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The steady MHD boundary-layer axis-symmetric flow of a third-grade fluid passing through an exponentially expanded cylinder in the vicinity of a magnetic field is investigated in this study. The problem is mathematically modeled. Suitable similarity transformations are carried out to convert the partial differential equations into nonlinear ordinary differential equations. The Runge–Kutta fourth-order shooting technique is used to solve the transmuted system of nonlinear ODEs. Graphical representations of numerical findings are used to examine the effects of various physical factors on the velocity and temperature profiles. The influence of fluid variables on the velocity curve, such as third-grade parameters, second-grade parameters, and Reynolds number, is illustrated and explored. The skin-friction coefficient expression is computed and given. The widths of the velocity and momentum boundary layers are revealed to be increasing functions of the curvature parameter. It is found that the third-grade fluid has a higher velocity profile than Newtonian and second-grade fluids. Also, the stretched cylinders cause a more progressive shift in heat and mass pattern for flow than flat plates do. [ABSTRACT FROM AUTHOR]

Originality: A novel category of working fluids, consisting of two substantial components diffused in a conventional fluid, has been identified and investigated widely in recent years. These types of fluids are called hybrid nanofluids. Problem statement: A wide range of engineering and industrial structures, including heat-transferring components, energy production, extrusion procedures, engine cooling purposes, thermal structures, thermal exchangers, chemical procedures, manufacturing processes and hybrid power plants, have been proposed for use with nanomaterials with improved thermal properties. These nanomaterial-based applications hold the promise of improved performance and efficiency in a variety of technological and industrial processes. The heat transmission and magnetohydrodynamic stagnation significance flow of hybrid nanofluids Fe3O4–ZrO2 and Fe3O4/water, the form factor of a stretched cylinder under the influence of heat production, nonlinear thermal radiation and nanoparticle volume fractions have been investigated in this study. Methodology: Utilizing proper similarity transformations, the processes of partial differential equations are further transformed into nondimensional solutions of ordinary differential equations. The bvp4c approach is employed to achieve a numerical solution. The flow and temperature profiles are displayed as a function of the contained factors. Graphs show the effects of changing the physical characteristics involved. Tables emphasize the skin friction factor and Nusselt numbers. Results: The temperature profile of fluids diminished due to an increment in the values of the temperature relaxation parameter and Eckert number. When the porosity factor is increased the temperature of fluids is improved. The effects of streamlines for various components are discussed. The 3D surface, contour plots and residual plots for various factors have also been investigated. Applications: Hybrid nanofluids have the potential to improve heat transfer efficiency in a variety of technical applications, including cooling structures, heat exchangers and thermal energy storage systems. [ABSTRACT FROM AUTHOR]

In this paper, the self-propelled movement on gyrotactic swimming microorganisms into this generalized slip flow by nanoliquid over the stretching cylinder with strong magnetic field is discussed. Constant wall temperature was pretended as well as the Nield conditions of boundary. The intuitive non-Newtonian particulate suspension was included into applying Casson fluid by the base liquid and nanoparticles. This formation on the bio-mathematical model gives the boundary value problem by the nonlinear partial differential equations. Primly, modeled numerical system was converted to nondimensional against this help on acceptable scaling variables and the bvp4c technique was used to acquire the mathematical outcomes on the governing system. This graphical description by significant parameters and their physical performance was widely studied. The Prandtl number has the maximum contribution (112.595%) along the selected physical parameters, whereas the Brownian motion has the least (0.00165%) heat transfer rate. Anyhow, Casson fluid was established for much helpful suspension of this method on fabrication and coatings, etc. Therefore, this magnetic field performs like the resistive force of that fluid motion, and higher energy was enlarged into the structure exhibiting strong thermal radiation. [ABSTRACT FROM AUTHOR]

The heat transfer phenomena connected to the flow of a ternary hybrid nanofluid through an inclined stretched cylinder are examined in this work. With its distinct thermal and rheological characteristics, the ternary hybrid nanofluid comprising submerged silver, aluminium, and copper nanoparticles is a good option for solar water systems. Apart from this new fluid, the impact of magnetic field, solar thermal radiation, and heat sink source are considered, providing a thorough study with practical implications. The Darcy–Forchheimer notion serves as the foundation for the problem's mathematical formulation, which considers the cylinder's surrounding porous material. The very effective Homotopy Analysis Method ('HAM') is used to resolve the governing partial differential equations, offering an analytical way to look at flow and heat transport properties. The key findings of this study reveal intriguing insights into the interplay between magnetic field effects, solar thermal radiation, and heat sink source on the ternary hybrid nanofluid's flow and heat transmission behaviours. The percentage heat enhancement is also calculated for heat transfer for a ternary hybrid nanofluid. It can be noticed that the combined nanoparticles with base fluid as water under magnetic, Darcy, and curvature parameters bring a remarkable enhancement in the heat transfer due to their resistivity to the velocity profile. It is seen that ternary nanofluid has higher values for skin friction and heat transfer phenomena. Overall, this research contributes to understanding complex metaphysical phenomena and offers valuable insights for engineers and scientists working on utilising nanofluids in heat transfer and energy conversion applications. [ABSTRACT FROM AUTHOR]

This study delves into the exploration of hybrid nanofluids within the context of a stretching cylinder, a domain that has captivated numerous researchers owing to its pivotal applications in industrial manufacturing processes, particularly in metal forming and stretch dies. The authors, recognizing the significance of these applications, have introduced a novel heat transfer fluid termed hybrid nanofluid, comprising molybdenum disulfide and carbon nanotubes suspended in the base liquid, water. The investigation focuses on the flow of the hybrid nanofluid within a stretching cylinder, considering various influential factors such as Joule heating, thermal radiation, porous medium, and magnetic field effects. To model this complex problem, we employed modified Navier–Stokes equations. Employing similarity transformations, assumptions, and non-dimensional parameters, the problem was effectively simplified. The MATLAB bvp4c technique, a well-established numerical approach, was then employed to solve the resulting mathematical formulation. Graphical representations are presented to illustrate various aspects of the flow, facilitating a comprehensive understanding of the system. Comparisons are drawn among the flow characteristics of mono nanofluid, and the developed hybrid nanofluid. It is noted from the current analysis that the temperature strength increases with higher values of the magnetic field parameter, curvature parameter, radiation parameter, and Eckert number in both fluid cases. The Nusselt number increases with higher values of Prandtl number and thermal relaxation parameter. The identified patterns in velocity distribution, temperature strength, and fluid behavior provide a valuable foundation for optimizing thermal efficiency in diverse industrial applications. By leveraging the insights gained from this research, manufacturers can make informed decisions to enhance heat transfer processes, particularly in areas such as metal forming and stretch dies. [ABSTRACT FROM AUTHOR]

