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This paper analyzes the thermodynamic second law analysis of mixed convection heat transfer of Carboxymethyl Cellulose (CMC)-water based viscoelastic hybrid nanofluid flow in a vertical parallel plate channel filled with porous medium. In mixed convection flow, where both buoyancy and viscous forces play significant roles in the flow behavior, the inclusion of viscous dissipation in the analysis is crucial. The governing equations of the problem are converted into a system of ordinary differential equations using appropriate similarity transformations, which are then solved by the Homotopy Analysis Method (HAM). The behavior of non-dimensional velocity, temperature, skin friction coefficient, Nusselt number, entropy generation and Bejan number profiles for a range of pertinent flow parameter values is displayed graphically and deliberated. Study reveals that a decrease in the dominance of viscous forces relative to inertial forces within the porous medium lowers entropy generation in the system. [ABSTRACT FROM AUTHOR]

The mathematical modeling of biological fluids holds paramount importance, given its diverse applications in the medical field. Understanding the peristaltic mechanism is crucial for gaining insights into various biological flows. This study focuses on numerically estimating the double-diffusive peristaltic flow of a non-Newtonian six constant Jefferys nanofluid within an irregular medium. The investigation considers the influences of nonlinear thermal emission, viscous dissolution, and induced magnetization, incorporating multiple slip conditions. The Buongiorno model is employed to underscore key features related to thermophoresis and Brownian diffusion coefficients. The convection of double diffusivity is elucidated through the Soret and Dufour variables. Lubrication technique is employed for mathematical simulation, and the resulting nonlinear coupled system of differential equations is solved numerically through the Mathematica program's built-in command (ND Solve function). The graphical representation of the impact of crucial flow variables, such as nanoparticle volume proportion, pressure gradient, solute density, temperature, pressure fluctuation per wavelength, and velocity distribution, provides valuable insight. The findings of the current study show that an increase in the Prandtl number and thermophoresis parameter leads to the expansion of thermal curves. Moreover, it is also noted that rising heat frequencies of radiation cause the concentration of nanoparticles to increase. [ABSTRACT FROM AUTHOR]

This research paper investigates a two-dimensional couple stress flow of hybrid nanofluid (HN) over a nonlinear stretching surface with heat transfer analysis. HNs are well-known for their exceptional heat transfer properties compared to conventional fluids. The mathematical modeling of the problem involves the formulation of basic governing equations, namely, continuity, momentum and energy equations. To simplify the analysis, a similarity transformation technique is employed to convert the dimensional NLPDEs into dimensionless NODEs. Subsequently, the obtained governing equations are analytically solved using the HAM. The investigation explores the impact of several parameters, including magnetic field inclination, slip parameter, couple stress parameter, nanoparticle volume fraction, nonlinear stretching parameter, EN, thermophoresis parameter and PN. This study presents graphical representations of temperature and velocity distribution to visualize the effects of these parameters on the HN flow. Furthermore, different graphs and tables are employed to explain the impact of the factors on SF and NN. Notably, the results indicate that the HN exhibits significantly enhanced heat transfer properties over the base fluid, particularly under the influence of an inclined magnetic field. This research is expected to contribute to the advancement of the field of condensed nanostructure and nanomaterials, opening new avenues for further exploration in heat transfer enhancement applications. [ABSTRACT FROM AUTHOR]

The magnetohydrodynamic (MHD), forced convective, rotating flow of nanofluid is investigated induced by eccentric rotations of a unsteady stretching porous disk and that of the fluid at infinity. The fluid is assumed to be incompressible, viscous, and electrically conductible. The disk and fluid away from the disk rotate about non-coincident axes at the same angular velocity. The forced convection is due to the temperature gradient between the uniform temperatures of the disk and that of the fluid far away from the disk. Consideration of the Joule heating as well as viscous dissipation have been taken into account. Nanofluids based on copper, alumina, and titania have also been assumed. Exact solution has been carried out for the velocity field. Numerical solution, on the other hand, is obtained using Crank–Nicolson algorithm for the temperature profiles. Several physical aspects of the investigation are discussed and explained by means of dimensionless parameters, Prandtl number Pr, Eckert number Ec, porosity parameter S, magnetic parameter M 2 and unsteady stretching parameter. With increasing nanoparticle volume fraction, the velocity profile is reduced, while the thickness of the boundary layer upsurges. As the unsteady parameter C gets higher values, the velocity profile enhanced whereas the temperature profile gets weaker. Fluid temperature decreases as suction parameter S raises. [ABSTRACT FROM AUTHOR]

