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As a means of influencing technological advancements in engineering applications and various fluid products, the generalized Fourier's and Fick's models have proven to be of great importance. Industries such as power station engineering, high thermal material processing, and bio-heat elements apply the concept of anomalous heat and mass transfer mechanism. The objective of this study is to stimulate the flow of a radiative magnetohydrodynamics Jeffery fluid over an expanding surface with anomalous heat and mass transfer dynamics subjected to nth order reaction and variable thermophysical properties. A set of similarity transformations is used to neutralize the governing equations into a nondimensionless form. To obtain the model parametric analysis, a numerical tool via the spectral local linearization method (SLLM) is deployed after transformation of the governing flow equation from a two-unknown partial differential equations to a one-variable ordinary differential equation. It is observed that the thermal boundary layer thickness is found to be enhanced with increasing parametric values of magnetic, Eckert and radiation parameters. For the radiation parameter R ∈ [ 0. 5 0 , 2. 5 0 ] , the skin drag force, Nusselt and Sherwood number increase by 0. 6 1 % , 4 8. 0 0 % and 0. 9 1 % , respectively. Additionally, a 2 0 0 % increment in the nth order parameter boosts the rate of heat transfer by 0. 7 8 %. while it downsizes the Sherwood number by 1 4. 3 2 %. [ABSTRACT FROM AUTHOR]

The objective of this research is to ascertain how 3D MHD heat transfer Casson fluid flow over a linearly porous stretched surface is affected by chemical reaction, radiation, and heat source/sink. The Roseland approximation is used to account for the radiation impact in the energy equation when examining the impacts of thermal radiation. Recently, there has been interest in heat transmission past a stretched sheet because of its numerous commercial applications and substantial impact on a variety of industrial processes. These consist of metal spinning, plastic sheet extrusion, condensation, heat exchangers, MHD generators, and power plants. The governing equations and related boundary conditions are reduced to a dimensionless form using similarity variables, and the Runge-Kutta-Fehlberg method is then used to solve the problem. An increase in the Casson fluid parameter, magnetic field parameter and Permeability parameter causes the velocity field to decrease in x and y directions and improve the temperature and concentration dispersion. Sherwood number and Skin friction coefficient over x and y direction are increasing function of Casson fluid parameter and Nusselt number is decreasing function while the reverse effect is seen in streatching sheet parameter. Nusselt number is increasing function of chemical reaction parameter, Schmidt number, Radiation parameter and heat heat source/sink parameters while the reverse effect is seen in Sherwood number. [ABSTRACT FROM AUTHOR]

Within fluid mechanics, the flow of hybrid nanofluids over a stretching surface has been extensively researched due to their influence on the flow and heat transfer properties. Expanding on this concept by introducing porous media, the current study explore the flow and heat and mass transport characteristics of hybrid nanofluid. This investigation includes the effect of magnetohydrodynamic (MHD) with chemical reaction, thermal radiation, and slip effects. The nanoparticles, copper, and alumina are combined with water for the formation of a hybrid nanofluid. Using the self-similar method for the reduction of Partial differential equations (PDEs) to the system of Ordinary differential equations (ODEs). These nonlinear equation systems are solved numerically using the bvp4c (boundary value solver) technique. The effect of the different physical non-dimensional flow parameters on different flow profiles such as velocity, temperature, concentration, skin friction, Nusselt and mass transfer rate are depicted through graphs and tables. The velocity profiles diminish with the effect of magnetic and slip parameters. The temperature and concentration slip parameters reduce the temperature and concentration profile respectively. The higher values of magnetic factor lessened the skin friction coefficient for both slip and no-slip conditions. An elevation in the thermal slip parameter reduced the boundary layer thickness and the heat transfer from the surface to the fluid. The Nusselt number amplified with the climbing values of the radiation parameter. The mass transfer rate depressed with the solutal slip parameter. Comparison is made with the published work in the literature and there is excellent agreement between them. [ABSTRACT FROM AUTHOR]

Abstract Within fluid mechanics, the flow of hybrid nanofluids over a stretching surface has been extensively researched due to their influence on the flow and heat transfer properties. Expanding on this concept by introducing porous media, the current study explore the flow and heat and mass transport characteristics of hybrid nanofluid. This investigation includes the effect of magnetohydrodynamic (MHD) with chemical reaction, thermal radiation, and slip effects. The nanoparticles, copper, and alumina are combined with water for the formation of a hybrid nanofluid. Using the self-similar method for the reduction of Partial differential equations (PDEs) to the system of Ordinary differential equations (ODEs). These nonlinear equation systems are solved numerically using the bvp4c (boundary value solver) technique. The effect of the different physical non-dimensional flow parameters on different flow profiles such as velocity, temperature, concentration, skin friction, Nusselt and mass transfer rate are depicted through graphs and tables. The velocity profiles diminish with the effect of magnetic and slip parameters. The temperature and concentration slip parameters reduce the temperature and concentration profile respectively. The higher values of magnetic factor lessened the skin friction coefficient for both slip and no-slip conditions. An elevation in the thermal slip parameter reduced the boundary layer thickness and the heat transfer from the surface to the fluid. The Nusselt number amplified with the climbing values of the radiation parameter. The mass transfer rate depressed with the solutal slip parameter. Comparison is made with the published work in the literature and there is excellent agreement between them.

Modern heat transport processes such as fuel cells, hybrid engines, microelectronics, refrigerators, heat exchangers, grinding, coolers, machining, and pharmaceutical operations may benefit from the unique properties of nanoliquids. By considering Al2O3{{\rm{Al}}}_{2}{{\rm{O}}}_{3} nanoparticles as a solo model and Al2O3–Cu{{\rm{Al}}}_{2}{{\rm{O}}}_{3}{\rm{\mbox{--}}}{\rm{Cu}} as hybrid nanocomposites in a hyperbolic tangent fluid, numerical simulations for heat and mass transfer have been established. To compare the thermal acts of the nanofluid and hybrid nanofluid, bvp4c computes the solution for the created mathematical equations with the help of MATLAB software. The impacts of thermal radiation, such as altering thermal conductivity and cross-diffusion, as well as flow and thermal facts, including a stretchy surface with hydromagnetic, and Joule heating, were also included. Furthermore, the hybrid nanofluid generates heat faster than a nanofluid. The temperature and concentration profiles increase with the Dufour and the Soret numbers, respectively. The upsurge permeability and Weissenberg parameter decline to the velocity. An upsurge variable of the thermal conductivity grows to the temperature profile. Compared to the nanofluids, the hybrid nanofluids have higher thermal efficiency, making them a more effective working fluid. The magnetic field strength significantly reduces the movement and has a striking effect on the width of the momentum boundary layer.

