.

The significance of studying biological interactions of micro swimmers in a complex wavy canal with MHD effects lies in its potential to provide insight into the behavior and dynamics of microorganisms in natural environments that contain complex fluid flow and magnetic fields. Current investigation explores the biological interactions between micro swimmers and Cross fluid with inclined MHD effects in a complex wavy canal. There are several factors of medium for micro swimmers like nature, magnetic field, liquid rheology and position. These interactions are hereby witnessed by utilizing the Cross fluid along with Taylor swimming sheet model under the influence of porous and inclined magnetic effect. Furthermore, two-dimensional complex wavy cervical canal is being utilized at inclined angle. By help of lubrication assumption, reduction of momentum equation is made and hence fourth-order differential equation associated with boundary conditions is obtained. Bvp4c command in Matlab is utilized for this boundary value problem. Obtained bvp4c solution is verified with finite difference method and found smooth agreement. Magnetic force enhances the swimming speed and reduction is seen for the power dissipation and effective role is seen for swimming motion with cross fluid rheology. The channel walls (peristaltic nature) and porous medium can be utilized as alternative factors to control the speed of the propeller.

Significance of Dufour and Soret aspects on dynamics of water based ternary hybrid nanofluid flow in a 3D computational domain.

The prime motive to conduct this communication is to explicate hydrothermal attributes of water by inducing new composition of nanoparticles termed as ternary particles. For this purpose, two differently natured groups one with lesser densities (Carbon nanotubes, Graphene and Aluminium oxide) and with higher densities (Copper oxide, Copper and Silver) are accounted. A 3D permeable surface is considered as a physical configuration of problem by providing dual stretching. Initially, mathematical structuring in dimensional representation expressing the constitutive relations for mass, momentum and energy conservation is manifested. Later on, a set of similar variables are executed to express attained coupled system into ordinary form. Numerical simulations are performed to find solution by employing shooting and RK-4 methods in conjunction. Description about change is displayed through graphical visualization. Subsequently, temperature distribution and heat flux coefficient against sundry variables are also measured and comprehensively discussed in pictorial and tabular format. Wall drag coefficients along (x, y) directions are also computed. It is inferred from the outcomes that velocity, temperature and concentration of base fluid is higher for ternary group 1 containing particles of low densities than for group 2 with more denser particles. It is also deduced that elevation in temperature of fluid is revealed against Soret number whereas contrary aspects is observed in view of concentration distribution. Dufour number has declining impact on temperature profile whereas it upsurges the mass distribution. It is depicted that skin friction in case of group containing particles with less densities are more than other group.

Significance of the inclined magnetic field on the water-based hybrid nanofluid flow over a nonlinear stretching sheet.

This work addresses a theoretical exploration of the water-based hybrid nanofluid flow over a nonlinear elongating surface. The flow is taken under the effects of Brownian motion and thermophoresis factors. Additionally, the inclined magnetic field is imposed in the present study to investigate the flow behavior at different angle of inclination. Homotopy analysis approach is used for the solution of modeled equations. Various physical factors, which are encountered during process of transformation, have been discussed physically. It is found that the magnetic factor and angle of inclination have reducing impacts on the velocity profiles of the nanofluid and hybrid nanofluid. The nonlinear index factor has direction relation with the velocity and temperature of the nanofluid and hybrid nanofluid flows. The thermal profiles of the nanofluid and hybrid nanofluid are augmented with the increasing thermophoretic and Brownian motion factors.CuO-H2Onanofluid flow has enhanced heat transfer rate thanAg-H2Onanofluid flow. On the other hand, theCuO-Ag/H2Ohybrid nanofluid has better thermal flow rate thanCuO-H2OandAg-H2Onanofluids. From this table it has noticed that, Nusselt number has increased by 4% for silver nanoparticles whereas for hybrid nanofluid this incrimination is about 15%, which depicts that Nusselt number is higher for hybrid nanoparticles.