This article investigates the effects of the various silicon dioxide (Si O 2 ) nanoparticles immersed in water (H 2 O) base fluid on velocity and heat transport over an unsteady stretching cylinder under the influence of magnetohydrodynamics (MHD), velocity slip, and convective boundary conditions. The physical model is initially developed in the form of partial differential equations (PDEs) by using the conservation principle. Employing suitable transformations, the set of PDEs has been transformed into a system of Ordinary differential equations (ODEs). The nonlinear equations in the proposed model are optimally and dynamically assessed. To produce numerical solutions for nonlinear systems, MATLAB's BVP4C solver technique is used. Furthermore, the numerical technique is validated by calculating residual error. The recent investigation's novel results include: the nanoparticles SiO 2 of play an important role in enhancing the thermal conductivity of the traditional base fluid H 2 O. The shape of the nanoparticles also plays a remarkable role in heat transfer enhancement. Increases in viscus dissipation, convective boundary conditions, and MHD parameters play a remarkable role in increasing the temperature of the nanofluid. Furthermore, platelet-shaped Si O 2 nanoparticles are reported to have the highest flow rate, highest temperature, and highest value of Nusselt numbers. [ABSTRACT FROM AUTHOR]

Current artifact aims to investigate attributes of nanofluidic transport mechanism developed for dynamics of Williamson liquid over an extendable cylinder with novel physical aspects of magnetic field. Additionally, Newtonian heating is accounted at cylinder surface and Reynold viscosity model is implemented to delineate the aspects of temperature dependent viscosity. Thermophoresis, Brownian motion, and variable viscosity effects have been studied for heat and mass transfer analysis. Formulation of problems characterized by governing physical laws is conceded in the form of dimensional partial differential setup by executing boundary layer approach. Conversion of attained differential system into ODE's is engrossed by capitalizing similarity transformations. Numerical procedures (Runge-Kutta and shooting) are implemented to resolve the problem and to attain solution. Effectiveness of sundry variables on associated distributions is revealed through graphical and tabular manner. Quantities of interest are also manipulated against the involved variables. Comparison of results to certify the numerical code is checked by making assessment with existing studies and found remarkable agreement. [ABSTRACT FROM AUTHOR]

Current artifact aims to investigate attributes of nanofluidic transport mechanism developed for dynamics of Williamson liquid over an extendable cylinder with novel physical aspects of magnetic field. Additionally, Newtonian heating is accounted at cylinder surface and Reynold viscosity model is implemented to delineate the aspects of temperature dependent viscosity. Thermophoresis, Brownian motion, and variable viscosity effects have been studied for heat and mass transfer analysis. Formulation of problems characterized by governing physical laws is conceded in the form of dimensional partial differential setup by executing boundary layer approach. Conversion of attained differential system into ODE’s is engrossed by capitalizing similarity transformations. Numerical procedures (Runge-Kutta and shooting) are implemented to resolve the problem and to attain solution. Effectiveness of sundry variables on associated distributions is revealed through graphical and tabular manner. Quantities of interest are also manipulated against the involved variables. Comparison of results to certify the numerical code is checked by making assessment with existing studies and found remarkable agreement.

The principal intention of the currently analysis is to investigate the impacts of the naturally convective nanofluid using a model of Carreau fluid with engine oil (CnH2n+2)as the base fluid and Manganese Zinc Ferrite (MnZnFe2O4)as the nanoparticle, the fluid flowing through a stretched cylinder in a fuzzy ambient. It examines the impact of assorted parameters, Weissenberg number(We), Prandtl numeral(Pr), Schmidt numeral (Sc), and curvature (k)with magnetic field(B) and nanoparticle parameter, in order to manipulate an analogous conversion, the regulating equations of velocity, energy, and concentration profiles permute from a set of partial differential equations stand to ordinary differential equations. The present analysis focuses on the no slip assumption, which gives rise to a nonlinear Dirichlet boundary condition in axial velocity. The bvp5c approach was utilized to solve the resulting series of equations by the MATLAB. This is a highly effective approach with minimal computing expenditure. The volume quantity of nanoparticles in MnZnFe2O4 is considered an uncertain parameter respect to TFNs (triangular fuzzy numbers) ranging [0, 0.5, 0.1]. Triangular membership function (TMF) is used to study the uncertainty variability while α − cut controls the TFNs. Fuzzy linear regression analysis makes use of TFNs to determine the middle (crisp), left, and right values of the fuzzy velocity profile. In comparison to the crisp velocity profile (mid value), the study's result and the fuzzy velocity profile have the maximum rate of flow. Tables and graphs are used to illustrate the outputs.

The process of convective thermal management in the radiative flow of Oldroyd-B fluid over the stretching cylinder is investigated in this paper. In engineering and applied sciences, the viewpoint of fluid flow due to vertically stretched cylinder covers both theoretical and practical significances. Nonlinear ordinary differential equations are first transformed from their corresponding partial differential equations, then rebuilt using sufficient transformations to produce a system of nondimensional equations, using a proper similarity technique, which is then calculated. The MATLAB built-in technique BVP4C, a standard numerical process, is used to solve the regulating flow equations. A comprehensive graphical depiction was used for characteristics like unsteadiness and curvature, Prandtl number, and thermal diffusivity. The relevant flow characteristics of the governing problem are depicted in graphs. [ABSTRACT FROM AUTHOR]