This study examines the effects of viscous dissipation, thermal radiation, nanofluid over a stretched surface, and viscous dissipation on a two-dimensional couple stress blood base for the enhancement of heat transfer rate. Gold and multiwall carbon nanotubes are two forms of nanoparticles that are taken into consideration, with blood serving as the base fluid. The NLPDE controls the considering problem. The NLPDE was converted to NODEs using the mentioned similarity transformation. The analytical method known as HAM was used to analyze the transform NODE analytically. Graphs are used to illustrate the effects of many parameters, such as magnetic factors, nanoparticle volume friction, velocity power index, PN, thermal radiation factors, and EN, which are derived from TE and VE. The current research work highlights how important it is to include viscous dissipation in nanofluid dynamics. The results show complex interactions among stretching, thermal properties, and micro-scale effects. The results may have an impact on the development and enhancement of biomedical devices and treatments that use nanofluidic systems, especially those that deal with blood. [ABSTRACT FROM AUTHOR]

The present study explores the nanofluid boundary layer flow over a stretching sheet with the combined influence of the double diffusive effects of thermophoresis and Brownian motion effects. For the purpose of transforming nonlinear partial differential equations into the linear united ordinary differential equation method, the similarity transformation technique is used. The Runge–Kutta–Fehlberg method was used to solve the equations of flow, along with sufficient boundary conditions. The effect on hydrodynamic, thermal and solutes boundary layers of a number of related parameters is investigated and the effects are graphically displayed. In conclusion, a strong agreement between the current numerical findings and the previous literature results is sought. [ABSTRACT FROM AUTHOR]

The 3-D Casson nanofluid flow over a nonlinear permeable stretching surface is examined in the present work. The generalized form of Fourier's heat flux and Fick's mass flux are incorporated with the additional impacts of the magnetic field, chemical reaction, thermal radiation, and convective conditions for heat transfer. Buongiorno's model is used for the analysis of Brownian motion and molecular diffusion. The flow mechanism has been formulated in the form of a nonlinear system of partial differential equations, which are converted to the nondimensional form of the system of ordinary differential equations, using the similarity substitution. The homotopy analysis method has been applied for the solution of a derived nondimensional set of differential equations. The consequences of flow constraints on the energy, mass, and velocity fields are presented. It has been noted that the mass and energy curves are the increasing functions of the Forchheimer number, porosity factor, Hartman number, and thermophoresis parameters. Furthermore, it is found that compared to passive control, active control of nanoparticles gives a higher rate of energy transmission. [ABSTRACT FROM AUTHOR]

Analytical effects of viscous dissipation on time-dependent Casson nanofluid (CN) on a stretching surface are the focus of the current research. We used the proper transformations to change a set of PDEs into NODEs. This scheme is the homotopy analysis method (HAM). Graphs are used to plan the effects of various parameters on energy and momentum profiles, such as the magnetic parameter, nanoparticles volume friction unsteady parameter, parandtl number thermophoresis parameter, and Eckert number. In order to simulate and assess the structures of flow features, such as temperature and velocity profiles, in response to changes in developing factors, a physical description is utilized. [ABSTRACT FROM AUTHOR]

This study examines the analytical study of magnetic hydrodynamic stagnation point flow with the impact variable viscosity on a movable surface along with the impact of thermal radiation. The problem is modeled with the help of momentum and energy conservation laws in the form of NLPDEs. The novelty of this study is the combined impact of variable viscosity and thermal radiation with the analytical method. Aluminum oxide nanoparticles and water are used as base fluids in this research work. The authors applied appropriate transformations to convert a collection of dimension forms of NLPDEs to dimensionless forms of NODEs. The transformed NODEs are solved with the help of an approximate analytical method known as the HAM. The effects of different parameters, including electric field, magnetic field, stagnation point flow, thermal radiation PN, and EN on energy and momentum profiles intended, and the results are planned with the help of graphs. [ABSTRACT FROM AUTHOR]

In this research work, we will carry out analytical investigation of MgO–CuO∖H2O, hybrid nanofluid magnetohydrodynamics (MHD) stagnation point flow with the influence of viscous dissipation for enhancement of heat transfer ratio. The flow system takes into account the impact viscous dissipation and transport dependence on the shape factor. Furthermore, velocity and temperature at the stretching surface are also considered in this study. To convert a collection of PDEs to nonlinear ODEs, we applied appropriate transformations. We utilize the Homotopy analysis method (HAM) to solve this set of equations. A physical description is used to simulate and evaluate the structures of flow features such as velocity, skin friction, Nusselt number and temperature profiles in response to changes in developing factors, the effects of different factors on temperature and velocities are shown in the form of graphs. It is hoped that this theoretical approach would contribute positively to improve the heat transformation ratio to satisfy the demands of the manufacturing and engineering sectors. [ABSTRACT FROM AUTHOR]

This article's objective is to examine the optimization of entropy in Darcy–Forchheimer cross-hybrid nanofluids as they flow toward a stretchy surface. There is a current because the surface is being stretched. The energy equation is broken down into its component parts including thermal radiation, heat source sink, and convective flow. In this case, copper oxide (CuO) and titanium dioxide (TiO 2 ) are taken into consideration as nanoparticles, while engine oil (EO) is taken into consideration as a continuous phase fluid. In addition, we carried out an investigation into the relative performance of copper oxide (CuO) and titanium dioxide (TiO 2 ) while they were suspended in water engine oil. The application of the second law of thermodynamics allows for the calculation of the rate of entropy optimization. Using a suitable transformation, nonlinear partial differential equations can be transformed into a standard system. In this work, we use the numerical built-in BVP4c solution method to generate numerical results for the derived nonlinear flow equation. Both copper oxide (CuO) and titanium dioxide (TiO 2 ) undergo a graphical analysis of the effects of varying technical factors on entropy optimization, velocity, the Bejan number, and temperature. Numerical computations of the skin friction coefficient and Nusselt number for a range of fascinating parameters are performed for both nanoparticles ( TiO 2 and CuO). It is clear from the data that entropy optimization improves as the size of the radiation and porosity estimates reduces. The porosity parameter exhibits direct relationships to both temperature and velocity. Tabular comparisons of the current study with the previously published literature show a high degree of agreement. Copper and titanium oxide nanoparticles are used to increase Engine oil ( EO ) thermal enactment, making it a more useful base fluid. Further, some significant industrial and engineering applications are related to the present problem discourse. [ABSTRACT FROM AUTHOR]

A thermal case study on a non-Newtonian fluid flow field resulting from a moving surface under the combined influence of solutal and thermal stratifications in convective flow regimes is presented in the current attempt. A perpendicular magnetic beam and a non-uniform heat source/sink are the physical manifestations of the temperature flow regime. The physical problem is interpreted mathematically in terms of a non-linear coupled differential system. The eventual flow differential equations in this direction are non-linear and, hence, difficult to obtain the exact solutions. Here, the exact solutions of the reduced ordinary differential equations are developed in the form of confluent hypergeometric function for Jeffrey fluid flow. The surface quantities, namely wall temperature and concentration gradients, are assessed for several significant physical domains. It is observed that the thermal profile of Jeffrey fluid is enriched by the contributions of the elasticity of the fluid, while temperature stratification contributes to diminishing the temperature distribution in the flow domain. Further, the mass transfer rate at the surface is enriched with solutal stratification and the Schmidt number.

