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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 recent years, energy consumption has become an essential aspect in the manufacturing industry, and low heat transfer is one of the obstacles that affect the quality of the final product. This situation can be managed by suspending nanoparticles into ordinary heat transferring fluid (the base fluid). This newly prepared colloidal suspension has better heat transport capabilities. Keeping such usage of nanofluids in mind, this research was performed to better understand the heat transport characteristics during flow analysis saturated in porous media subject to Al2O3-SiO2/water hybrid nanofluids. This flow problem was generated by a stretching/shrinking surface. The surface of the sheet was under the influence of mass suction and second-order partial slip. The boundary layer flow was formulated in a system of partial differential equations by utilizing basic conservation laws in conjunction with the Tiwari and Das nanofluid model. Then, the appropriate form of the similarity transformation was adapted to transform the model into a system of ordinary differential equations. The built-in function, i.e., the bvp4c function in the MATLAB software, solved the reduced form of the boundary layer model. The novelty of this study lay in the predicting of two different exact and numerical solutions for both the flow and temperature fields. The computed results showed that the medium porosity as well as the nanoparticle volume fraction widened the existence range of the dual solutions. In addition, the investigational output exposed the fact that the temperature fields were significantly enhanced by the higher nanoparticle volume fraction. Moreover, the outcomes of this study showed a superb correlation with existing works. The present results can be utilized in various branches of science and engineering such as the polymer industry and in the treatment of different diseases. [ABSTRACT FROM AUTHOR]

Cross nanofluid possesses an extraordinary quality among the various fluidic models to explore the key characteristics of flowing fluid during very low and very high shear rates and its viscosity models depend upon shear rate. The current study establishes the numerical treatment regarding variable viscosity-based mixed convective inclined magnetized Cross nanofluid with varying thermal conductivities over the moving permeable surface. Along with variable thermal conductivities, we considered thermal radiation, thermophoresis, and the Brownian motion effect. An inclined magnetic field was launched for velocity scrutiny and the heat transfer fact was numerically seen by mixed convective conditions. Similarity variables were actioned on generated PDEs of the physical model and conversion was performed into ODEs. Numerical results showed that the frictional force and Nusselt quantity considerably influence the skinning heat transfer processes over the geometry of a moving permeable surface. Furthermore, less velocity was noticed for the greater suction parameter and the Brownian motion parameter corresponds to lower mass transport. [ABSTRACT FROM AUTHOR]

Background: The infinite shear viscosity model of Carreau fluid characterizes the attitude of fluid flow at a very high/very low shear rate. This model has the capacity for interpretation of fluid at both extreme levels, and an inclined magnetic dipole in fluid mechanics has its valuable applications such as magnetic drug engineering, cold treatments to destroy tumors, drug targeting, bio preservation, cryosurgery, astrophysics, reaction kinetics, geophysics, machinery efficiency, sensors, material selection and cosmology. Novelty: This study investigates and interprets the infinite shear rate of Carreau nanofluid over the geometry of a cylindrical channel. The velocity is assumed to be investigated through imposing an inclined magnetic field onto cylindrical geometry. Activation energy is utilized because it helps with chemical reactions and mass transport. Furthermore, the effects of thermophoresis, the binary chemical process and the Brownian movement of nanoparticles are included in this attempt. Formulation: The mathematics of the assumed Carreau model is derived from Cauchy stress tensor, and partial differential equations (PDEs) are obtained. Similarity transformation variables converted these PDEs into a system of ordinary differential equations (ODEs). Passing this system under the bvp4c scheme, we reached at numerical results of this research attempt. Findings: Graphical debate and statistical analysis are launched on the basis of the obtained computed numerical results. The infinite shear rate aspect of Carreau nanofluid gives a lower velocity. The inclined magnetic dipole effect shows a lower velocity but high energy. A positive variation in activation energy amplifies the concentration field. [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]

Described in this article is a numerical study on the Jeffery–Hamel flow of hybrid fluid consisting of Copper and Graphene oxide nanoparticles. The nanofluid are considered as single-phase fluid and their heat transport performance is also investigated. The flow is carried out in a convergent/divergent channel where the channel walls can stretch or shrink. Additionally, the impact of magnetic field on flow and heat transfer analysis are examined. The flow governing equations are modeled under the Boussinesq approximations using cylindrical polar coordinates. These partial differential equations have been changed into system of ordinary differential equations by means of dimensionless formulation. Later, the numerical solution of governing problem is obtained with a developed code in MATLAB software which employs boundary-value problem solver (bvp4c). The effects of eminent flow parameters on skin friction coefficient, Nusselt number, velocity, and temperature distributions in case of both convergent and divergent channels are plotted and investigated. It is concluded from current analysis that the local skin friction coefficient significantly reduces with higher magnetic parameter. We further observed that the fluid velocity increases with increasing values of Reynolds number in case of convergent channel, while an inverse is noted for divergent channel. The present review indicates that the rate of heat transfer has been enhanced due to greater Prandtl number. [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]

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]