The principal intention of the currently analysis is to investigate the impacts of the naturally convective nanofluid using a model of Carreau fluid with engine oil (C n H 2 n + 2) as the base fluid and Manganese Zinc Ferrite (M n Z n Fe 2 O 4) as the nanoparticle, the fluid flowing through a stretched cylinder in a fuzzy ambient. It examines the impact of assorted parameters, Weissenberg number (We) , Prandtl numeral (Pr) , Schmidt numeral (Sc) , and curvature (k) with magnetic field (B) and nanoparticle parameter, in order to manipulate an analogous conversion, the regulating equations of velocity, energy, and concentration profiles permute from a set of partial differential equations stand to ordinary differential equations. The present analysis focuses on the no slip assumption, which gives rise to a nonlinear Dirichlet boundary condition in axial velocity. The bvp5c approach was utilized to solve the resulting series of equations by the MATLAB. This is a highly effective approach with minimal computing expenditure. The volume quantity of nanoparticles in M n Z n Fe 2 O 4 is considered an uncertain parameter respect to TFNs (triangular fuzzy numbers) ranging [0, 0.5, 0.1]. Triangular membership function (TMF) is used to study the uncertainty variability while α − cut controls the TFNs. Fuzzy linear regression analysis makes use of TFNs to determine the middle (crisp), left, and right values of the fuzzy velocity profile. In comparison to the crisp velocity profile (mid value), the study's result and the fuzzy velocity profile have the maximum rate of flow. Tables and graphs are used to illustrate the outputs. [ABSTRACT FROM AUTHOR]

This paper investigates the stagnation point flow of a second-grade nanomaterial, considering nanofluid effects via thermophoresis and Brownian motion. The study addresses convective heat and mass transfer conditions within the flow induced by a stretching cylinder. The transformed systems are solved using the optimal homotopy solutions (OHAM) method, revealing the impact of various parameters on the quantities of interest. The results indicate that an increase in curvature, viscoelasticity, velocity ratio and injection parameters leads to an enhancement in velocity, while the opposite trend is observed due to suction. The viscoelasticity and curvature parameters also increase skin friction. Additionally, thermophoresis enhances the temperature and concentration fields, while Brownian motion reduces mass diffusion. [ABSTRACT FROM AUTHOR]

AbstractA nonlinear mixed convective sutterby nanofluid flow along a stretching cylinder is being studied in this article. The set of partial differential equations (PDEs) that control fluid flow is nonlinear and subject to surface constraints and similarity transformation reduces a system of PDEs to non-dimensional ordinary differential equations (ODEs), which are then solved in MATLAB Bvp5c solver which is based on the Runge–Kutta method and Shooting technique. We provide a graphic evaluation of the significant contributions made by the various physical terms to engineering measurements in the curiosity and transport domains. The study discovers that temperature distribution increases heat border viscosity but reduces thermal diffusion, whereas nonlinear convection heat improves surface heat transfer. The periodic magnetic field raises the fluid temperature while decreasing the rate of energy transfer. Furthermore, experiments have demonstrated that oscillating magnetic fields induce fluctuations with a sinusoidal pattern. Furthermore, the current study has applications in the design and manufacture of cylinder-shaped objects in various fields such as aerospace engineering, geophysics, and nuclear engineering. These include core catchers in nuclear power plant steam turbines, waxy crude oils or foodstuffs in centrifugal pumps, and deformation rates that frequently occur in practical turbomachinery and other industrial processes. [ABSTRACT FROM AUTHOR]

This work investigates a non-Newtonian MHD Carreau nanofluid over a stretched vertical cylinder of an incompressible boundary layer with mobile microorganisms. The flow exists in permeable media and follows the modified Darcy's law. An unchanged normal magnetic strength to the walls saturates the system. Ohmic dissipation, heat source, modified chemical reaction with activation energy properties, heat, volumetric nanoparticles fraction as well as microorganism profiles are covered. Thermal conductivity and mass diffusivity are taken as functions of heat and nanoparticle concentration, correspondingly. The fundamental governing system of nonlinear partial differential equations (PDEs) is converted into nonlinear ordinary differential equations (ODEs) by employing appropriate similarity transforms. The latter system is numerically analyzed through fourth-order Runge–Kutta (RK-4) simultaneously with the shooting process. The numerical outcomes showed that the curvature coefficient, magnetism and chemically activated energy perform a significant role in the velocity, heat, nanoparticle and chemical organism distributions. The impacts of several physical restrictions are tested and portrayed in a group of graphs. It is observed that the presence of microbes and nanoparticles, which are described in buoyancy terms, causes the flow to decay and slow down. By lowering the buoyancy and bio-convection characteristics, this infection can be prevented. With the development of all heat-related elements, heat transfer is enhanced, which is a significant feature associated with the current flow. These insights are important and useful in various physical and engineering fields. [ABSTRACT FROM AUTHOR]

This study offers the impacts of MHD Jeffery fluid research on a stretching cylinder. The Cattaneo–Christov heat model is acquired instead of the Fourier law of heat conduction to construct the energy equation. The order analysis of a fluid model is performed using the boundary layer theory. On differential equations, appropriate similarity transformations are used to attain the differential equations. The following nonlinear equations were then mathematically solved utilising the shooting method. The visual inspection of the conclusions of the velocity, thermal and concentration profiles is completed for several important thermophysical parameters. For numerous thermos physical variables, the numerical variation in the valuations of the mass transport rate, coefficient of skin friction and heat rate transfer has been assessed and provided in a table. The main conclusions of the study show that temperature, concentration distribution and flow speed all decrease as the curvature parameter increases. It has also been deduced in this investigation that the higher values of the Lewis number higher the mass transfer rate and lower the heat flux at the surface of the cylinder. These results exhibit a more favourable agreement across all findings when compared to previous findings. [ABSTRACT FROM AUTHOR]

This study explores the complex dynamics of magnetohydrodynamic (MHD) flow within a porous medium while considering the impact of thermal radiation. The primary focus of the investigation centers on a cylinder that is vertically elongating, serving as a means to characterize the behavior of a viscous, incompressible fluid. Notably, the analysis introduces an added layer of intricacy by incorporating both second-order momentum slip and first-order thermal slip boundary conditions. By applying well-suited similarity variables, the governing equations encompassing continuity, momentum, and energy are transformed into a set of non-linear ordinary differential equations. The method employed to effectively handle these equations is the finite element method, known for its robustness in numerical approaches. This approach facilitates the exploration of detailed insights into the distribution of velocity and temperature, consequently revealing nuanced patterns and prevailing trends. A thorough examination of diverse physical parameters offers a comprehensive understanding of their respective influences, thus providing a holistic perspective on their roles within the system. The research goes on to present explicit formulations for critical parameters, including the skin-friction coefficient, Nusselt number, fluid velocity, and temperature surrounding the cylinder. These formulations are visually elucidated through informative graphical depictions. Beyond its theoretical contributions, this research carries tangible practical significance across domains such as thermal engineering, fluid dynamics, and energy systems. Its insights have the potential to impact the optimization and design of real-world processes and systems, underscoring its relevance to technological advancements in these fields. [ABSTRACT FROM AUTHOR]