The hybrid nanofluid (HNF) flow consists of polymer/CNT matrix nanocomposite material (MNC) across coaxial cylinders is numerically described in this study. The HNF flow is inspected under the consequences of thermal radiation, exponential heat source/sink and viscous dissipation. The HNF is prepared by adding polymer/CNT MNC in water. MNCs are highly productive elements with unique designs and properties. The MNCs are widely used in biomedicine and electrical applications due to their exceptional thermophysical properties. Based on their exceptionally high electrical conductivity, CNT/polymer nanoparticles (NPs) are also utilized as shielding for electrostatic discharge and electromagnetic interference (EMI). The HNF flow is modeled with the help of energy, continuity, and momentum equations. MATLAB package bvp4c is used to numerically handle the modeled equations. It has been perceived that the intensifying numbers of polymer/CNT MNC will lessen the fluid velocity and temperature profile in cases of both nanofluid and HNF. [ABSTRACT FROM AUTHOR]

The current research deals with analytical analysis of Marangoni convection on ethylene glycol base hybrid nanofluid two-dimension flow with viscous dissipation through a porous medium, which have some important application in mechanical, civil, electronics, and chemical engineering. Two types of nanoparticles one is sliver and other is graphene oxide and ethylene glycol is used as base fluid in this research work. The authors applied appropriate transformations to convert a collection of dimension form of nonlinear partial differential equations to dimensionless form of nonlinear ordinary differential equations. The transformed nonlinear ordinary differential equations are solved with the help of an approximate analytical method known as the homotopy analysis method. The effects of various parameters, including nanoparticle volume fraction, porosity parameter, Marangoni convection, and Eckert number, on energy and momentum profiles are analyzed, with the results illustrated using graphs. A physical explanation is provided to simulate and evaluate the behavior of nanofluid structures, such as temperature and velocity, in response to changes in these influencing factors. [ABSTRACT FROM AUTHOR]

In this analysis, the collective effects of rotation, viscous dissipation and vertical throughflow on the onset of convective movement in Jeffrey fluid saturated permeable layer is studied. The improved Darcy model is applied to depict the rheological performance of Jeffrey fluid flow in porous medium. The approximate analytical solution with overall error 0.4 % and numerical solution accurate to one decimal place are presented using the Galerkin process. The analysis reveals that the convective motion concentrates in the top layer if it occurred with sufficiently high value of the Darcy–Eckert number. The rotation factor and the Péclet number postponement the onset of convective drive while, the Gebhart number quicken it weakly. In the occurrence of rotation, the Jeffrey factor displays dual impact on the coming of convective movement. The magnitude of the convection cell declines with increasing the rotation factor, the Jeffrey factor and the Péclet number, while it decreases with enhancing the Gebhart number. It is also found that in the lack of rotation, the Jeffrey factor has no impression on the extent of the convective cell, whereas in the nonexistence of the Péclet number, the Gebhart number has no impact on the arrival of convective drive as well as on the magnitude of the convective cells. [ABSTRACT FROM AUTHOR]

This paper explores the effects of velocity slip and power-law nanofluid flow on tetrahybrid nanofluids across a stretching sheet. Tetrahybrid nanofluids, which combine four distinct nanoparticles Ag, S i O 2 , CuO, and ZnO with engine oil as the base fluid, are investigated for their potential to enhance thermal performance. Engine oil plays a critical role in reducing friction and wear in mechanical systems by forming a protective layer on components such as cylinders, pistons, and bearings. Using MATLAB’s bvp4c, the study solves a set of ordinary differential equations derived from boundary layer equations, applying appropriate similarity transformations. It is observed that two unique velocity profiles intersect at a specific location, which shifts away from the stretching sheet as the velocity slip parameter increases. The findings indicate that tetrahybrid nanofluids offer superior heat transfer rates compared to standard nanofluids, showing improvements of 7.43, 6.27, and 5.35% over hybrid and tri-hybrid nanofluids, respectively. This study provides graphical representations of how various parameters, including the Prandtl number, power-law index, slip parameter, magnetic field parameter, and Reynolds number, affect temperature and velocity profiles. It is revealed that increasing the value of the solid volume fraction causes the tetrahybrid nanofluid velocity to decrease and its temperature to rise. The innovation of this work lies in its detailed examination of tetrahybrid nanofluids, extending beyond earlier research on simpler nanofluids and offering valuable insights for advanced thermal management solutions.Article highlights: Increasing nanoparticle volume fraction thickens and densifies the nanofluid layer, raising resistance to flow The tetrahybrid nanofluid’s temperature rises as nanoparticles enhance thermal conductivity and heat transfer capacity. The tetrahybrid nanofluid’s temperature rises as nanoparticles enhance thermal conductivity and heat transfer capacity. [ABSTRACT FROM AUTHOR]

