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Entropy generation with activation energy has garnered worldwide attention from researchers due to its extensive applications in thermodynamic design, chemical engineering, and optimization processes. One of the primary reasons for focusing on entropy is the global energy crisis, driven by massive consumption against limited resources. This study elucidates the double diffusion process in the dynamics of a viscous fluid over a stretching cylinder, incorporating considerations of entropy generation and activation energy. The non‐Fourier heat flux model is employed to describe the thermodynamics of the thermal system, while non‐Fick's law is used to elucidate the mass diffusion process. The unsteady phases of axisymmetric flow of the viscous fluid are thoroughly discussed. Transport equations in cylindrical configuration are transformed into ordinary differential equations, and an efficient mathematical method (i.e., homotopy analysis method) is applied to solve the transformed system. The graphical examination reveals the impact of flow parameters on velocity configuration, entropy configuration, temperature configurations, and concentration configurations. Additionally, a comparative benchmark is established with the results from previously published work for authentication and validation purposes. It is noted that concentration and temperature configurations are directly related to the unsteady stretching parameter. Entropy generation exhibits an inverse relationship with the unsteady stretching parameter when close to the stretching cylinder, whereas it shows a direct relationship when the fluid is flowing away from the surface. [ABSTRACT FROM AUTHOR]

In this study, a novel neuro heuristic approach is designed to investigate the flow properties of magnetohydrodynamic (MHD) nanofluid along an exponentially extending sheet with a permeable medium with the impact of radiation as well as fluctuating heat source/sink. The designed scheme to handle the suggested problem is established through the well‐known biologically inspired neural networks (BINNs) by exploiting the inverse multiquadric kernel (IMQK), that is, BINNs‐IMQK which is quite a new approach. The partial differential equations (PDEs) which govern the fluidic flow are reformed into a nonlinear system of ordinary differential equations (ODEs) using the most fitted similarity transformations rules and numerically solved by varying the parametric values including unsteady parameter, Brownian motion parameter, suction/injection parameter, radiation parameter, Schmidt number together with Prandtl number to visualize the velocity, thermal gradient, and mass transfer in the suggested fluid problem. It is noticed that nanofluid temperature hikes by uplifting the value of the Brownian motion parameter but this effect is reversed in case of unsteady parameter. The obtained numerical results are verified through reference solution using the well‐known Adams method and the efficacy of the suggested solver is endorsed using a variety of statistical operators. [ABSTRACT FROM AUTHOR]

The present investigation aims to explore the influence of a mixed convection and nonuniform heat source/sink on unsteady flow of a chemically reactive nanofluid driven by a bidirectionally expandable surface. Convective heat transport phenomenon is used to maintain the temperature of the surface. Moreover, zero mass flux is also accounted at the surface such that the fraction of nanomaterial maintains itself on strong retardation. The governing nonlinear set of partial differential equations is transformed into a set of ordinary differential equations via a suitable combination of variables. The Keller‐Box scheme has been incorporated to make a numerical inspection of the transformed problem. The spectacular impacts of the pertinent constraints on thermal and concentration distributions are elucidated through various plots. Graphical outcomes indicate that the thermal state of nanomaterial and nanoparticles concentration are escalated for elevated amounts of Biot number, porosity parameter and nonuniform heat source/sink constraints. Furthermore, it is also seen that escalating amounts of unsteady parameter, temperature controlling indices, Prandtl number, and expansion ratio parameter reduce the thermal and concentration distributions. Numerical results for the rate of heat transference have been reported in tabular form. The grid independence approach is used to verify the convergence of the numerical solution and the CPU run time is also obtained to check the efficiency of the numerical scheme adopted for finding the solution. [ABSTRACT FROM AUTHOR]

Inspired by spectacular applications of nonlinear resources in the field of nanotechnology, we formulate a mathematical relation for unsteady radiative flow of a magneto-Carreau nanoliquid as the consequence of a bidirectionally stretchable surface using the Buongiorno model. Practically, this newly mentioned approach is more genuine where we account for the fact that the surface temperature and surface heat flux are adjusted themselves on the boundaries, accordingly. With the utilization of this approach, industrial and engineering quantities of interest are investigated in a more effective manner. A suitable combination of variables is used to alter the partial differential equations into ordinary differential equations and then computationally solved by employing the Keller box method. The great significance of the involved constraints on the Carreau nanomaterial velocity components, temperature, and concentration fields is depicted graphically and elucidated in detail. The foremost outcomes for drag forces, surface temperature gradient, and concentration gradient for the Carreau nanomaterial are anticipated and arranged through tables. For endorsement of the present solution, the attained outcomes are linked with formerly published work in a particular case and found in marvelous agreement. It is observed that an escalating amount of radiative parameter Rd enhances the temperature of the Carreau nanomaterial. Moreover, the amounts of heat and mass fluxes are significantly improved by increasing the temperature of the surface. [ABSTRACT FROM AUTHOR]

The present contribution determines the impacts of viscous dissipation and Ohmic heating with magnetic coating on Prandtl nanofluid flow driven by an unsteady bidirectionally moveable surface. Random motion of nanoparticles and thermophoretic diffusion are elaborated through a two-phase nanofluid model. The novelty of the investigation is fortified by prescribed heat flux and prescribed mass flux mechanisms. The appropriate combination of variables leads to a system of strong nonlinear ordinary differential equations. The formulated nonlinear system is then tackled by an efficient numerical scheme, namely, the Keller-Box method. Nanoliquidtemperature and mass-concentration distributions are conferred through various plots with the impacts of miscellaneous-arising parameters. The rates of heat and mass transferences are also discussed through tables. The thermal states of the nanomaterial and mass concentration are reduced for incremental amounts of the unsteady factor, ratio parameter, elastic parameter, and Prandtl fluid parameter. Moreover, escalating amounts of the Brownian parameter, Eckert number, magnetic factor, and thermophoresis parameter enhances the temperature of the nanoliquid. An error analysis is also presented to predict the efficiency of the method used for the computational work. [ABSTRACT FROM AUTHOR]

This study analyzes Hall current and Joule heating effects on the ferro‐nanofluid flow by the rotation of the disk incorporated with generalized slip condition. By using the well‐known Von Karman transformation, formulated flow equations are modeled into ordinary differential equations. Numerical solutions of the governing flow equations are attained by utilizing the shooting method consolidated with the fourth‐order Runge–Kutta scheme. The impacts of different parameters on skin friction coefficient, velocity, temperature, and Nusselt number are given in graphs and tables and investigated in detail. Furthermore, an association with formerly published articles is given and met in remarkable correspondence. [ABSTRACT FROM AUTHOR]