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Heat absorption and thermal radiation have significant roles in engineering and research. These two principles have applications in thermal transportation, gas turbines, nuclear power plants, electrical fuel, aerospace engineering, projectiles and renewable energy. The present work analyses the stagnation point ternary nanofluid motion over a circulating sphere in the presence of a magnetic field and radiation absorption. The nonlinear controlling equations are replaced by ordinary differential equations by applying a suitable comparison factor. The bvp4c process was used to establish numerical outcomes of the partial differential equations. This mathematical numerical findings are presented graphically. The results of ternary nanoparticles (Cu–Ag–CuO/water), hybrid nanoparticles (Cu–Ag/water) and copper (Cu) nanoparticles have also been compared, and this comparison suggests that ternary nanoparticles (Cu–Ag–CuO/water) are more effective at attenuating hemodynamic factors (such as wall shear stress and heat transfer) than hybrid and copper (Cu) nanoparticles. Comparison with previous literature results is also done and the results are found to be in very good agreement with those published earlier. [ABSTRACT FROM AUTHOR]

In this paper, the free convection flow phenomenon on magnetized second-grade nanofluid over a nonlinear elongating surface has been modeled under the assumptions of generalized Fick's and Cattaneo–Christov heat flux relations. The non-uniform heat source and sink and thermal radiation effects are used in the energy equation with the Buongiorno nanofluid model. The effect on activation energy and chemical processes is also examined, making the current numerical scrutinization innovative. The current mathematical model begins with partial derivative equations (PDEs), which are then transformed into ordinary derivative equations (ODEs) using similarity transformations. The outcomes are obtained using a combination of the finite-difference scheme with the collocation method, approximated up to desirable accuracy, and the effects of various parameters on the modified second-grade nanofluid are discussed using tables and graphs. The temperature distribution for the thermal boundary layer is raised with nonlinear thermal radiation and Brownian motion parameters. The present thorough analysis identified several technical and industrial applications, including Biomedical applications in cancer treatment, electrical wire manufacturing, oil friction control in pipelines, manufacturing processes, and aerodynamic expulsion utilizations. [ABSTRACT FROM AUTHOR]

The importance of bioconvection into the application of nanoparticles has had a significant impact on fundamental technological and industrial functions in recent years. These discussions are being carried forward by the bioconvection appearance on that flow by attracting nanoparticles into additional features on thermal radiation and activation energy. The investigation had been proposed on the appealing features of the mass and thermal convective boundary constraints. The high desirable subclass on rate-type fluid, especially Williamson fluid, was used to anticipate the absolute rheological parameters. The designated partial differential system was modified along with nonlinear ordinary differential equations applying enhance being related conversion, the designated partial differential system was modified along nonlinear ordinary differential equations. The governing equations are interpreted into ordinary differential equations, and in the following, shooting process was obeyed to build up the mathematical classification on the convert dimensionless flow problem. This value of physical restraint was displayed on the table and plots tests. This noted theoretical imitation could be highly successful in improving the solar energy systems and thermal extrusion processes. The outcomes reported that the rise in Weissenberg number and Hartmann number decreased the nanoparticles velocity distribution. The progressing temperature distribution was observed to develop radiation parameter and thermal conductivity parameter. That was further noted to modify bioconvection Lewis number and Peclet number that were reduced into motile microorganism distribution effectively. [ABSTRACT FROM AUTHOR]

The thermal radiation and convective condition principles were working on specific functions like gas turbines, electrical fuel, renewable energy, projectiles, nuclear power plants, aerospace engineering, and thermal transportation. Considering the aforementioned functions, the present analysis inspected the stagnation point hybrid nanofluids movement over the rotating sphere on the behavior of viscous dissipation and thermal radiation. Silver and Ferrous nanoparticles including the host fluid water were held into affected the flow. The presence of convective boundary conditions is incorporated within the system. Applying appropriate correspondence factors, nonlinear governing equations were transformed with ordinary differential equations. This finite element method is applied to find the mathematical solutions to the boundary conditions and simplified equations. These outcomes convey to temperature was decreased about accelerated factor, although primary velocity was found into increased. The heat transfer was magnified by thermal Biot number, and that rate of development was greater about hybrid nanosuspension. The heat transport method was reduced by the Eckert number; also that reduction rate was similarly dull on hybrid. [ABSTRACT FROM AUTHOR]

Exploiting the impact of Lorentz force and convective heating boundary on second-grade nanofluid flow alongside a Riga pattern is the main objective of the present work. Modelling of the present work is done through Grinberg term and a Lorentz force applied parallel to the wall of a Riga plate. The nanoparticles fraction on the solid surface of Riga pattern maintained a strong retardation because of zero mass flux. Theories of Cattaneo–Christov heat flux and generalized Fick's relations are employed by following the modern aspects of heat and mass transportations. In the current study, additional features of thermal radiation are also included in the energy equation in terms of linear expressions. In order to make the analysis more worthy, effect of chemical reaction is also included. By applying the suitable variables, constituted problem is converted into dimensionless form. Solution of the problem with desired accuracy is obtained by utilizing popular method called Runge–Kutta–Fehlberg. The graphical representations are used to illustrate the flow controlling parameters involved by their attractive physical consequences. Velocity distribution is observed for the increase with the second-grade parameter. Further, an improved nanoparticles temperature distribution is observed with the increase in radiation parameter and Biot number. Additionally, the distribution of the concentration of nanoparticles increases with increase in values of the thermophoretic parameter. Based on the scientific calculations obtained, it is established that the reported results may play a useful role in production processes and in the improvement of energy and thermal resources. [ABSTRACT FROM AUTHOR]

The consequences of Soret in addition to Dufour of natural convection heat and mass transfer for the unsteady three‐dimensional boundary layer flow through a perpendicular condition of the existence of viscous dissipation, invariable suction, Hall as well as ion slip consequences into relation. The prevailing partial differential equation is dissolved digitally utilizing the implicit Crank–Nicolson finite difference method. The velocity, temperature, as well as concentration dispensations, is addressed computationally and demonstrated by the graphs. Numerical values of the Nusselt number, skin friction as well as Sherwoods numbers nearby the plate are discussed for a choice of values of substantial parameters and are displayed in a tabular manner. It is noticed that the temperature of the fluid diminishes with higher Prandtl numbers. The resulting velocity diminishes with the growing Hartmann number. Rotation, Soret, and Dufour parameters strengthen the velocity and momentum boundary layer thickness. The velocity intensifies through growing Hall and ion‐slip parameters and the revoke trend is acquired with enhancement in suction parameter. [ABSTRACT FROM AUTHOR]