In this proceeding the main focus to scrutinize the heat and mass transfer rate increment due to the involvement of motile microorganisms in the Carreau nanofluid flow through an inclined stretchable cylinder under the consequences of activation energy and thermal radiation. This phenomenon has many physical applications in the field of civil, mechanical and seismographic engineering. The research focuses on creating and analyzing new nanocomposites with applications in energy storage, showcasing the transformative impact of nanotechnology on the advancement of high-performance materials. First of all, for the numerical treatment of the above physical model mathematical model is developed in the form of partial differential equations (PDE's) by considering all involving quantities. The resultant model is highly nonlinear and of higher order. Appropriate similarity variables are defined to transform this system of PDE's into first order ordinary differential equations (ODE's). For numerical results we develop a numerical algorithm from nonlinear ODE's and use ‘bvp4c’ built in package of MATLAB. Numerical results are acquired from software in the form of graphical visuals and tabular data as narrated in the results and discussion section. Using this tabular data streamlines are constructed for the better understanding of heat and mass transfer through this phenomenon under the defined constraints. From results, velocity profile increased by the augmentation of values of curvature parameter. Thermal profile is stronger when values of thermophoresis parameter is boosted, Concentration of nanoparticle profile get smoother when temperature coefficient increased, and motile microorganism's density profile is enlarged upon inclining the values of bioconvection lewis number.

This paper studies the Carreau nanofluid employed by modified Buongiorno's model to theoretically analyze a homogeneous-heterogeneous process-influenced numerical solution of a Carreau nanofluid flowing through a stretched cylinder. In steady of Carreau nanofluid model proposed by Buongiorno's flow across a linearly extending cylinder influenced by homogeneous/heterogeneous responses are examined and express the changes of moment, energy, and concentration in both graphical and numerical. The following impact factors are consequences of the result, the stretching limiting factor, the curvature limiting factor and other limiting factors. The effects of both convection and heat generation are seen in flow field analysis. In comparison to ambient fluid, the stipulated exterior temperature and concentration are hypothetically increased. For the regulating equations of velocity, energy, and concentration profiles are permuting from a set of partial differential equations stand to ordinary differential equations manipulating an equivalent conversion. The resulting sequence of equations was solved at the boundary value problem in the fifth-order method. The velocity, temperature, concentration, skin friction coefficient, local Nusselt number, and local Sherwood number fields are studied, and then the outputs are illustrated in graphs and tables.

The melting phenomenon plays a critical role in optimizing the performance of power storage, electronic cooling, and semiconductor devices. The present study aims to analyze the melting effect on the flow of Carreau fluid over a stretchable cylinder, with special consideration given to the impact of quadratic thermal radiation. Similarity variables and the homotopy analysis method are used to simplify and determine the semi-analytical homotopic solutions of the governing equations. The present findings reveal that the melting parameter increases the heat transfer rate by more than 10% for both fluids, water (Pr = 0.71), and polymer (Pr = 10). However, as the temperature ratio due to quadratic radiation increases, the local Nusselt number for water has been reduced by 25%, and an even more substantial reduction is observed for the polymer. The present study offers valuable insights into achieving optimal efficiency in electronic devices.

The main aim of this paper is to provide numerical simulation for viscous nanofluid by stretching cylinder using Buongiorno's model. Dissipation, Joule heating and magnetic impact with irreversibility analysis are examined. Furthermore, Brownian movement and thermophoresis diffusion effects are studied. Through constitutive relations, nonlinear equations are obtained. By adopting suitable variables, the partial differential equations are changed to ordinary differential equations. Entropy rate is calculated using thermodynamics second law. ND-solve technique in Mathematica is employed to tackle dimensionless ordinary differential equations. The behavior of flow controlling parameters is examined graphically. Physical quantities are discussed through tables. A decrement in velocity is seen through magnetic effect, while opposite impact is seen for entropy rate. A similar scenario is seen for thermal field through random and thermophoresis variables. Reduction in concentration is seen for reaction parameter and Schmidt number. Important findings are presented. [ABSTRACT FROM AUTHOR]

The flow and heat transfer of a steady, viscous biomagnetic fluid containing magnetic particles caused by the swirling and stretching motion of a three-dimensional cylinder has been investigated numerically in this study. Because fluid and particle rotation are different, a magnetic field is applied in both radial and tangential directions to counteract the effects of rotational viscosity in the flow domain. Partial differential equations are used to represent the governing three-dimensional modeled equations. With the aid of customary similarity transformations, this system of partial differential equations is transformed into a set of ordinary differential equations. They are then numerically resolved utilizing a common finite differences technique that includes iterative processing and the manipulation of tridiagonal matrices. Graphs are used to depict the physical effects of imperative parameters on the swirling velocity, temperature distributions, skin friction coefficient, and the rate of heat transfer. For higher values of the ferromagnetic interaction parameter, it is discovered that the axial velocity increases, whereas temperature and tangential velocity drop. With rising levels of the ferromagnetic interaction parameter, the size of the axial skin friction coefficient and the rate of heat transfer are both accelerated. In some limited circumstances, a comparison with previously published work is also handled and found to be acceptably accurate. [ABSTRACT FROM AUTHOR]

