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The goal of this study is to determine the maximum energy and solute particles' transportation growth in a 3D-heated region of Prandtl martial through a dynamic magnetic field. The effects of this field on the properties of solvent molecules and heat conduction are studied. A correctly stated functional method and a finite element approach are comparable to a certain type of differential equations. In order demonstrate the effects of various factors such as mass diffusion, heat generation, and thermal diffusivity on the investigation of the diffusion coefficient and thermal mass in a three-dimensional Newtonian flow, the study of viscous and heat conduction rates is presented. The results show that the comparisons of hybrid nanofluid F e 2 O 3 and A l 2 O 3 with base fluid and w.r.t Local skin friction coefficient, Nusselt number and Sherwood number. [ABSTRACT FROM AUTHOR]

In the current study, a vertical, 3D-heated plate is used to replicate the generation of heat energy and concentration into Prandtl liquid. We discuss how Dufour and Soret theories relate to the equations for concentration and energy. In order to see how effectively particles, interact with heat and a solvent, hybrid nanoparticles are used. It does away with the phenomena of viscous dissipation and changing magnetic fields. The motivation behind the developed study is to optimize solvent and heat storage uses in the biological and industrial domains. This article's major goal is to explore the aspects of thermal energy and mass transfer that influence how nanoparticles, hybrid nanoparticles, and 3D melting surface sheets behave. Variable thermal efficiency and variable mass transfer are combined. The system of generated PDEs (difference equations) includes the concentration, velocity, and heat energy equations. The numerical calculations are done for Silver (Ag), Molybdenum Disulfide (MoS2) nanoparticles with Ethylene glycol (C2H6O2) as the base fluid using a boundary layer approach to the mathematical formulation. The system of ODEs is formulated through transformations in order to find a solution. A Galerkin finite element algorithm (G-FEA) is adopted to analyze various aspects versus different parameters. It has been found that motion into hybrid nanoparticles is reduced by motion into nanoparticles. Additionally, differences in heat energy and solvent particle sizes are associated with modifications in magnetic, Dufour, Eckert, and Soret numbers. In contrast to hybrid nanostructures, the output of thermal energy is usually observed to be substantially higher. The magnetic field parameter decreases the particle velocity. In contradiction to the Eckert number, bouncy parameter, and magnetic parameter set values, the maximum quantity of heat energy is obtained. variable thermal conductivity's function. The 3D heated vertical surface convective heat transfer of nanofluids and hybrid nanofluids under the impact of a heat source, thermal radiation, and viscous dissipation has not yet been studied, as far as the authors are aware. [ABSTRACT FROM AUTHOR]

In our research work, we have developed a model describing the characteristics of the bio-convection and moving microorganisms in the flows of a magnetized generalized Burgers' nanoliquid with Fourier's and Fick's laws in a stretchable sheet. Considerations have been made to Cattaneo–Christov mass and heat diffusion theory. According to the Cattaneo–Christov relation, the Buongiorno phenomenon for the motion of a nanoliquid in the generalized Burgers' fluid has also been applied. Similarity transformations have been used to convert the control system of the regulating partial differential equations (PDEs) into ordinary differential equations (ODEs). The COMSOL software has been applied to obtain mathematical results of non-linear equations via the Galerkin finite element method (G-FEM). Logical and graphical measurements for temperature, velocity, and microorganisms analysis have also been examined. Moreover, nanoparticle concentrations have been achieved by examining different approximations of obvious physical parameters. Computations of this model show that there is a direct relationship among the temperature field and thermal Biot number and parameter of the generalized Burgers' fluid. The temperature field is increased to grow the approximations of the thermal Biot number and parameter of generalized Burgers' fluid. It is reasonable to deduce that raising the chemical reaction parameter and concentricity relaxation parameter or decreasing the Prandtl number, concentricity Biot quantity, and active energy parameter can significantly increase the nanoparticles concentration dispersion. [ABSTRACT FROM AUTHOR]

Fluid–structure interaction (FSI) gained a huge attention of scientists and researchers due to its applications in biomedical and mechanical engineering. One of the most important applications of FSI is to study the elastic wall behavior of stenotic arteries. Blood is the suspension of various cells characterized by shear thinning, yield stress, and viscoelastic qualities that can be assessed by using non-Newtonian models. In this study we explored non-Newtonian, incompressible Casson fluid flow in a bifurcated artery with a stenosis. The two-dimensional Casson model is used to study the hemodynamics of the flow. The walls of the artery are supposed to be elastic and the stenosis region is constructed in both walls. Suitable scales are used to transform the nonlinear differential equations into a dimensionless form. The problem is formulated and discretized using Arbitrary Lagrangian–Eulerian (ALE) approach. The finite element method (FEM) technique is used to solve the system of equations, together with appropriate boundary conditions. The analysis is carried out for the Bingham number, Hartmann number, and Reynolds number. The graphical results of pressure field, velocity profile, and load on the walls are assessed and used to study the influence of hemodynamic effects on stenotic arteries, bifurcation region, and elastic walls. This study shows that there is an increase in wall shear stresses (WSS) with increasing values of Bingham number and Hartmann number. Also, for different values of the Bingham number, the load on the upper wall is computed against the Hartmann number. The result indicate that load at the walls increases as the values of Bingham number and Hartmann number increase. [ABSTRACT FROM AUTHOR]

The use of hybrid nanoparticles to improve thermal processes is a key method that has implications for a variety of interventions utilized in many sectors. This paper aimed to look into the impacts of ternary nanoparticles on hyperbolic tangent materials to establish their thermal characteristics. Flow describing equations have been explored in the presence of heat production, non-Fourier heat flux, and an induced magnetic field. Boundary layer analysis, which generates partial differential equations, was used to model the physical situation under several major physical properties (PDEs). The flow rheology is expanded and calculated in a rotating frame by supposing that the flow is created by a spinning disk. The solution of complicated generated PDEs was calculated using the Galerkin finite element technique (G-FEM) after translating them into corresponding ODEs. Several major bodily repercussions have been seen and documented because of increasing the implicated influencing factors. Additionally, finite element approaches are provided for approximating the solution of nonlinear system problems encountered in flowing fluid and other computational physics areas. [ABSTRACT FROM AUTHOR]

This article models a system of partial differential equations (PDEs) for the thermal and solute characteristics under gradients (concentration and temperature) in the magnetohydrodynamic flow of Casson liquid in a Darcy porous medium. The modelled problems are highly non-linear with convective boundary conditions. These problems are solved numerically with a finite element approach under a tolerance of 10 − 8. A numerical algorithm (finite element approach) is provided and a numerical procedure is discussed. Convergence is also observed via 300 elements. Simulations are run to explore the dynamics of flow and the transport of heat and mass under parametric variation. To examine the impact of a temperature gradient on the transport of mass and the role of a concentration gradient on the transport of heat energy, simulations are recorded. Remarkable changes in temperature and concentration are noted when Dufour and Soret numbers are varied. [ABSTRACT FROM AUTHOR]