Hybrid nanofluid problems are used for augmentation of thermal transportation in various industrial applications. Therefore, the present problem is studied for the heat and mass transportation features of hybrid nanofluid caused by extending surface along with porous media. In this investigation, the authors have emphasized to analyze hybrid nanofluid flow containing diamond and copper nanoparticles on an extending surface. Furthermore, the velocity, temperature, and concentration slip constraints are adopted to examine the flow of fluid. Heat source, chemical reactivity, thermal radiation, Brownian motion and effects are taken into consideration. Nonlinear modeled equations are converted into dimensionless through similarity variables. By adopting the homotopy analysis method, the resulting equations are simulated analytically. The impacts of various emerging factors on the flow profiles (i.e., velocities, temperature, concentration, skin frictions, local Nusselt number, and Sherwood number) are shown using Figures and Tables. The major key findings reveal that the hybrid nanofluid temperature is higher but the concentration is lower for a Brownian diffusivity parameter. Moreover, increment role of heat transport is achieved due to the increment in radiation factor, thermophoresis, Brownian motion factors, and Eckert number. It has also been observed that velocity in x-direction converges in the region −0.8≤ℏf≤0.5-0.8\le {\hslash }_{\text{f}}\le 0.5, in y-direction velocity is convergent in the zone −0.6≤ℏg≤0.35-0.6\le {\hslash }_{\text{g}}\le 0.35, while temperature converges in the region −0.6≤ℏθ≤0.4-0.6\le {\hslash }_{\text{θ}}\le 0.4 and concentration converges in the region −0.5≤ℏφ≤0.4-0.5\le {\hslash }_{\text{φ}}\le 0.4.

This article presented micropolar hybrid nanofluid flow comprising copper and alumina nanoparticles over a flat sheet. The mixed convection phenomenon is studied under the effect of gravity. Some additional forces such as magnetic field, thermal radiation, Eckert number, heat source, and thermal slip condition are adopted in this analysis. The leading equations are transformed into dimensionless format by employing appropriate variables and then evaluated by homotopy analysis method (HAM). The obtained results are compared with published results and found a good agreement with those published results. Also, the results of HAM are compared with those of numerical method and found a good agreement as well. The fluctuations within the flow profiles are showcased utilizing figures and tables, followed by an in-depth discussion and analysis. The outcomes of this work show that the higher volume fractions of copper and alumina nanoparticles improved the hybrid nanofluid viscosity, which results in the augmenting variation in the velocity profiles. The higher volume fractions of copper and alumina nanoparticles improved the hybrid nanofluid thermal conductivity, which results in the augmenting variation in thermal distribution. The growing mixed convection factor amplifies the buoyancy force toward the stagnation point flow, which enlarges the velocity panel. The effects of hybrid nanoparticles (Cu-Al2O3/water) at the surface are smaller on friction force and larger in case of thermal flow rate when compared to the nanofluids (Cu/water and Al2O3/water).

Background: The mechanics of heat and mass transfer via nanofluid flow across many media are currently being discussed. "Nanofluids" are fluids that include highly heat-conductive nanoparticles, and they are essential for resolving engineering problems. Under the effects of activation energy, thermal radiation, and motile microorganisms, the process of heat and mass transfer through steady nanofluid flow crosses over stretched surfaces in this scenario. Methodology: For mathematical evaluation, the system of partial differential equations (PDEs) is used to describe this physical framework. By introducing suitable similarity variables with a set of boundary conditions, this mathematical system of PDEs has become a system of ordinary differential equations (ODEs). To obtain numerical results, the MATLAB built-in program "bvp4c" is used to solve the system of first-order equations. Results: In the findings and discussion section, the resulting outcomes are thoroughly examined and visually shown. The flow rate in these systems increases due to the erratic movement of microorganisms. The graphical representation shows the impacts of involving physical factors on the microorganism, thermal, concentration, and momentum profiles. Variations/ changes in these profiles can be observed by adjusting the parametric values, as depicted in the graphs. Consequently, thermal transport is boosted by 25%. Additionally, the skin friction, Nusselt, Sherwood, and microbe density numbers are determined numerically. The findings demonstrate that increasing the magnetic field parameter causes the velocity profile to decrease, increasing the radiation parameter leads to an increase in temperature description, and increasing the Lewis number causes the microorganism profile's transport rate to decrease. [ABSTRACT FROM AUTHOR]

The current communication has as its goal the investigation of the flow properties of carbon nanotubes (CNTs) across a stretching surface, which has been accomplished. Furthermore, the effects of radiation, chemical reactions and activation energy are considered. With the use of boundary layer approximations, we can obtain flow expressions. The nondimensional form of flow equations is achieved by applying appropriate transformations. The bvp4c code from MATLAB is used to solve the model that has been obtained. The graphic representation of the relationship between pertinent variables and momentum, temperature field and concentration is used. It is observed that, for larger values of ϕ booms, the micro-rotation distribution. Furthermore, the solutal boundary layer thickness if thinner for thicker values of σ. [ABSTRACT FROM AUTHOR]

The aim of this research paper is to analytically investigate graphene oxide blood base nanofluid with the impact of dynamic viscosity and viscous dissipation. The increased thermal conductivity of nanofluids over regular fluids motivates this research. The basic flow equations are used to model the flow problem in nonlinear partial differential equations (NLPDEs). The dimensionless parameters, classical lie group, and thermo-physical properties are applied to transform the developed NLPDEs into dimensionless ordinary differential equations (ODEs). The resultant ODEs are resolved using the homotopy analysis method (HAM), and graphical and tabular interpretations are used to note the effects of contributing parameters including magnetic parameter, dynamic viscosity, nanoparticle volume friction, Eckert number, and Prandtl number on the velocity profile and temperature distribution. From the obtained results, we see that the velocity profile is decreasing by increasing magnetic parameter, dynamic viscosity, nanoparticle volume friction, and the temperature profile is increasing by increasing dynamic viscosity and Eckert number. The tabular descriptions of convergence of the presented fluid flow are also provided. [ABSTRACT FROM AUTHOR]