AbstractA mathematical framework is conceived to analyze the flow of Darcy–Forchheimer Casson nanofluid around a vertically stretchable cylinder, taking into account the convective boundary conditions. The heat and mass transport phenomena are visualized in the existence of activation energy and gyrotactic microorganisms with buoyancy effects. Additionally, an external magnetic field is applied to the flow problem. This particular model finds applications in biomedical engineering, the oil and gas industry, heat exchangers and thermal systems, environmental engineering, and renewable energy. By employing suitable transformations to transform partial differential equations into ordinary ones, the MATLAB function bvp4c package is utilized to numerically solve the equations. The findings presented through graphs illustrate the influence of various parameters on velocity, heat and mass transfer, and the density of gyrotactic microorganisms. The analysis revealed that fluid momentum decreases with increasing porosity numbers, while higher activation energy values enhance concentration. Moreover, an increase in the Peclet number reduces the microorganism’s distribution. Tables compute the motile microorganism’s density, Nusselt number, and Sherwood number. A substantial rise in activation energy prominently increases concentration, accompanied by a decrease in the Sherwood number. The density of microorganisms rises with higher values of the curvature parameter, Prandtl number, and Brownian motion parameter, but decreases with an increasing Hartman number. Noteworthy concordance is noted when juxtaposing the findings of this investigation with those of earlier scholarly research. [ABSTRACT FROM AUTHOR]

The current study theoretically analyzes the magnetohydrodynamic Williamson fluid flow along with convective boundary conditions over a stretching cylinder. The modified Fourier's and modified Fick's law is considered in view of the response of heat and mass transfer. The effect of heat generation/absorption is also considered. With the suitable similarity transformations, the flow equations are converted into dimensionless ordinary differential equations. Runge–Kutta method is used to solve the current problem numerically by adopting shooting scheme. Influences of various physical parameters on the flow fields are shown graphically and skin friction parameter, local Nusselt and Sherwood numbers are presented in tabular form. To verify the accuracy of our numerical results in light of previous results, a comparison table has been generated. The results revealed that the velocity of fluid increases by increasing curvature parameter while decreases for magnetic parameter and Williamson fluid parameter. The temperature and concentration profiles rises due to increase in heat and mass Biot number parameters. [ABSTRACT FROM AUTHOR]

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

The thermal behavior of an electrically non-conducting magnetic liquid flowing over a stretching cylinder under the influence of a magnetic dipole is considered. The governing nonlinear differential equations are solved numerically using a finite element approach, which is properly validated through comparison with earlier results available in the literature. The results for the velocity and temperature fields are provided for different values of the Reynolds number, ferromagnetic response number, Prandtl number, and viscous dissipation parameter. The influence of some physical parameters on skin friction and heat transfer on the walls of the cylinder is also investigated. The applicability of this research to heat control in electronic devices is discussed to a certain extent. [ABSTRACT FROM AUTHOR]

Quadratic thermal radiation is a fundamental term within the field of radiative heat transfer, which pertains to the interaction of thermal radiation. It encompasses a quadratic correlation between temperature and radiative qualities. Although linear thermal radiation is more prevalent in numerous everyday applications, non-linear thermal radiation is important in some situations, particularly where a more precise representation of the radiative transfer of heat is required. The phenomenon assumes a crucial function in some contexts that need enhanced accuracy in modeling radiative heat transfer. In view of this, the present investigation is carried out to examine the hybrid nanofluid flow across a cylinder under the influence of quadratic, nonlinear and linear thermal radiation and activation energy. The governing system of nonlinear differential equations is transformed into a system of ordinary differential equations via similarity transformations. The current study presents the results utilizing the shooting and Runge-Kutta Fehlberg 45 numerical scheme. The outcomes show that the curvature constraint will improve all three profiles while solid fraction decreases velocity and raises the other two profiles. Quadratic thermal radiation shows less temperature distribution, followed by linear and non-linear thermal radiation cases. The rate of thermal distribution improves 0.60 % for linear thermal radiation case, 0.52 % for nonlinear thermal radiation case and 0.656 % for quadratic thermal radiation case from hybrid nanofluid to nanofluid. Further, the rate of mass transfer shows 0.068 % improvement for from hybrid nanofluid to nanofluid. The results provide useful insights that may be used to enhance system efficiency across various applications, including but not limited to the mechanics of fluids, chemical technology, and thermal administration.

AbstractBased on peak thermal performances of nanofluid, different mathematical models are developed. In current analysis, the investigation for heat and mass transfer phenomenon associated to the magnetized nanofluid is examined. The analysis for heat transfer is addressed with applications of radiative phenomenon. The multiple slip effects are entertained for governing problem. The cause of induced flow is stretched cylinder. Mathematical model is solved shooting scheme. The validation for predicted results is presented to justify the solution. The analysis is observed for specific range of parameters like 0≤M≤1.5,0≤γ≤0.6,0≤S≤0.3,0≤R≤0.5,0≤Nt≤0.4,0.5≤A≤2, and 0.2≤B≤0.8. The significance of thermally entertained nanofluid problem is physically inspected. It is evaluated that heat and mass transfer enhances due to curvature parameter. Low concentration field is examined for solutal stratification parameter. The obtained results present applications in enhancing thermal efficiency of solar systems, energy applications, heat transfer devices, chemical processes, cooling phenomenon, etc. [ABSTRACT FROM AUTHOR]

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

This study aims to investigate the impact of suction/injection on a quadratic mixed convection magnetohydrodynamics Carreau fluid over a stretching cylinder. The effects of heat generation, Joule heating, convective boundary conditions, and variable thermal conductivity in the fluid region are considered. The developed partial governing equations are transformed into ordinary differential equations using the similarity transformation technique and then solved using the homotopy analysis method to determine the analytic approximation solutions. Due to the numerous pertinent parameters, the variations of the heat and mass distribution, as well as the physical quantities, such as the local skin friction and the Sherwood and Nusselt number, are analyzed through graphs and tables. Quadratic convection has enhanced the movement of the fluid, heat transport, and mass transfer in a situation without inflow either at the surface of the cylinder or flat plate. The mass transition phenomenon has reduced the impact of quadratic convection. Furthermore, in the suction situation, the concentration and velocity of the fluid field are increased but an opposite tendency in the temperature distribution is observed. The present analysis is essential in controlling the quality of wire coating, pipe coating, or heat exchangers, which depends on the fluid characteristics, as well as its concentration and thermal diffusion. [ABSTRACT FROM AUTHOR]