This paper focuses on flow structures and thermal fields of the Carreau–Yasuda (CY) nanofluid model through a two-dimensional, wavy, complicated vertical asymmetrical conduit filled with porous elements. Formulations of the viscous dissipation in the case of CY nanofluids are derived and nonlinear radiation flux as well as joule heating are examined. Buongiorno's nanofluid approach, which involves Brownian motion and thermophoresis aspects is considered. The electrical conductivity of the suspension is considered as a variable where it depends upon the ambient temperature and concentration distributions and the Joule heating impacts are not neglected. The approach of solving the problem is contingent upon converting the system to dimensionless form then the lubrication approach with low magnetic Reynold numbers is applied. Numerical solutions are found for the resultant system, and wide ranges are considered for Weissenberg number We, non-Newtonian parameter n and Darcy number D a , namely, 0 ≤ We ≤ 2 , − 0. 5 ≤ n ≤ 1. 5 and 0 ≤ D a ≤ 1. 6 , respectively. The major results indicated that gradients of the pressure are higher in case of shear thickening (n > 1) comparing to in the instance of shear thinning (n < 1). Also, the velocity is enhanced, close to the channel's lowest portion, as the Weissenberg number is growing. The variable electrical conductivity gives a higher mass transfer rate compared to the constant property. [ABSTRACT FROM AUTHOR]

The objective of this study is to numerically investigate and compare the characteristics of two distinct hybrid nanofluids EG-MoS2-SiO2 and H2O-Cu-Al2O3 flowing steadily over a channel created by two non-parallel absorbent porous walls. Further, the considered fluid flow is under the influence of exponential space-based heat source, viscous dissipation, Joule heating, radiation, and external magnetic field. The nonlinear partial differential equations and subjecting boundary conditions of the flow are transformed into a system of nonlinear ordinary differential equations through suitable similarity transformations and are solved by combining the shooting technique with the traditional Runge–Kutta method. The consequential results are produced utilizing MATLAB software. The comparisons of the velocity profiles, temperature profiles, surface drag, and Nusselt number for both hybrid nanofluids are illustrated as graphs. The findings indicate that H2O-Cu-Al2O3 exhibits better velocity profiles, EG-MoS2-SiO2 displays enhanced temperature profiles, while H2O-Cu-Al2O3 has improved skin friction and Nusselt number. It is noteworthy to mention that numerous industries, including manufacturing, power generation, chemical processes, microelectronics, and transportation, depend on improving heat transfer coefficients. Hence, the significance and novelty of this work lie in the evaluation of optimization and sensitivity analysis of the EG-MoS2-SiO2 hybrid nanofluid to enhance heat transmission using Response Surface Methodology. [ABSTRACT FROM AUTHOR]

Our focus here is on examining the behavior of a boundary layer that regulates the movement of a non-Newtonian fluid undergoing a chemical reaction on a radiative paraboloid surface. This includes studying the fluid’s movement, temperature, and mass transfer. The fluid being studied pertains to the Williamson fluid model, which is described as a type of extended Newtonian fluid. We have considered the effects of Joule heating and dissipation through viscous phenomena based on the rules of heat and mass movement. The equations in the mathematical structure of partial differential equations (PDEs) governing the fluid continue to flow model in the problem. A subsequent evolution of these equations into ODEs by incorporating similarity variables. The velocity field’s schematic behavior is attributable to the magnetic parameter, thickness parameter, and the Weissenberg number, which exhibit velocity profile decline. In this research, both thermal radiation and Eckert number are highlighted, and it is concluded that both of these variables substantially raise the temperature field. We continue to track the concentration-reducing chemical reaction characteristic that remains tracked along with concentration transfer. Furthermore, the study includes a comprehensive presentation of comparative analyses with previously published scholarly works. [ABSTRACT FROM AUTHOR]

This paper aims at developing non-similar solutions for heat transfer augmentation in ternary hybrid nanofluids. Nanofluid is composed of three distinct (Silver, Copper, Aluminum oxide) nanosize particles while water is considered as a base fluid. Darcy–Forchheimer expression with variable porosity and permeability is adopted. Joule heating and viscous dissipations are also considered. Non-similar approach is utilized. Numerical solutions are computed by bvp4c solver of MATLAB. Graphical illustrations for flow and thermal fields behavior are provided. Comparative results are obtained for ternary hybrid nanofluid and nanoliquid. Physical quantities such as skin drag coefficient and Nusselt number are computed and interpreted. Our results reveal that rate of heat transfer augments substantially for Ag/water nanofluid in comparison to other classes of nanofluid. [ABSTRACT FROM AUTHOR]