The two-dimensional boundary layer of steady mixed convective magnetohydrodynamic Carreau dusty fluid flow across a stretched sheet was investigated in this study. The primary focus of this study is to examine the impact of Carreau nanofluid on dusty flow dynamics in the presence of the Lorentz force. The partial differential equations governing the fluid flow, temperature, and concentration fields for both the fluid and dust phases are transformed into ordinary differential equations using an appropriate set of similarity transformations. Numerical outcomes are acquired employing the Runge–Kutta technique combined with the shooting method, implemented on the MATLAB platform. The numerical outcomes are compared to previous research and confirmed to be in very good accord. Finally, the impacts of relevant factors of physical and technical importance on flow and thermal transport characteristics are visually and tabulated. The results for the linear density and the quadratic density profile, it is noted that the linear density decreases compared to the quadratic density for velocity, but the opposite behavior is observed for temperature profile. The advancement of dusty nanofluids has resulted in significant enhancements in the heat transfer mechanism, which finds application in manufacturing, industry, and nanotechnology research. Research on dusty flows benefits on is beneficial in air pollution studies, dust entrainment in a cloud formed during a nuclear, vehicle emissions of smoke and other pollutants, crude oil purification, petroleum production, combustion, industrial effluent emissions, capillary blood flow, paint sparing, and, more.

The theory of thermal radiation and viscous heating are crucial in space engineering and high temperature activities. This inquiry analyzes the consequence of energy source/sink on steady Magnetohydrodynamic(MHD) flow of stretchable surface via porous channel taken into account the introduction of thermal radiation and viscous heating. The transformed nondimensionalized nonlinear governing model is numerically classified and resolved to derive solutions for the physical terms using shooting techniques along with 4th order Runge Kutta method. The flow behavior represented through the physical parameters are discussed via tables and graphs. Examined are the effects of skin friction as well as Sherwood and Nusselt numbers. It is revealed from the research that increase in micropolar term leads to higher velocity and temperature while microrotation falls. Also, increase in temperature is observed for every increase in porosity, Eckert, radiative and heat source terms. It is deduced from the investigation that the temperature can be enhanced as both radiative and viscous heating terms improves.

The magnetohydrodynamic (MHD) nanofluid flow at non-orthogonal stagnation point, with suspended carbon nanotubes in water on a stretched sheet in a permeable media with non-linear thermal radiation is studied. This work aims to explore the inclined magnetic field impacts on normal velocity, tangential velocity and temperature for both types of carbon nanotubes (CNTs). The governing flow equations which are continuity equation, momentum equation and energy equation are reformed into ordinary differential form with the proper boundary conditions using appropriate transformations. The computational solution of the nonlinear ODEs is obtained using the Bvp4c method. The graphs are presented to show the influence of certain physical factors which ranged as magnetic parameter (0.5 ≤ M ≤ 2.5), inclination angle of the magnetic field (п/2 ≤ ζ ≤ п/4), permeability parameter (0 ≤ Ω ≤ 2), volume fraction of nanoparticle (0.03 ≤ Φ ≤ 0.07), stretching ration parameter (0.3 ≤ γ2 ≤ 0.7), Radiation parameter (0.5 ≤ Nr ≤ 0.9), the heating parameter (0.5 ≤ θw ≤ 1.5) and Prandtl number (5 ≤ Pr ≤ 10). The normal and tangential velocity drops with the augmentation of (M), (ζ) and (Ω), while the temperature rise with enhance of (Nr) and (θw). This study's findings may be used to manage the heat transmission and fluid velocity rate to achieve the required final product quality in numerous manufacturing processes such as electronic cooling, solar heating, biomedical and nuclear system cooling. Validation against previous research available in the literature in specific situations shows excellent agreement. [ABSTRACT FROM AUTHOR]

This article focuses on the effects of Brownian motion and thermophoresis convection in the stagnation point flow of a Maxwell upper-convected fluid over a non-Darcian porous surface with slip conditions and a magnetic inclination effect. The Maxwell dissipative fluid accounts for Joule heating due to an imposed magnetic field and porous medium resistance. At the same time, the Cattaneo-Christov heat flux model represents thermal relaxation in contrast to the conventional Fourier law. The resulting nonlinear partial differential equations are transformed into ordinary differential equations (ODEs) using similarity variables. The analysis revealed the influence of dimensionless numbers, including Deborah, Eckert, Prandtl, chemical reaction, thermal relaxation, inclination and slip parameters. The findings were presented using graphs and tables. An increase in the thermophoresis parameter notably led to higher concentration and temperature profiles. In contrast, increasing Brownian motion (Nb) decreased the solutal boundary layer thickness but enhanced the thermal boundary layer. [ABSTRACT FROM AUTHOR]

AbstractThis research article delves into the crucial role that polymers play in controlling the boundary layer flow and heat transfer of non-Newtonian fluids past a stretching surface. To explore the various behaviors of non-Newtonian fluid flow, two classical viscosity models—Reiner–Philippoff and Powell–Eyring—are utilized. Taking into account the microstructure and concentration of polymers, a molecular approach is employed to describe the viscoelasticity effect. Through numerical similarity analysis, the impact of polymers on flow and heat transfer control of non-Newtonian fluids is examined in detail. The article also discusses the behavior of skin friction and the Nusselt number in the presence of polymers. It is observed that the viscosity of the fluid decreases in the vicinity of the surface as the polymers interact with velocity gradients in the boundary layer. However, as the distance from the surface increases, the viscosity returns to its original value. Moreover, the addition of polymers within the non-Newtonian fluid leads to a reduction in heat transport and an enhancement in skin drag. Overall, this study sheds light on the crucial role of polymers in optimizing heat transfer and controlling flow behavior in non-Newtonian fluids. [ABSTRACT FROM AUTHOR]

The current research wishes to scrutinize the heat and mass transmission features on magnetohydrodynamic stream of Williamson liquid owed to stretching surface with cross dispersion impacts. The stimulus of radiative heat, mutable heat sink/source, dissipation, Joule's heat and chemical reaction is taken. With the support of similarities the original PDEs are transmuted into ODEs and then obtain a numerical solution by the well-known numerical method R.K. with shooting procedure. The impact of dissimilar dimensionless constraints on the flow fields are conversed over displays and the same parameters on skin friction coefficient, local heat plus mass transport rates are deliberated through table. An improvement in thermal field is perceived for thermic heat constraint and Eckert number. On the other hand, it is witnessed that escalating the values of Dufour number augments the distribution of heat, while a contrary result is perceived in the distribution of concentration. [ABSTRACT FROM AUTHOR]