This work presents a novel approach to active and passive control of fluid flow on a stretching cylinder, considering the collective effects of electromagnetism, and chemical reactivity. The Maxwell fluid flow over the stretched surface of a cylinder is responsible for the improvement in heat transfer. The proposed methodology leverages the power of Artificial Neural Networks (ANN) to effectively manipulate and optimize fluid flow behavior in this complex system. By integrating ANN into the control strategy, we achieve enhanced propulsion system design and optimization capabilities, enabling improved performance around cylinders. Additionally, insights into the interconnection of electromagnetic effects and heat sources provide valuable implications for thermal management systems, where understanding and controlling fluid flow behavior are essential for efficient heat transfer. The design approach for addressing different aspects of the fluid problem consists of a sequence of operations, which encompass training, testing, and validation using a reference dataset. Furthermore, visual representations are employed to portray the flow model parameters concerning momentum, energy, and concentration profiles, effectively illustrating the results of the investigation, all of which are closely aligned with each other on average 10−8. [ABSTRACT FROM AUTHOR]

Earlier research work related to the unsteady flow of thin liquid film on a heated stretching cylinder has considered the boundary‐layer approximation under the assumption that the film thickness is thick. In this article, we have considered the full set of Navier–Stokes equations to study the unsteady film development over a porous heated stretching cylinder with the assumption that film height either coincides or lies within the boundary‐layer thickness. The effects of magnetic field, suction/injection, and cooling or heating of the cylinder have been considered for investigation. The governing set of coupled nonlinear partial differential equations is solved numerically by the implicit finite difference scheme (Crank–Nicolson). It was found that the film thinning rate diminishes with rising values of the porosity parameter and Hartmann number. It is also noted that the film thickness is enhanced for injection whereas opposite results are observed for suction through the porous cylinder. The thermocapillary effect showed that the thinning rate of the liquid film decreases or increases according to the surface of the cylinder being heated or cooled. It is observed that continuously increasing the stretching speed of the cylinder produces faster thinning of the liquid film. The temperature of the liquid film is the maximum at the surface of the cylinder and it decreases toward the free surface when the cylinder is heated. But the opposite phenomenon occurs when the cylinder is cooled. [ABSTRACT FROM AUTHOR]

This paper investigates the second-order slip effect under multiple convective conditions. Nanofluid flow is taken over a permeable stretching cylinder. Suction and injection of nanofluid together with Brownian motion and thermophoresis is also incorporated in this research. Renovation of leading partial differential equations is done with the help of appropriate similarity transfiguration. Obtained nonlinear Ordinary differential equations (ODEs) are solved by Runge–Kutta 4th order (RK-4) method with shooting technique. MAPLE-2019 software is used to simulate the system with a degree of precision of 1 0 − 6 . Several graphs and tables are included to showcase the findings in this investigation. Heat transfer allocation was changed by 17.52% for injection to suction of nanofluid in the system but mass transfer is changed by 9% approximately for the same situation. Skin friction co-efficient diminished in case of higher value of Reynolds number by 2.52% for suction of nanofluid and 2.68% for injection of nanofluid. Upshots of several parameters are compared under suction and injection. [ABSTRACT FROM AUTHOR]

This study focusses on the heat and mass transfer and micro-organisms of the bioconvectional nanofluidic flow in the presence of activation energy. A mathematical model for the bioconvection has been incorporated with the existing nanofluid model past a stretching cylinder for which limited research works are present. The system of partial differential equations has been converted into ordinary differential equation by using suitable similarity transformation, and furthermore is solved by applying spectral quasilinearisation method, a newly developed numerical scheme. The obtained results are depicted graphically and analysed. Some observations regarding Brownian motion, thermal radiation, etc. are also seen in past research works, but explanation of these observations is provided in this study. Furthermore, we have reported some unprecedented behaviours of temperature and solute, microbe concentration as our conclusion, the explanation of which will be regarded as our future scope of research. [ABSTRACT FROM AUTHOR]

Due to its widespread applications in areas including heat exchangers, cancer therapy, heat storage devices, biomedicine, and biotechnology, nanofluid has become one of the most important fluids in thermal engineering. One difficulty with these applications of nanofluids is the improvement of heat conductivity via nanoparticles. This aims to illustrate the bioconvectional cross-flow of a nanofluid in the existence of swimming gyrotactic microorganisms over a vertical stretching cylinder. We consider the chemical reaction and thermal radiation in the energy and concentration equations. Through the use of appropriate dimensionless variables, a nonlinear system of partial differential equations has been transformed into ordinary differential equations (ODEs). The BVP4c method is applied to construct the resultant governing ODEs. The significance of physical variables is demonstrated through plots and tabular data. Our finding explains that the temperature intensifies due to larger curvature parameters and Weissenberg variables, while the opposite effect is examined in the velocity profile. With upsurge in thermophoresis parameter, the temperature upsurges accordingly. As the bioconvection Lewis number rises, microbial concentration falls. The results obtained in this investigation could be useful in practical applications like numerous areas of engineering, biotechnology, nanotechnology, and medical sciences etc.

The main goal of this research is to present the concept of enhancing heat transfer within emerging technology. To achieve this, tiny metal and nonmetal particles ranging from 1 to 100 nm in size are introduced into base liquids. These nanoscale particles are utilized to improve the thermal performance of the liquids, leading to what are termed nanofluids. The utilization of these fluids and the examination of the flow of thin films have valuable implications across various sectors such as engineering, technology, and industries. This research focuses on analyzing the convective flow behavior of nanofluids, specifically, graphene oxide-ethylene glycol (GO−EG) and graphene oxide-water (GO−W) on a moving surface. The study investigates the impacts of magnetic fields and varying viscosity. By making use of the thermophysical characteristics of the base fluid and the nanofluid, as well as implementing a similarity transformation within the fundamental equations that govern energy and momentum, we formulate a 5th order nonlinear ordinary differential equation (NODE) to describe the velocity profile. This is combined with a second-order NODE that describes the distribution of temperature. To solve this derived NODE, we employ a method known as the Homotopy Analysis Method (HAM) for analytical solution. The impact of the relevant factors, Prandtl number, including magnetic field parameter, thickness of the liquid, couple stress parameter, temperature distribution, dynamic viscosity, and Eckert number, on the skin friction, velocity profile, and Nusselt's number are interrogated through graphical representation. The velocity field exhibits a decline as the couple stress parameter, magnetic field parameter, liquid thickness, and dynamic viscosity experience an increase. Conversely, the temperature field displays a rise as the Eckert number and dynamic viscosity experience an increase. To ensure the convergence of the issue, dual solutions of the problem are employed, and this is verified through the utilization graphs and tables. Due to the considerable challenge encountered in heat transfer applications for cooling diverse equipment and devices across industries like automotive, microelectronics, defense, and manufacturing, there is a strong expectation that this theoretical methodology could make a favorable contribution towards enhancing heat transfer efficiency. This improvement is sought to meet the requirements of the manufacturing and engineering sectors.