Significance: The thermal energy transfer in nanofluid flow over an exponentially stretching surface has crucial practical configurations in various industrial processes, and it has potential applications in heat exchangers, chemical engineering, energy harvesting, and material processing. Purpose: This study is devoted to exploring the features of free convection in the thermally stratified, unsteady flow of Casson fluid over an inclined, exponentially stretching surface. Moreover, the implications of nonlinear thermal radiation, activation energy, and thermal/salute stratification effects are examined over the thermal energy transport distributions. Diffusion-thermo and thermo diffusion impressions are also taken into consideration. Methodology: By introducing reasonable transformations, partial differential equations are altered into ordinary differential equations. A nonlinear system of differential equations is solved numerically by employing the Midrich numerical technique. Findings: The impacts of diverse fluid parameters like the Soret/Dufour number, temperature difference parameter, radiation parameter, thermal/salute stratification parameter, magnetic parameter, and Prandtal number are assessed and depicted in plots by explaining the physical justifications of each parameter. Also, numerical values of sink friction and local Nusselt and Sherwood numbers are computed and examined for different values of pertinent variables involved in the problems. It is found that the rate of thermal energy transport is significantly enhanced by the larger estimation of the radiation parameter. Furthermore, it is perceived that the escalation in the temperature ratio constant leads to increased thermal convection in the fluid, while the larger thermal stratification constant decays the rate of heat transport in the fluid. Additionally, the rate of thermal transport is de-escalated due to the escalation in the intensity of thermal stratification parameter. [ABSTRACT FROM AUTHOR]

This study fills a gap in the literature by exploring the complex interplay between microrotation, magnetic fields, and temperature factors in hybrid nanofluids, improving our understanding of their behavior and potential usage. For hybrid nanofluids, this study examines their combined effect rather than individual components. The hybrid nanofluids, specially engineered mixture of base fluid, which is water, and two types of nanoparticles, titanium dioxide (TiO2) and iron oxide (Fe3O4), known for their remarkable energy transfer capabilities, are investigated. These fluids find applications in heat generation, micropower generation, and solar collectors. The research focuses on understanding the impact of various factors, including microrotation, inertial characteristics, thermal radiation, melting heat transfer, and Joule dissipation, on surface heating in the presence of a radially stretchable rotating disk. The governing equations are transformed into ordinary differential equations using similarity variables, and the study employs the homotopy analysis method for a semi-analytical solution. The results reveal how temperature, velocities, heat transmission rates, and skin-friction change under different material properties. This research has implications for magnetohydrodynamics in space propulsion, radiative heat transfer in high-temperature applications, and solar thermal systems. It also contributes to environmental engineering and automotive cooling systems. [ABSTRACT FROM AUTHOR]

The objective of this paper is to investigate the heat transfer mechanism while considering the attributes of viscous dissipation, Joule heating, and nonlinear thermal radiations in the three-dimensional steady incompressible flow of Carreau liquid on an extendable rotating disk. By using the similarity transformation, the governed equations were converted into the nonlinear coupled ordinary differential equations. The essential characteristics of various variables like Prandtl number, Lewis number, Carreau liquid parameter, Brownian motion, thermophoresis parameter, radiation parameter, Eckert number and Hartmann number on velocity, thermal, and concentration are discussed through graphs and tables. The presented investigation divulges that the thermal and mass transfer rates enhance when Brownian motion and thermophoresis processes extended and manifest as opposing features on the concentration field. [ABSTRACT FROM AUTHOR]

The enormous potential of nanotechnology has drawn attention to many different fields. Using nanoparticles, bio-convection has become a key phenomenon in industrial and technical applications. Nanofluids have emerged as effective solutions for addressing complex heat transfer challenges in modern engineering. This study aims to develop a comprehensive three-dimensional model of Sutterby nanofluid flow with bio-convection, investigating the effects of nonlinear thermal radiation, gyrotactic microorganisms, and magnetic fields on thermal efficiency and entropy generation. By investigating entropy optimization, chemical processes, activation energy, viscous dissipation, and magnetic field effects, the research aims to improve Sutterby nanofluid efficiency. This model reveals the dynamics of Sutterby nanofluid behavior by using partial differential equations (PDEs) and successively converted into an ordinary differential equation (ODE) system. The converted equations are solved numerically using numerical technique bvp4c. The results of analyses show relationships between the concentration of nanofluid, Biot numbers, and microorganism profiles. The results indicate that while an increase in Biot number improves microorganism profiles, an increase in Lewis and Peclet numbers decreases nanofluid concentration. Critical elements that greatly affect mass distribution, heat transmission, and flow dynamics include magnetic fields, chemical processes, and activation energy. With the help of tables, the effects of physical parameters on skin friction, Nusselt numbers, and local Sherwood numbers are thoroughly investigated. [ABSTRACT FROM AUTHOR]

