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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]

The present study probed the creation of heat energy and concentrating into Newtonian liquids across vertical 3D-heated plates. The role of the Soret and Dufour theories in concentrating and energy formulas is discussed. The role of hybrid nanoparticles is introduced to illustrate particle efficiency in terms of solute and thermal energy. It is removed a viscous dissipation process and a changing magnetic field. The proposed approach is motivated by the need to maximize solute and thermal energy uses in biological and industrial domains. The constructed system of (partial differential equations) PDEs includes concentration, momentum, and thermal energy equations within various thermal characteristics. Transformations are used to formulate the system of (ordinary differential equations) ODEs for solution. To assess various features vs various variables, a Galerkin finite element approach is used. Motion into nanoscale components is shown to be smaller than motion into hybrid nanoparticles. Furthermore, fluctuations in heat energy and solute particle counts are seen in relation to changes in Soret, Eckert, magnetic, and Dufour numbers. The basic finding is that the generation of thermal energy for hybridized nanomaterials is much higher. [ABSTRACT FROM AUTHOR]

This paper adopts a theoretical approach to explore the heat and mass transport features for MHD Jeffery–Hamel flow of viscous nanofluids through convergent/divergent channels with stretching or shrinking walls. Recently, this type of flows generated by nonparallel inclined plates with converging or diverging properties has been frequently utilized in various industrial and engineering processes, like, blood flow through arteries, different cavity flows and flow through canals. The current flow model is formulated mathematically in terms of partial differential equations (PDEs) in accordance with conservation laws under an assumption that the flow is symmetric and purely radial. In addition, heat and mass transport mechanisms are being modeled in the presence of Brownian motion and thermophoretic aspects using Buongiorno's nanofluid model. The dimensionless variables are employed to get the non-dimensional forms of the governing PDEs. The built-in MATLAB routine bvpc4 is implemented to determine the numerical solutions for governing the nonlinear system of ordinary differential equations (ODEs). Numerical results are presented in the form of velocity, temperature and concentration plots to visualize the influence of active flow parameters. The simulated results revealed that the Reynold number has an opposite effect on dimensionless velocity profiles in the case of convergent and divergent channels. Besides, the temperature distributions enhance for higher values of Brownian motion parameter. [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]

The physical aspects of inclined MHD nanofluid toward a stretching sheet embedded in a porous medium were visualized, which has numerous applications in industry. Two types of nanoparticles, namely copper and aluminum oxide, were used, with water (limiting case of Casson liquid) as the base fluid. Similarity transformations were used to convert the partial differential equations into a set of ordinary differential equations. Closed solutions were found to examine the velocity and temperature profiles. It was observed that an increment in the magnitude of the Hartmann number, solid volume fraction, and velocity slip parameter brought a reduction in the velocity profile, and the opposite behavior was shown for the permeability parameter in C u –water and A l 2 O 3 –water nanofluids. The temperature field, local skin friction, and local Nusselt number were further examined. Moreover, the study of C u and A l 2 O 3 is useful to boost the efficiency of thermal conductivity and thermal energy in particles. Reduction was captured in the velocity gradient and temperature gradient against changes in the thermal radiation number. The opposite trend was tabulated into motion with respect to the volume fraction number for both cases ( C u –water and A l 2 O 3 –water). [ABSTRACT FROM AUTHOR]

Nanoparticles are frequently used to enhance the thermal performance of numerous materials. This study has many practical applications for activities that have to minimize losses of energy due to several impacts. This study investigates the inclusion of ternary hybrid nanoparticles in a partially ionized hyperbolic tangent liquid passed over a stretched melting surface. The fluid motion equation is presented by considering the rotation effect. The thermal energy expression is derived by the contribution of Joule heat and viscous dissipation. Flow equations were modeled by using the concept of boundary layer theory, which occurs in the form of a coupled system of partial differential equations (PDEs). To reduce the complexity, the derived PDEs (partial differential equations) were transformed into a set of ordinary differential equations (ODEs) by engaging in similarity transformations. Afterwards, the converted ODEs were handled via a finite element procedure. The utilization and effectiveness of the methodology are demonstrated by listing the mesh-free survey and comparative analysis. Several important graphs were prepared to show the contribution of emerging parameters on fluid velocity and temperature profile. The findings show that the finite element method is a powerful tool for handling the complex coupled ordinary differential equation system, arising in fluid mechanics and other related dissipation applications in applied science. Furthermore, enhancements in the Forchheimer parameter and the Weissenberg number are necessary to control the fluid velocity. [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]