The present article describes the impact of variable thermal conductivity on the flow of ternary hybrid nanofluid with cylindrical shape nanoparticles over a stretching surface. Three nanoparticles combine in base fluid polymer. The assumption made will be used to model an equations. Modeled equations are in the form of a system of partial differential equations are difficult to solve can be converted to system of an ordinary differential equations, through resemblance substitutions, and will be solved numerically. Numerical scheme of Runge–Kutta order four is coupled with the shooting method to solve the resulting equations. The graphs in the study illustrate how physical quantities, such as magnetic field, injection/suction, nanoparticles volume fraction, and variable thermal conductivity, affected the velocity, skin friction, temperature, and local Nusselt number. The velocity profiles deflate as the volume fraction rises. While the temperature rises with an increase in the volume fraction of nanoparticles for both injection and suction, the velocity profiles also decline as the injection and suction parameter increases. Furthermore, as the magnetic field increases, the temperature profile rises while the velocity profile falls. The temperature curves increase as thermal conductivity increases. Finally, as the magnetic field is strengthened, the Nusselt number and skin friction decrease. The combination of mathematical modeling, numerical solution techniques, and the analysis of physical quantities contributes to the advancement of knowledge in this ternary hybrid nanofluid. [ABSTRACT FROM AUTHOR]

Abstract In this research, we explore the potential of magnetohydrodynamic (MHD) bioconvective nanofluids with varying viscosity through non-similarity analysis, aiming to enhance the thermal performance of biological and industrial systems. Recent years have witnessed significant advancements in energy applications, motivating our investigation. To enhance heat transfer, we employ propylene glycol as the base liquid, incorporating silicon dioxide and molybdenum disulfide nanomaterials. This unique configuration enables efficient heat dissipation and accommodates inner heat sources or sinks. Our model relies on partial differentials, and we derive a non-similar dimensionless representation of the governing system using appropriate transformations. We utilize ordinary differential equations (ODEs), approximating local non-similarity (LNS), to estimate transformed non-similar partial differential equations (PDEs). Numerical simulations are performed using the bvp4c algorithm. Throughout our analysis, we present various physical parameters, demonstrating their importance in fluid flow and thermal transport through graphical and tabular representations. Our findings show that alterations in the magnetic parameter lead to changes in fluid velocity and temperature profiles. Similarly, adjustments in the viscosity parameter affect fluid velocity, and variations in the temperature-dependent viscosity parameter influence velocity profiles, with temperature profiles responding to changes in the Brinkman number and heat source parameter. Additionally, we observe concentration profile adjustments with shifts in the Schmidt number and enhanced migration of particles or components within the nanofluid with rising Soret numbers, impacting the concentration profile. Furthermore, an increased Peclet number positively influences microorganism profiles, while the Lewis number exhibits contrasting behavior. To further validate our approach, we present comparative analyses of skin friction coefficients and Nusselt numbers in tabular form. Our primary objective in this study is to formulate non-similar transformations tailored to the specific problem under consideration. These transformations aim to produce accurate and efficient results, providing valuable insights for future research endeavors in the field of nanofluid flows. [ABSTRACT FROM AUTHOR]

Abstract The main attention of this research is to examine the nature of the flow behavior of nanofluids and energy transfers past an expanding sheet with second-grade fluid model. The system is also situated in an absorbent area, which affects the effects of heat and mass transport and chemical reaction. The numerical calculations and visualization for various flow parameters are performed using a finite difference code that is developed in the built-in bvp4c solver scheme of MATLAB. This involves adopting a set of new variables to change the character of the governing equations of this study. To the best of the authors’ knowledge, many authors have contributed to this field, but they do not take into account the above fluid model associated with the energy transfers with the influences of Brownian motion, thermophoresis effect, and chemical reaction parameters, etc., in their study. Major findings of this study is to achieve a higher amount of thermal transference using the physical parameters, such as magnetic, visco-elastic, thermophoresis, and Brownian motion parameters, etc. Also, using smaller values of the magnetic parameter can be an effective way to minimize the impact of drag force of the fluid at the surface. The considering fluid model has multifarious industrial applications, such as food and cosmetic industry and pharmaceutical and biomedical industry, etc., due to its versatile rheological characteristics. [ABSTRACT FROM AUTHOR]

Abstract Background Many investigations have been conducted by researchers across the globe to examine the behavior of fluids with respect to the influence of some constituent parameters and novel results have been obtained. However, the combined effect of thermal radiation and chemical reaction on micropolar nanofluid flow over an inclined stretching surface has not been well elucidated. This article, therefore, employed the mathematical model of Buongiorno for hydromagnetic micropolar nanofluids to study the effect of thermal radiation and chemical reaction on such fluids. The model examined the influence of thermophoresis, Brownian motion and the angle of inclination to the stretching surface on the fluid flow. The set of governing equations were transformed into ordinary differential equations using some similarity transformations and then numerically simplified through Chebyshev collocation method on MATHEMATICA software. Results The graphs thus derived were used to interpret the effect of some physical parameters on the fluid flow. It was observed among other results obtained, that thermal radiation, Brownian motion and thermophoresis enhanced the temperature profile of the flow while the inclination angle and chemical reaction declined the velocity and concentration, respectively. Conclusions These parameters tested on the various profiles proved observably effective on micropolar nanofluids and should be considered whenever improvement or decrease in the profiles are needed.

The fluid flow model is evaluated with the mass and energy transfer through the trihybrid nanofluid (Thnf) past a stretching permeable sheet. The proficiency of the nanofluid could be more effective, improved and stable by introducing nanoparticles with various thermal and rheological properties. The trihybrid nanoliquid has been prepared by the dispersion of silver (Ag), cobalt ferrite (CoFe2O4), and magnesium oxide (MgO) nanocomposites in water. The consequences of Darcy-Forchheimer are engaged in the momentum equation, to evaluate the permeability effect. The fluid flow is expressed in the form system of PDEs with effect of natural convection, magnetic field and heat source. Which are converted into a non-dimensional set of ODE by using similarity variables substitutions. Moreover, the numerical approach PCM (parametric continuation method) is used to deal the derived set of ODEs. The results are relatively compared to the existing study for accuracy purposes. It has been noted that the Thnf has higher thermal conductivity than ordinary and hybrid nanoliquid. The velocity field rises with the mounting values of the thermal Grashof number. The velocity curve drops with the effect of a power law, Forchheimer's, and porosity parameters.

In this study, a partial velocity slip of the boundary layer flow and an analysis of the MHD two-dimensional ternary hybrid nanofluid with fluid based on polymers with variable thermal conductivity are conducted. On a stretching sheet with a convective boundary condition, the investigation was conducted. Model equations with boundary conditions were transformed into a set of ODEs in order to study the flow. The resulting system of equations was solved by using the Runge-Kutta fourth-order method in conjunction with the shooting method. A numerical analysis was done to determine the impact of several key factors on the system's heat transfer characteristics and flow field velocity. Computed the flow field's velocity and heat transfer properties by varying these physical parameters, then graphically displayed the results. Additionally, tables covered the local shear stress and rate of heat transfer respectively, describe the flow's resistance to motion and the rate of local heat transfer of ternary hybrid nanofluid. For a thorough comparison, the results were compiled in tables. Additionally, the results were compared to data already available for regular fluids, and it was discovered that there was a very high degree of agreement between the two sets of results. This raises confidence in the precision of their numerical computations. New findings: The explicit formulas that have been derived make it simple to understand how changes in temperature-dependent thermal conductivity and nanoparticle volume fraction affect significant parameters, such as sk.fsdain friction and heat transfer rate, in the study of ternary hybrid nanofluids.