This paper focuses on applying the Corcione model to the microchannel. The Corcione model is highly relevant because it provides accurate empirical relationships for forecasting the dynamic viscosity and effective thermal conductivity of nanofluids. These qualities are crucial for building and improving different thermal systems. The model presents and discusses two simple empirical correlating equations for forecasting the dynamic viscosity and effective thermal conductivity of nanofluids. Hence the aim of this work is to use Corcione’s model to demonstrate the fully developed laminar flow of an electrically conducting nanoliquid through an inclined microchannel. The energy equation takes into account the physical impacts of the heat source/sink, temperature jamp, and viscous dissipation. TiO2 nanoparticles in water are taken into consideration in this work for enhanced cooling. Using the numerical program Maple, Runge–Kutta–Fehlberg 4th–5th-order method is utilized to solve the present research. Making use of graphs, all of the flow parameters are shown, and the physical consequences on the flow and temperature profiles are thoroughly examined. It is noted that a higher inclined angle enhances the velocity profile whereas a larger temperature jump declines the temperature profile. Furthermore, Corcione’s model often has greater velocities, temperatures, and reduced surface drag forces than the Tiwari–Das model. [ABSTRACT FROM AUTHOR]

The present study investigates the entropy generation of chemically reactive micropolar hybrid nanoparticle motion with mass transfer. Magnetic oxide (Fe3O4) and copper oxide (CuO) nanoparticles were mixed in water to form a hybrid nanofluid. The governing equations for velocity, concentration, and temperature are transformed into ordinary differential equations along with the boundary conditions. In the fluid region, the heat balance is kept conservative with a source/sink that relies on the temperature. In the case of radiation, there is a differential equation along with several characteristic coefficients that transform hypergeometric and Kummer's differential equations by a new variable. Furthermore, the results of the current problem can be discussed by implementing a graphical representation with different factors, namely the Brinkman number, porosity parameter, magnetic field, micropolar parameter, thermal radiation, Schmidt number, heat source/sink parameter, and mass transpiration. The results of this study are presented through graphical representations that depict various factors influencing the flow profiles and physical characteristics. The results reveal that an increase in the magnetic field leads to a reduction in velocity and entropy production. Furthermore, temperature and entropy generation rise with a stronger radiation parameter, whereas the Nusselt number experiences a decline. This study has several industrial applications in technology and manufacturing processes, including paper production, polymer extrusion, and the development of specialized materials. [ABSTRACT FROM AUTHOR]

Researchers are mainly interested in using soft computing artificial intelligence (AI) methods due to their broad applications in analysis, modelling and simulations. Backpropagation neural networks, one of the supervised learning algorithms, is commonly used to train data networks by optimizing the error between actual and predicted values. To optimize this process of training data, Levenberg-Marquardt algorithm is applied; particularly beneficial for solving nonlinear fluid flow problems. Little knowledge is known about the ternary-hybrid nanofluid flow caused by a stretching surface with heat generation, viscous dissipation, magnetic effect and porosity etc. This article presents a novel machine-learning approach using backpropagation neural networks augmented with the Levenberg-Marquardt procedure to figure out the ternary-hybrid nanofluid flow generated by a stretching sheet. It uniquely examines the mixture of copper, Iron oxide and silicon dioxide nanoparticles inside a single base fluid within a magnetic field, tackling the research gaps in the effects of heat generation, viscous dissipation, porosity, and magnetic effects on fluid flow system and heat transfer. Shooting numerical technique (RK-5th) is used for solving the governing ordinary equations. Graphical illustration, error analysis, mean squared error, histograms and regression analysis justify the proposed method, showing better performance for ternary nanofluids. [ABSTRACT FROM AUTHOR]

In this work, computational intelligence methodologies are used to investigate the trihybrid nanofluid, a new theoretical model with remarkable thermal transmission properties to enhance liquid thermal performance. The nanostructure Cu, Al2O3, and TiO2 were immersed in the base liquid (C2H6O2) to produce (Cu + Al2O3 + TiO2/C2H6O2) trihybrid nanofluid. In a Darcy-Forchheimer porous medium over a stretching Riga sheet, this study examines the electromagnetic ternary hybrid nanofluid flow under various slip situations. The study takes into account the complex interactions between a number of variables, including as viscous dissipation, radiation, heat sources, and chemical reactions. Similarity transformations are used to convert complex partial differential equations for flow, energy, and concentration into nonlinear ordinary differential equations. The highly nonlinear equations of the problem are solved numerically with the use of techniques from the bvp4c approach. The results of the bvp4c method produce the reference dataset required for the Levenberg-Marquardt backpropagation of neural networks (LMBNN). The neural network performance is validated using regression analysis, mean square errors, and error histogram data. The model problem's consistency and precision are evaluated using the absolute error, which is given for each model instance at around 10−06–10−08, 10−05–10−10 and 10−06 05–10−09. In order to reduce mean square error, the nonlinear fluid dynamics system's numerical solutions have been taken into consideration. Using the comparative configurations of MSE, error histograms, state transitions, correlation, and regression, the reliability and competence of the stochastic technique are verified. [ABSTRACT FROM AUTHOR]