The incompressible two-dimensional steady flow of Sutterby fluid over a stretching cylinder is taken into account. The magnetic Reynolds number is not deliberated low in the present analysis. Radiation and variable thermal conductivity are considered to debate the impact on the cylindrical surface. The Dufour and Soret impacts are considered on the cylinder. The mathematical model is settled by employing boundary layer approximations in the form of differential equations. The system of differential equations becomes dimensionless using suitable transformations. The dimensionless nonlinear differential equations are solved through a numerical scheme(bvp4c technique). The flow parameters of physical effects on the velocity, temperature, heat transfer rate, and friction between surface and liquid are presented in tabular as well as graphical form. The velocity function declined by improving the values of the Sponginess parameter. The fluid temperature is reduced by increment in curvature parameter.

This study carries significant importance in its exploration of the consequences of thermal diffusion and diffusion-thermal energy on a Maxwell fluid near a stretching cylinder. It also considers the influence of Brownian motion and thermophoresis, alongside examining the impact of the Prandtl number and magnetohydrodynamics (MHD) and radiation into the analysis. The primary aim of this study is to investigate the impact of thermal diffusion, diffusion-thermal energy, and various influencing factors on a Maxwell fluid near a stretching cylinder. This investigation aimed to shed light on the behavior of critical parameters, particularly in the presence of Brownian motion, thermophoresis, and variations in the Prandtl number. Additionally, this study sought to adapt a Bvp4c inbuilt software in MATLAB to solve the governing equations, enabling the visualization of velocity, energy, and concentration contours. This study mainly investigated the results for the mentioned parameters for both flat plate (Curvature parameter αc = 0) and cylinder (αc = 1) on temperature, concentration, and velocity profiles. The major conclusions drawn from this study are the concentration profiles exhibited opposing behaviors as thermophoresis, Brownian motion and the Dufour effect increased. However, the temperature profile increases for these parameters. Secondly, concentration displayed an increasing behavior as the Soret number increased.

Energy transfer and boundary layer flow on a stretching cylinder are used in extrusion procedures, fiber technology, the manufacture of polymer sheets, and the creation of plastic films. In view of these applications, this article examines a transport model for a boundary layer flow with magnetohydrodynamics derived from a Maxwell fluid flow under the influence of radiation, Brownian motion, thermo phoresies and Stefan blowing on a stretching cylinder. Using MATLAB bvp4c function, the governing equations are numerically solved after being changed into ordinary differential equations via similarity renovations. Calculations and analyses determined how various emergent parameters affected the flow field, heat transfer and mass transfer. Some characteristics were discovered to affect the width of the boundary layer. The influence on MHD (M), radiation (Rd), the Schmidt number (Stc), Brownian motion (Nb), thermo phoresies (Nt) and the Stefan blowing parameter (Sb) on the velocity, energy and concentration profile have been explored. Excellent assessment is recognized over a tabular explanation to validate the adopted numerical technique. Significantly the Stefan blowing parameter rises the profiles on velocity and temperature. For an increasing value of the Maxwell fluid parameter, the skin friction coefficient decreases compared to the Stefan parameter.

In this paper, numerical investigations have been performed on intricate double stratification impact with a radiative mixed convective nanofluid over a cylinder. Double stratifications comprise heat transfer used in many practical applications like power station engineering, ground-water reservoirs, thermal stratification of reservoirs, and rivers, density stratification of atmosphere, oceans, different heterogeneous mixtures, and manufacturing processing. Characteristics of heat and mass transfer have also been considered. The developing mathematical expression for momentum, energy transportation, and nano-concentration involving Brownian motion and thermophoresis inspiration are considered. The modeled equations are formulated into ordinary differential equations by applying a suitable similarity approach, which is then tackled numerically via MATLAB. Graphical illustrations of dimensionless velocity, energy, and volumetric concentration distribution are drawn against a few values of appropriate parameters. Results elucidate that enhancement occurs in the concentration profile, whereas decrement is noted for the temperature field for different values of thermophoresis and thermal stratification parameters. Our results elucidate good agreement as compared with the previously published one. The higher value of Hartmann number indicates a higher coefficient of friction. [ABSTRACT FROM AUTHOR]

Magnetic fluids with magnetic field effect mediated by magnetic particles such as NiZnFe3O4 into base fluid like blood ignite new medical applications interests. Magnetic particles are investigated due to their remarkable properties like as exceptional thermal conductivity, which is considered one of the vital in modern nanotechnology to improve the thermal properties as coolants in heat transfer equipment such as drug administration, cancer treatment, and electronic cooling system. Therefore, the research on novel heat transfer of biomagnetic fluids is extremely potent and inspiring. Hence, the present computational study investigates a NiZnFe3O4–blood magnetic fluids steady heat and flow transmission mechanisms performance past a swirling stretchable cylinder. In addition, due to the difference in rotation between NiZnFe3O4 and blood for the purposes of the effects of rotational viscosity in flow, a magnetic field is applied in both radial and tangential directions. The governing equations describing the physical problem accompanied by boundary conditions have been transformed into a dimensionless form using a suitable similarity transformation. With the aid of the MATLAB computer program, the modified system of nonlinear ordinary differential equations has been computationally resolved using a precise numerical technique known as the parametric continuation method to explore the significance of pertinent physical parameters. With the use of graphs and tabular representations, the role of emerging physical factors in this model, including the Reynolds number, effective magnetization number, ferromagnetic interaction parameter, and particle volume fraction, is described in opposition to the flow and heat fields. The numerical results ultimately demonstrate that, when adding magnetic particles to base fluid (blood), which is superior to conventional fluids, Reynolds number and magnetization force play a key influence in the flow distributions and improvement of heat transfer. It is seen that fluid velocity reduced with enhancement values of ferromagnetic interaction parameter, and particles' volume fraction. Additionally, it is discovered that for Reynolds number, particles' volume fraction, and effective magnetization number, the rate of heat transfer is increased. With authors' best information, till to date, the study of heat and flow transmission of blood with NiZnFe3O4 particles under magnetic field effect over swirling extended cylinder has not been attempted by anyone. Sooth to say, the findings of this paper are entirely original and such numerical outcomes were never published by any scholar researchers. The present model can be applicable in medical sectors especially in drug delivery, cancer treatment, separation, and magnetic resonance imaging. [ABSTRACT FROM AUTHOR]