This study examines Marangoni convection in blood-based carbon nanotubes nanofluid's stagnation point flow over a time-dependent stretching surface. This study is inspired by the emerging importance of nanofluids in a variety of scientific and technical fields due to their unique and varied uses and effective thermal activities. Some examples of potential applications of these fluids include cancer treatment, magnetic refrigeration, drug delivery, and magnetic resonance imaging. Two types of nanoparticles are considered name is single wall carbon nanotube and multi wall carbon nanotube blood is takin as base fluid. Nonlinear partial differential equations are used to simulate the specified flow issue using momentum and energy conservation principles. Using a similarity transformation, the resultant is transformed into nonlinear with reduced dimensions. The relations for velocity profile and temperature distribution are calculated from the developed nonlinear ordinary differential equation by using an approximate analytical technique called the homotopy asymptotic method. Subsequently, these equations are implemented and executed within Mathematica software. The investigation focuses on significant outcomes such as momentum filed, energy filed, Skin friction coefficients, and Nusselt number. Graphs are used to interpret the effects of several factors, including the Marangoni parameter, nanoparticle volume friction, stretching parameter, slip parameter, and Prandtl number. The behavior of Nusselt's number and skin friction coefficient was also checked with the help of graphs and tables. The convergence of the solutions is checked with the help of auxiliary functions as well.

The magnetohydrodynamic (MHD) rotating flow that occurs across a stretching surface has numerous practical applications in a variety of domains. These fields include astronomy, engineering, the material sciences, and space exploration. The combined examination of magnetohydrodynamics rotating flow across a stretching surface, taking into consideration fluctuating viscosity and nanoparticle aggregation, has significant ramifications across several different domains. It is essential for both the growth of technology and the attainment of deeper insights into the complicated fluid dynamics to maintain research in this field. Given the aforementioned motivation, the principal aim of this study is to examine the effects of variable viscosity on the bidirectional rotating magnetohydrodynamic flow over a stretching surface. Aggregation effects on nanoparticles are used in the analysis. Titania (TiO2) is taken nanoparticle and ethylene glycol as base fluid. The nonlinear ordinary differential equations and the boundary conditions that correspond to them can be transformed into a dimensionless form by using a technique called similarity transformation. To get a numerical solution to the transformed equation, the Runge-Kutta 4th order (RK-4) method is utilized, and this is done in conjunction with the shooting method. The impact of various leading variables on dimensionless velocity, the coefficients of temperature, skin friction and local Nusselt number are graphically represented. Velocity profiles in both direction increases with increasing values of φ. The Nusselt number increases with increasing values of the radiation and temperature ratio parameters. When a 1 % volume fraction of nanoparticles is introduced, the Nusselt number exhibits a 0.174 % increase for the aggregation model compared to the regular fluid in the absence of radiation effects. When the aggregation model is used with a 1 % volume fraction of nanoparticles, the skin friction increases by 0.1153 % in the x direction and by 0.1165 % in the y direction compared to the regular fluid. Tables show the variation in Nusselt numbers, as well as a comparison of the effects of nanoparticle's aggregation model without and with radiation. Moreover, the numerical results obtained were compared with previously published data, demonstrating a satisfactory agreement. We firmly believe that this finding will have extensive implications for engineering and various industries.

In this study, the convective transport phenomena of Williamson nanofluid flow with variable thermal conductivity on Darcy–Forchheimer porous medium past unsteady stretching cylindrical sheet is presented. The conservation laws of mass, momentum, energy and concentration are used to formulate the governing boundary value problem of the flow regime. The flow is expressed with a couple of nonlinear partial differential equations. An appropriate similarity transformation and techniques are used to transform the couple of partial differential equations into a system of initial value problems. The system of initial value problems is then solved numerically using the Runge–Kutta fourth order with the shooting technique. The Python programming tool is used to carry out the computation. The influence of unsteady parameter, thermal and concentration Biot numbers, thermal conductivity parameter and other parameters on velocity, temperature and concentration profiles of the nanofluid are examined. The responses of the three transfer rates (i.e momentum, mass and heat) to many pertinent parameters are also investigated. Most flows in industries are in a controlled manner hence the cylindrical geometry is used to study the flow regime. The results of the study show that the convective mass transfer is initiated with a rise in thermal and concentration Biot numbers whereas the convective heat transfer is motivated and demotivated with a rise in thermal and concentration Biot numbers, respectively. Larger values of the unsteady parameter on the other hand creates substantial wall friction to the motion of the nanofluid. Further, the numerical method used is found in excellent agreement with some earlier works under common assumptions.

Background: Many investigations have been conducted by researchers across the globe to examine the behavior of fluids with respect to the influence of some constituent parameters and novel results have been obtained. However, the combined effect of thermal radiation and chemical reaction on micropolar nanofluid flow over an inclined stretching surface has not been well elucidated. This article, therefore, employed the mathematical model of Buongiorno for hydromagnetic micropolar nanofluids to study the effect of thermal radiation and chemical reaction on such fluids. The model examined the influence of thermophoresis, Brownian motion and the angle of inclination to the stretching surface on the fluid flow. The set of governing equations were transformed into ordinary differential equations using some similarity transformations and then numerically simplified through Chebyshev collocation method on MATHEMATICA software. Results: The graphs thus derived were used to interpret the effect of some physical parameters on the fluid flow. It was observed among other results obtained, that thermal radiation, Brownian motion and thermophoresis enhanced the temperature profile of the flow while the inclination angle and chemical reaction declined the velocity and concentration, respectively. Conclusions: These parameters tested on the various profiles proved observably effective on micropolar nanofluids and should be considered whenever improvement or decrease in the profiles are needed. [ABSTRACT FROM AUTHOR]

This study explores the unsteady hybrid nanofluid (NF) flow consisting of cobalt ferrite (CoFe2O4) and copper (Cu) nano particulates with natural convection flow due to an expanding surface implanted in a porous medium. The Cu and CoFe2O4 nanoparticles (NPs) are added to the base fluid water to synthesize the hybrid NF. The effects of second-order velocity slip condition, chemical reaction, heat absorption/generation, temperature-dependent viscosity, and Darcy Forchheimer are also assessed in the present analysis. An ordinary differential equation system is substituted for the modeled equations of the problem. Further computational processing of the differential equations is performed using the parametric continuation method. A validation and accuracy comparison are performed with the Matlab package BVP4C. Physical constraints are used for presenting and reviewing the outcomes. With the increase in second-order velocity slip condition and unsteady viscosity, the rates of heat and mass transition increase significantly with the variation in Cu and Fe2O4 NPs. The findings suggest that the uses of Cu and Fe2O4 in ordinary fluids might be useful in the aerodynamic extrusion of plastic sheets and extrusion of a polymer sheet from a dye.