This study investigates the dynamic properties of a Casson hybrid nanofluid flow over a rotating disk, emphasizing the influences of Electroviscous forces and Cattaneo-Christov heat flux. The nanofluid comprises Silver (Ag) nanoparticles and Multi-Walled Carbon Nanotubes (MWCNTs) dispersed in a water base fluid, chosen for their superior thermal properties and stability. A comprehensive mathematical model, comprised of Partial Differential Equations (PDEs) transformed into Ordinary Differential Equations (ODEs) through a similarity transformation method, is developed to explore this complex phenomenon. The analysis combines multiple variables including magnetic fields, viscous dissipation, Joule heating, and radiative as well as convective effects. The findings reveal significant impacts on skin friction, fluid flow characteristics, and heat transfer behavior due to the synergistic effects of the considered parameters. The study’s novelty lies in its detailed examination of Electroviscous effects within a rotating disk setup, extending beyond traditional analyses by integrating the specific thermal and viscous properties of Silver and MWCNT nanoparticles. This approach offers new insights into optimizing heat transfer applications in industrial processes, particularly in high-speed rotational systems. [ABSTRACT FROM AUTHOR]

The present research focuses on the MHD second-grade nanofluid flow with induced magnetic field and viscous dissipation over an exponentially stretching surface. The solutal and thermal energy equations are analyzed in the presence of thermophoretic effect and variable thermal conductivity. The solutal and thermal slip boundary conditions are imposed on the surface of the sheet. In the mathematical modeling, the Brownian motion, and thermophoresis consequences are also discussed. The physical appearance of the induced magnetic field on the second-grade nanofluid is the central aim of this investigation. The mathematical flow model which is in the form of nonlinear PDEs is transformed into the system of couple ODEs by the usage of suitable similarity variables. These couple equations are tackled numerically with the help Bvp4c Matlab approach. The illustration of parameters on the flow model is discussed via graphs and tables. It is noted that the induced magnetic field profile and velocity of fluid intensify for the stronger values of second-grade parameter. Further, the numerical result shows that skin friction rate boosts via greater estimation of second-grade parameter and it reduces for magnetic Prandtl number. [ABSTRACT FROM AUTHOR]

This thermal research communicates the thermal aspect of hybrid Casson nanofluid in the presence of entropy generation and double stratification. The contributions of Buoyancy force are studied through mixed convection. Darcy Forchheimer condition is also applied in momentum equation along with the effects of thermal radiation, viscous dissipation and convective condition. The flow is generated by stretching a thin needle. Double stratification effect is implemented in boundary conditions of the thermal and concentration equation. Transformations are implemented to form ordinary differential equations from partial differential equations. The shooting numerical method is used to find the solution of local similar expressions. The motion of the fluid slows down for higher Casson fluid parameter and Forchheimer number. The temperature shows the contrast behavior for Brinkman number and thermal relaxation parameter. Solutal relaxation parameter and thermophoresis parameter have opposite behavior for concentration parameter. The entropy generation enhances for Forchheimer number and Casson fluid. [ABSTRACT FROM AUTHOR]

This study numerically investigated the entropy production in nanofluids' dissipative unsteady oscillatory flow characterized by variable electric conductivity and magnetic heating effects. The imposition of the non-isothermal boundary condition on the oscillatory stretching sheet plays a crucial role in establishing the self-similar solution in the presence of viscous heating. An external magnetic field (uniform in space and time) is imposed perpendicular to the plane of the oscillating stretched boundary. The energy equation, incorporating viscous dissipation effects and momentum equation, is reduced to nonlinear coupled partial differential equations and numerically solved using the Gear-generalized differential quadrature scheme.Additionally, to ensure the precision and reliability of the outcomes, the numerical code undergoes a thorough validation process that involves comparing its outputs to the findings of previous available studies. The Corcione model is implemented to describe the nanofluid's effective viscosity and thermal conductivity. Furthermore, expressions for entropy production and relative irreversibility parameter (Bejan number), considering variable electric conductivity, are derived and computed based on solutions obtained from momentum and energy equations. The impacts of parameters such as magnetic parameter, variable electric conductivity parameter, Eckert number, Strouhal number, Prandtl number and temperature difference parameters on flow, heat transfer, entropy generation, and Bejan number are systematically illustrated and examined. We observed that increasing the variable electric conductivity parameters reduces the velocity profiles while improving the thermal fields. Similar behavior is found when the strength of a magnetic field is increased. The skin friction coefficient exhibits an augmentation in response to the Eckert number, dimensionless time, Strouhal number, nanoparticle volume fraction, magnetic parameter, and variable thermal conductivity parameter. Conversely, the Nusselt number increases concerning the Strouhal number and nanoparticle volume fraction. At the same time, it declines in association with the magnetic parameter, dimensionless time, Eckert number, and variable electric conductivity parameter.This comprehensive investigation enhances our understanding of nanofluid dynamics and provides valuable insights for optimizing thermal management systems across various engineering disciplines. [ABSTRACT FROM AUTHOR]

