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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]

developments in nanotechnology have attracted the attention of scientists towards the interaction of nanoparticles due to their fascinating applications in thermal engineering and solar energy systems. Convinced by such motivating applications, the current research project addresses the utilization of nanoparticles in the unsteady three‐dimensional chemically reactive flow of an Oldroyd‐B fluid induced by a bidirectional oscillatory stretching surface. The effects of mixed convection are also considered here. The prime features of the nanofluid namely thermophoresis and Brownian motion characteristics are explored by introducing the famous Buongiorno's nanofluid model. The relevant equations for the formulated theoretical model have been reduced by the appropriate transformations for which the analytic solution is deliberated via the homotopic technique. Later on, a complete graphical analysis for distinct flow parameters is deliberated for dimensionless velocities, concentration, and temperature distributions with the relevant physical implications. Moreover, stimulating physical quantities like local Nusselt and Sherwood numbers are numerically calculated and discussed. The study emphasizes that decreasing variation in both components of velocities has been reported with an increment of relaxation time, while the impact of the retardation time constant is quite opposite. It is further claimed that the velocity distribution has an increasing tendency in the horizontal direction for a higher buoyancy ratio and mixed convection parameters. Moreover, an increment in thermophoresis parameter enhances both temperature and concentration distributions. [ABSTRACT FROM AUTHOR]

In this study, unsteady bidirectional stretched flow and heat transport of a Cu–water nanomaterial in the presence of a magnetic environment embedded in a porous medium occupying boundary‐layer region is investigated. Moreover, heat transport investigation is conceded out by simultaneous heat sources, namely, prescribed surface temperature and prescribed heat flux. The considered problem is converted into a set of four coupled differential equations with the help of a suitable combination of variables. The Keller–Box method is then implemented to get the numerical solution for velocity components and temperature distributions. Nanomaterial volume fraction ψ impact on the velocity components and temperature distributions are studied. Through reduced skin friction coefficients and Nusselt numbers, it is detected that the heat transport capacity of nanomaterial is better than that of the base fluid. An exponentially decaying behavior of velocity components and temperature distributions is observed at far‐field for various amounts of involved flow parameters. [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]

The current exploration reveals the unsteady three‐ dimensional flow of Jeffrey nanofluid over a bidirectional oscillatory stretching surface. The Brownian motion and thermophoresis phenomenon has been scrutinized by utilizing Buongiorno's nanofluid model. The heat transfer analysis is carried out in the presence of thermal radiation and heat generation/ absorption features. Furthermore, chemical reaction and magnetic effects are also deliberated. The flow has been generated by a bidirectional periodically accelerated heated surface. The formulated nonlinear problem is condensed into a dimensionless form via apposite transformations, and then analytic series solution is computed via homotopic technique. Comprehensive graphical evaluations for numerous prominent flow constants on associated profiles are performed. In addition, the tabulated numerical calculations for the local Nusselt and Sherwood numbers are also presented. The current analysis reported that both components of velocities have an increasing tendency for higher Deborah number, whereas an adverse influence is observed for the ratio of relaxation and retardation times parameter. Moreover, the concentration profile diminishes for the increasing variation of the chemical reaction parameter. [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]

Here, we have endeavored the rheological aspects of Oldroyd-B fluid induced by an accelerated and periodically moving sheet. The heat transfer evolution has been characterized with employment of novel Cattaneo-Christov law. Further features of heat transfer are characterized with heat generation/ absorption and thermal conductivity depending upon the temperature. The governing equations have been constituted properly with utilization of associated laws. After truncating the flow problem in dimensionless form, we follow famous analytic procedure, namely, homotopy analysis technique to simulate the solution. The convergence of the solution is established by sketching the h-curves. While assigning suitable constant values to involved physical parameters like Deborah number, thermal relaxation parameter, Prandtl number, and heat source/sink constants, the change in particles movement and heat transfer rate has been examined. It is observed that the velocity profile decreases with increments in Deborah constant, in terms of relaxation time constant. The presence of variable thermal conductivity and heat source parameters enhance the temperature distribution efficiently. Significance of Results: Recently, non-Newtonian fluids have attracted the interest of scientists due to their significant use in various chemical, mechanical, and processing industries. Some essential applications of such materials arise in polymer processing, food industries, paints, petroleum industries, biomedical engineering, and so forth. Besides this, the heat transportation phenomenon in non-Newtonian fluids flow engaged diverse novel applications in area of engineering processes, and also appeared in chemical, mechanical, and processing industries. The present problem may find engineering applications in paper production, glass blowing, polymer solution, and metal extrusion. The proposed results are useful in extrusion system applications, energy production, and manufacturing processes. [ABSTRACT FROM AUTHOR]

In this manuscript, heat transfer analysis of a nonaxisymmetric Homann stagnation-point flow of a Maxwell fluid is performed using a heat source and sink. The governed system of partial equations is reduced to the system of ordinary equations by employing the similarity variables. The numerical and asymptotic results are computed by employing the shooting technique. The effects of various parameters are analyzed on velocity and temperature profiles. Numerical results for skin friction coefficient and Nusselt number are computed for different involved parameters. The sound effects of 𝛾=𝑏/𝑎 (𝑏 is the shear rate and 𝑎 is strain rate) are examined for different profiles over (−∞,∞). Solutions for diverse values of heat source/sink parameter 𝑆, Deborah number 𝛽1, and 𝛾 are obtained. Local Nusselt number and wall shear stress parameter are compared with their large-𝛾 asymptotic behavior. It is found through analysis that the heat transfer rate increases for Deborah 𝛽1 and Prandtl number 𝑃𝑟. However, the addition of a source declines the heat transfer rate, whereas the sink enhances the heat transfer rate. However, the temperature of the fluid decreases as 𝛾 and 𝑃𝑟 increase. Meanwhile, the temperature of the fluid increases as 𝑆 increases. [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]