The aim of this study is to provide numerical solutions to magnetohydrodynamic (MHD) cross flow with heat and mass transfer over a stretching sheet in a hybrid nanofluid with suction/injection and convective boundary conditions. This will be accomplished by presenting numeric solutions. Nanoparticles of graphene oxide and silver were suspended in kerosene oil as the base fluid taken into consideration is a nanofluid hybrid. After that, the physical flow problem is modeled as a set of partial differential equations, which are then transformed into an equivalent system of nonlinear ordinary differential equations (ODEs) by making use of the relevant similarity transformations. To gain different graphical and numerical results for analyzing the influence of numerous physical restrictions on velocity, heat, and mass profiles, the system of ODEs is solved using the computing power of the Lobatto IIIA technique. The plot of the velocity profile, temperature, concentration, entropy generation and Bejan number with separating magnitude like that power index number (0.1

Nanofluid has numerous industrial and engineering applications, especially for the improvement of heat transmission. Engine oil is a highly versatile lubricant that is extensively used across diverse industries and engineering fields for a wide range of applications. The applications of engine oil are the aerospace industry, automotive industry, marine industry, power generation, construction and mining, manufacturing and machinery, railroad and transportation, agriculture, etc. Therefore, in the existing problem, 3D flow of Maxwell nanoliquid along the stretched sheet through the porous medium with a melting heat transport mechanism is studied. Nanofluid is made by a mixture of graphene nanoparticles in the engine oil base liquid. Additionally, the physical significance of the Darcy-Forchheimer is discussed on the flow behavior. The computation for heat and mass transference is performed due to the applications of thermal radiation, heat source/sink, Brownian and thermophoresis diffusivity, and chemical reaction. Simulation of the existing model is made by using the idea of velocity slip conditions along with convective boundary and zero mass concentration conditions. In the flow analysis, the magnetic effect is applied normally to the surface, therefore, the features of the magnetic field are studied. On the basis of flow assumptions, the current flow problem is modeled in the system of highly nonlinear PDEs. Appropriate similarity transformation is exploited for the conversion of these PDEs into ODEs. By using the concepts of the Homotopic method (HAM), the attained coupled nonlinear higher-order ODEs are simulated. The graphs are used to discuss how numerous physical factors affect the flow profile, highlighting their distinctive characteristics. Several noteworthy findings of this study are that both primary and secondary velocities declined due to the Lorentz force by using the applications of magnetic impact. Also, it is distinguished that the nanoliquid thermal profile is amplified for the thermal Biot number. Also, the nanoliquid concentration is lesser for the greater Schmidt number. The present nanofluid problem is also investigated for its significant practical applications. Further, it is examined that the Nusselt number is greater for the thermal Biot number.

A thorough investigation of MHD third‐grade differential‐type fluid flow over a heated stretching sheet is performed in this work. In particular, we analyze the film thinning process, when the thermal sensitive fluid parameters vary due to the effect of heat supplied to the stretching sheet. Starting with a two‐dimensional (2D) free surface boundary value problem of non‐Newtonian third‐grade fluid, we present a systematic derivation of a 1D transient thin‐film height equation using longwave analysis with respect to the small aspect ratio of the fluid domain. The derived model is used to study the impact of Newtonian and non‐Newtonian parameters with variable fluid properties on the thin film height. The model is discretized using an upwind discretization in space and implicit time integration to guarantee first‐order convergence. The model is analyzed thoroughly with the help of numeric computing software MATLAB. The existing findings for a Newtonian fluid are in excellent agreement with derived evidence. In comparison to Newtonian fluid, the study finds that the third‐grade parameter causes thinning under different parametric restrictions. Simulations on the coupling effect explain that, the film thickness can be reduced with a high Marangoni number for highly viscous fluids. Also, since the effect of the conductivity parameter can be reduced at a low Prandtl number, the fluid shows a thinning effect. The film thinning rate, on the other hand, is reduced by the magnetic field. [ABSTRACT FROM AUTHOR]

The objective of this research is to examine the two-dimensional flow of a non-Newtonian water-based hybrid nanofluid containing silver and alumina nanoparticles over a stretching surface with convective conditions. The flow is considered to be steady, laminar and incompressible. The mathematical modeling of the flow analysis is considered in the form of partial differential equations which are then transformed into ordinary differential equations by mean of suitable similarity transformations. The present problem is solved with the help of semi-analytical technique called HAM. Convergence of HAM is shown with the help of Figure. The impacts of embedded parameters like magnetic parameter, Joule heating, activation energy and nonlinear thermal radiation on the flow profiles are displayed with the help of Figures and Tables. Our results showed that the greater magnetic parameter reduced the velocity profile, while a reverse impact magnetic parameter is found against temperature profile, skin frication and heat transfer rate of the hybrid nanofluid. Concentration profiles of the hybrid nanofluid flow are augmented with the increasing activation energy while reduced against chemical reaction parameter. Sherwood number has shown increasing behavior due to larger value of Schmidt number and decreasing on larger value of temperature relative parameter.

Continuous two-dimensional boundary layer heat transfer in an electroconductive Newtonian fluid from a stretching surface that is biased by a magnetic field aligned with thermal radiation is the subject of this study. The effects of magnetic induction are induced because the Reynolds number is not small. The sheet is traveling with a temperature and velocity that are inversely related to how far away from the steady edge it is from the plane in which it is traveling. We also imposed external velocity u = u e x = D x p in the boundary. The necessary major equations are made dimensionless by the local non-similarity transformation and become a system of non-linear ordinary differential equations after being transformed from non-linear partial differential equations. The subsequent numerical solution of the arisen non-dimensional boundary value problem utilizes a sixth-order Runge–Kutta integration scheme and Nachtsheim–Swigert shooting iterative technique. A good correlation is seen when the solutions are compared to previously published results from the literature. Through the use of graphical representation, the physical impacts of the fluid parameters on speed, induced magnetic field, and temperature distribution are carried out. Furthermore, the distributions for skin friction coefficient and local Nusselt number are also studied for different scenarios. The skin friction coefficient and local Nusselt number are observed to increase with greater values of the temperature exponent parameter and velocity exponent parameter. However, as heat radiation increases, the local Nusselt number decreases even though temperatures are noticeably higher. The study finds applications in magnetic polymer fabrication systems. [ABSTRACT FROM AUTHOR]

In this study, we investigate the flow of electrically conducting hybrid nanofluid (Ag+Cu/H2O), due to rotating disks, along with thermal slip, heat generation, and viscous dissipation. The nonlinear differential system is modelled and transformed into dimensionless partial differential equations using suitable dimensionless variables. To obtain solutions for the considered model, a finite difference toolkit is implemented, and numerical solutions are achieved. Graphical results are presented to display the influences of different dimensionless variables on flow velocity and temperature. This research contributes to a better understanding of hybrid nanofluid flows and can inform the design of cooling systems and other practical applications.