This paper reports the mass and energy transmission characteristics of an electrically conducting mixed convective nanofluid flow past a stretching Riga plate. An additional effect of viscous dissipation, Arrhenius activation energy and heat source is also studied. The energy and mass transmissions are evaluated by a zero-mass flux of nanoparticle and convective boundary conditions. Buongiorno's relations are proposed for the Brownian motion and thermophoretic diffusion. The similarity substitutions are employed to derive the non-dimensional set of modeled equations. The obtained set of equations is numerically processed via parametric continuation method (PCM). Several flow factors affecting the velocity, energy, and mass distributions are graphically discussed. It has been perceived that the fluid velocity field declines with the influence of velocity power index (m), while improves with the upshot of modified Hartmann number (Q). The effect of Schmidt number and chemical reaction diminishes the concentration profile φ (η). Furthermore, the energy curve enhances with the effect of thermophoresis factor, Biot and Eckert number. [ABSTRACT FROM AUTHOR]

Understanding and optimizing heat transfer processes in complex fluid systems is the driving force behind studying the magnetohydrodynamic (MHD) flow of Al2O3–Cu∕H2O nanofluid across a radiative moving wedge, taking into account the impacts of viscous dissipation and Joule heating. Nanofluids, such as Al2O3–Cu∕H2O, increase heat transmission and thermal efficiency. However, the complicated challenges caused by fluid characteristics and radiative heating need a thorough investigation. This study examines MHD hybrid nanofluid heat transfer via a permeable wedge using joule heating, mass suction, viscous dissipation, variable viscosity, thermal radiation, variable thermal conductivity, and variable Prandtl number. We use similarity transformation to solve the ordinary differential equations that follow from the governing partial differential equations. We then check the results for correctness and dependability. To ensure the reliability and validity of the outcomes, source parameters are crucial to the validation process. The consequence of changing these parameters on the heat transmission properties of the MHD hybrid nanofluid is studied for both the scenario without and with thermal radiation by methodically analyzing the percentage increase or reduction. The validation process also includes a comparison of the computed values, such as the heat transfer rate and skin friction factor, with established theoretical predictions. This examination guarantees that the numerical solution, executed using the bvp4c technique in MATLAB, corresponds to the anticipated physical behavior of the system being studied. In addition, the findings exist using both graphical and tabular forms, which allows for a clear and succinct illustration of how different physical limitations affect flow characteristics. [ABSTRACT FROM AUTHOR]

This study looks into two-dimensional, incompressible magnetohydrodynamic flow of ternary hybrid nanofluid passing a stretched surface through a porous material taking into consideration activation energy, heat sink, chemical reaction parameter, and viscous dissipation. This study’s aim is to analyse the flow behaviour for temperature, concentration and velocity with entropy in the presence of titanium dioxide, aluminium oxide, and copper oxide nanoparticles. An effective similarity conversion procedure is used to transform partial differential equations to a nonlinear ordinary differential equations system. Employing proper boundary restrictions, the nonlinear equations are solved using the MATLAB bvp4c technique. A number of physical flow parameters including velocity, thermal and concentration profiles are investigated through tables and graphs in order to assess the flow behaviour. The main outcomes indicate that the velocity profile was decreased by the magnetic parameter and porosity parameter. Also, the Brinkmann number rises the entropy generation rate, while radiation and Brinkmann number decrease the Bejan number. The Sherwood number falls with larger activation energy and magnetic parameter, while it improves with increased Schmidt number, radiation parameter and chemical reaction parameter. [ABSTRACT FROM AUTHOR]

Bioconvection in nanofluids refers to the sensation where biological microorganisms, such as bacteria or algae, interact with nanoparticles suspended in a fluid, resulting in convective motion. This phenomenon has garnered interest due to its vital applications in diverse fields such as biotechnology, nanotechnology, and environmental engineering. This paper deals with the magneto-hydrodynamic (MHD) Reiner-Rivlin nanofluid flow by a stretchable porous sheet in the manifestation of the gyrotactic type of microorganisms. The Reiner-Rivlin nanofluid is considered to be incompressible and electrically conducting. Energy relation is developed by accounting the effects of dissipative forces, Joule heating, and radiative heat flux. Brownian dispersion and thermophoretic characteristics of solid tiny particles are accounted. Furthermore, chemical responses with modified Arrhenius kinetics are reflected in mass concentration relation. The acquired system of highly nonlinear partial differential equations (PDEs) is reduced into ordinary differential equations (ODEs) through appropriate transformations and then elucidated numerically via the shooting method (Runge–Kutta–Fehlberg). The study investigates the impact of various factors on fluid velocity, thermal field, heat and mass transfer rates, mass concentration, and microorganism motile density through graphs and tables. It is observed that Reiner-Rivlin fluid velocity decays versus Hartmann number and porosity constant, whereas the reverse scenario is observed for fluid material constant. Thermal field upsurges due to Hartmann and Eckert numbers. Moreover, the intensity of heat transfer escalates for higher Prandtl number and thermal radiation parameters. [ABSTRACT FROM AUTHOR]

Nanofluids have improved thermophysical properties compared to conventional fluids, which makes them promising successors in fluid technology. The use of nanofluids enables optimal thermal efficiency to be achieved by introducing a minimal concentration of nanoparticles that are stably suspended in conventional fluids. The use of nanofluids in technology and industry is steadily increasing due to their effective implementation. The improved thermophysical properties of nanofluids have a significant impact on their effectiveness in convection phenomena. The technology is not yet complete at this point; binary and ternary nanofluids are currently being used to improve the performance of conventional fluids. Therefore, this work aims to theoretically investigate the ternary nanofluid flow of a couple stress fluid in a vertical channel. A homogeneous suspension of alumina, cuprous oxide, and titania nanoparticles is formed by dispersing trihybridized nanoparticles in a base fluid (water). The effects of pressure gradient and viscous dissipation are also considered in the analysis. The classical ternary nanofluid model with couple stress was generalized using the fractal–fractional derivative (FFD) operator. The Crank–Nicolson technique helped to discretize the generalized model, which was then solved using computer tools. To investigate the properties of the fluid flow and the distribution of thermal energy in the fluid, numerical methods were used to calculate the solution, which was then plotted as a function of various physical factors. The graphical results show that at a volume fraction of 0.04 (corresponding to 4% of the base fluid), the heat transfer rate of the ternary nanofluid flow increases significantly compared to the binary and unary nanofluid flows. [ABSTRACT FROM AUTHOR]

In this analysis, we have considered heat transmission in two-dimensional steady laminar nanofluid flow past a wedge. Magnetohydrodynamic (MHD), Brownian motion, viscous dissipation and thermophoresis effects are considered over the porous surface. Similarity transformations have been used to change the governing partial differential equations (PDEs) into nonlinear higher-order ordinary differential equations (ODEs). Governing ODEs with boundary conditions are then converted to the system of first-order initial value problem. After that the modeled system is solved numerically by RK4 technique. Impact of the magnetic number, Eckert number, Prandtl number, Lewis number, Brownian motion, thermophoresis and permeability parameters on the flow domain is analyzed graphically as well as in tabular form. It is noted that magnitude of Nusselt number for the flow regime increases with the increase of nondimensional parameter P r , N b , N t while opposite behavior is observed in case of R. [ABSTRACT FROM AUTHOR]

Purpose: This investigation delves into the rationale behind the preferential applicability of the non-Newtonian nanofluid model over alternative frameworks, particularly those incorporating porous medium considerations. The study focuses on analyzing the mass and heat transfer characteristics inherent in the Williamson nanofluid's non-Newtonian flow over a stretched sheet, accounting for influences such as chemical reactions, viscous dissipation, magnetic field and slip velocity. Emphasis is placed on scenarios where the properties of the Williamson nanofluid, including thermal conductivity and viscosity, exhibit temperature-dependent variations. Design/methodology/approach: Following the use of the OHAM approach, an analytical resolution to the proposed issue is provided. The findings are elucidated through the construction of graphical representations, illustrating the impact of diverse physical parameters on temperature, velocity and concentration profiles. Findings: Remarkably, it is discerned that the magnetic field, viscous dissipation phenomena and slip velocity assumption significantly influence the heat and mass transmission processes. Numerical and theoretical outcomes exhibit a noteworthy level of qualitative concurrence, underscoring the robustness and reliability of the non-Newtonian nanofluid model in capturing the intricacies of the studied phenomena. Originality/value: Available studies show that no work on the Williamson model is conducted by considering viscous dissipation and the MHD effect past over an exponentially stretched porous sheet. This contribution fills this gap. [ABSTRACT FROM AUTHOR]