The transfer of heat is a phenomenon that is significant in a variety of contexts due to the different ways in which it may be utilized in industrial settings. To increase the rate at which heat is transferred, carbon nanotubes (CNTs), which can either be single-wall or multi-walled, are suspended in base fluids, and the resulting mixture is referred to as a “nanofluid. This study looks at how heat transfers through nanofluids that are suspended in carbon nanotubes with different lengths and radii over a stretching surface. It also looks at how changing viscosity and joule heating affect motion. Water is taken as base fluid. This study looks at both carbon nanotubes with one wall and those with more than one. The flow is governed by a series of partial differential equations, which, to control the flow, are transformed into a series of nonlinear ordinary differential equations. Similarity transformation is used to convert the obtained nonlinear ordinary differential equations and accompanying boundary conditions into a form that is dimensionless. To numerically solve the transformed equation, RK-4 with shooting method is used. Graphs and in-depth discussions are used to look at how velocity and temperature profiles are affected by the leading variables. The expression for skin friction and local Nusselt number are written down and graphs show how these two numbers change for different parameter values. The temperature profile goes down when the viscosity parameter goes down, but the velocity profile goes up. When the magnetic parameter goes up, the velocity profile f′(η), goes down, but the velocity profile g(η) and temperature θ(η) both go up at the same time. The rate of heat transfer increases with the addition of φ and S. When the suction parameter (S = 2.1) with 1% of φ is used, it is reported that rate of heat transfer increases by 1.135% for Single walled and 1.275% for Multi Walled carbon nanotubes. To determine whether or not the proposed numerical model is legitimate, a comparison is made between the current results and those that have previously been published.

The non-linear mixed convective heat and mass transfer features of a non-Newtonian Casson liquid flow over a stretching surface are investigated numerically. The stretching surface is embedded in a Darcian porous medium with heat generation/absorption impacts. The fluid flow is assumed to be driven by both buoyancy and Arrhenius kinetics. The governing equations are modelled with the help of Boussinesq and Rosseland approximations. The similarity solutions of the non-dimensional equations are obtained using two numerical approaches, namely fourth fifth Runge - Kutta Fehlberg method and the shooting approach. The velocity, temperature and concentration profiles are discussed for important physical parameters through various graphical illustrations. The skin friction, the non-dimensional wall temperature, and the concentration expressions were derived and analysed. The results indicate that the increasing values of linear and nonlinear convection due to temperature, nonlinear convection due to concentration, and heat of reaction increase the dimensionless wall temperature. The dimensionless wall concentration rises with the increasing values of heat of reaction, linear and nonlinear convection due to temperature, and nonlinear convection due to concentration parameters.

The influence of slip parameter, viscous dissipation, and Joule heating parameter on MHD boundary layer nanofluid flow over a permeable wedge-shaped surface was analysed. The PDEs and the associated boundary conditions were transformed to a set of non-similar ODEs and the obtained system of equations was solved numerically with the help of the spectral quasi-linearization method (SQLM) by applying suitable software. This method helps to identify the accuracy and convergence of the present problem. The current numerical results were compared with previously published work and are found to be similar. The fluid velocity, fluid temperature, and nanoparticle concentration within the boundary layer region for various values of the parameters such as the slip effect, magnetic strength, Prandtl number, Lewis number, stretching ratio, viscous dissipation, suction, Brownian motion, Joule heating, heat generation, and thermophoresis are studied. It is observed that the Brownian motion, Joule heating, viscous dissipation, and thermophoresis lead to decreases in the heat and mass transfer rate. The skin friction coefficient enhances with slip, magnetic, permeability, and suction parameters, but reduces with the Brownian motion, wedge angle, and stretching ratio parameters whereas there is no effect of mixed convection, thermophoresis, heat generation parameters, the Prandtl and Eckert number.

In the current study, we focused on the shape effects of copper (Cu) nano-particles on heat transmission of three-dimensional magnetohydrodynamic (MHD) nano-fluid. A particular type of flow is considered, i.e., rotating flow over an exponentially stretching sheet. Significant actions of thermal radiation and Grashof number are also formulated to study. The modified Chebyshev wavelets method is introduced to examine the numerical solutions of the accomplished model. Error analysis and further comparison with existing results reflect the appropriateness of the proposed modification. Graphical behavior of dimensionless velocities, temperature, Nusselt number, and skin friction under the inspiration of several parameters is also presented. The attained solutions propose that the modification is beneficial and can be protracted to other highly nonlinear problems. The modified Chebyshev wavelets technique lowers computing time, according to the study. The research takes into account the form impacts of nano-particles. There are three kinds of nano-particles to examine (spherical, laminar, and cylinder). The behavior of various particles varies depending on the flow and temperature profile. For microparticles with a laminar structure, velocity and temperature have higher values.

In this work, we analyzed the hybrid nanofluid (Ag+CuO+kerosene oil) flow past a bidirectionally extendable surface in the presence of a variable magnetic field. The hybrid nanofluid flow considered is electrically conductive and steady. For the simulation of the problem, the Cattaneo–Christov double-diffusion (CCDD) model was considered, which generalizes Fourier's and Fick's laws. The impact of the Hall current produced was taken into account. The physical problem was transformed into a mathematical form with the help of suitable transformations to reduce the complexity of the problem. The transformed system of coupled ordinary differential equations (ODEs) was solved with the semi-analytical method. The results are plotted in comparison with the ordinary nanofluid (CuO+kerosene oil) and hybrid nanofluid (Ag+CuO+kerosene oil). The impact of various parameters (P r , S c , γ 0 , m , M , N b , N t , ϵ 1 , ϵ 2) on the state variables is described. The velocity gradient under the impact of the mass flux and magnetic parameter shows a decreasing behavior, while the Hall parameter and the stretching ratio show an increasing behavior. Moreover, the skin friction, rate of heat, and mass transfer are numerically displayed through tables. In this work, we found that the thermal and concentration relaxation coefficients showed a decreasing behavior for their increasing trends. For the validation of the implemented technique, the squared residuals are computed in Table 2, which shows that the increasing number of iterations decreases the squared residual error. The results show that Ag+CuO+kerosene oil has good performance in the reduction of the heat transfer rate. [ABSTRACT FROM AUTHOR]