In this analysis, Sutterby nanofluid flow with an induced magnetic field at a nonlinear stretching cylinder is deliberated. The effects of variable thermal conductivity, Darcy resistance, and viscous dissipation are discussed. Thermal radiation and chemical reaction are considered to analyze the impact on the nonlinear stretching cylinder. The governing model of the flow problem is developed under the boundary layer approximation in terms of partial differential equations. Partial differential equations are transformed into ordinary differential equations by performing the suitable transformations. A numerical structure is applied to explain ordinary differential equations. The impact of each governing physical parameters on the temperature, concentration, skin friction, Sherwood, and Nusselt number is presented in graphs and tabular form. Increment in Prandtl number, which declined the curves of the temperature function. Temperature declined because the Prandtl number declined the thermal thickness as well as reduce the temperature of the fluid. Temperature curves showed improvement as Eckert number values increased because the Eckert number is a ratio of kinetic energy to the specific enthalpy difference between the wall and the fluid. As a result, increasing the Eckert number causes the transformation of kinetic energy into internal energy via work done against viscous fluid stresses.

This article evaluated the effects of heat generation and the chemical reaction of Maxwell fluid over a porous stretching cylinder. Partial differential equations are framed using the mentioned parameters. The partial differential equations for momentum, heat, and mass are changed using similarity transformations into highly nonlinear ordinary differential equations. These equations are answered numerically via the Runge-Kutta with the shotting scheme of the 4th order in MATLAB with the help of inbuilt software bvp4c. Results are offered graphically and in tabular format for essential parameters over a velocity, temperature, concentration, skin friction coefficient, Sherwood number, and Nusselt number. We checked our coding against an existing article and obtained a good match. The essential findings of this research are that velocity decreases as the permeability parameter rises. It has been observed that a viscoelastic fluid parameter induces a decreasing velocity profile. Due to the Maxwell fluid, porosity, heat generation, and chemical reaction parameters, the thermal profile has been improved. These results have several manufacturing applications, including metal turning, the fabrication of glass filaments, the formation of elastic sheets, wire drawing, the ejection of polymer sheets by oil companies, and the synthesis of polymers.

The magnetic outcomes are frequently implemented for assessing fluid specifications around stretching magnetized surfaces and energy producing technology of thermodynamics. Magnetohydrodynamic reactors and magneto-hydrodynamic generators are two primary methods for producing magnetic flux through ionized fluids along a warmed and magnetized stretched surface. The desired outcomes of the current work are to investigate magnetic flux and heat transmission in the presence of convective boundary conditions using an electrically-conducting fluid over a stretchable cylinder. Most of the parameters are considered in the discussion with intensity and variance due to time dependent methodology. The suggested fluctuating dynamic computational framework is formulated for associated forms of coupled model under boundary variables. The appropriate non-dimensional variables are used to transform the complicated mathematical expression into a non-dimensional representation. To make the non-dimensional representation easier to work for efficient statistical calculations, it is reduced further. Later, for a variety of variables, significant computations are performed via the implicit finite difference methodology. The main finding of current communication is to explore the prominent slip effect in temperatures for every Biot number around all positions. From a physical standpoint, the phenomenon was predictable since surface heat flux is employed as sporting source to increase heat transmission in electric-conducting fluids. For every possible angle, the field of magnetism increases with minimal intensity of surface heat flux. Since, magnetizing functions referred to as an insulating layer that diminishes high temperatures across surfaces and fluids.

This work covers the theoretical and computational examination of the Ellis hybrid nanofluid flow model with magnetic, Darcy-Forchheimer, and non-linear thermal radiation effects across the stretching cylinder. The convective slip boundary condition is imposed on the surface of the cylinder. Hybrid nanoparticles (AA7072 and AA7075) are scattered in base fluid (water) to create a hybrid nanofluid. The phenomenon of fluid flow has been analytically developed for energy and fluid velocity as a non-linear partial differential equation (PDE)-based system. Through appropriate similarity replacements, the design of PDEs is further streamlined to the set of ordinary differential equations (ODEs). Utilizing a built-in MATLAB (R2020b) algorithm called bvp4c, numerical solutions are found for the obtained dimensionless equations. Graphical discussions are used to illustrate the outcomes of velocity and temperature profiles. The velocity profile of mono and hybrid nanofluids declined for higher inputs of Darcy–Forchheimer and magnetic parameters. Additionally, it has been observed that the energy contour is improved caused of thermal radiation and thermal Biot number. Moreover, our results are consistent with the existing literature.

In this analysis, Sutterby fluid flow of induced magnetic hydrodynamic at a stretchable cylinder is deliberated. The viscous dissipation impacts with temperature-dependent properties are applied on the fluid flow. The governing equations are developed using boundary layer approximation in terms of differential equations. The differential equations are dimensionless by means of suitable transformation. The dimensionless system is elucidated by the numerical procedure. Governing physical parameters influences are offered through graphs as well as tabular form. The curves of the velocity function show to enhance due to an increment in the decay-resistant parameter. The curves of the velocity function increased due to higher values of the magnetic field parameter. The sponginess parameter and velocity have inverse relation presented in graph. Temperature augmented due to increasing values of ε. The variable thermal conductivity and temperature have direct relation. Due to this relation, temperature boosted up by boosting the thermal conductivity.

This paper explores the active and passive control implementation on the nanofluid flow over a stretching cylinder. Realistic velocity slip and thermal jump properties are clutched. Appearance of external heat source and magnetic influence is also reckoned. Concentration and temperature profiles are modified due to integration of Brownian motion together with thermophoresis. Leading equations are transfigured into ODEs by well-qualified similarity transfiguration and hence solved by RK-4 shooting technique. Entire simulation is settled by MAPLE software with proper rate of accuracy and the outcomes are portrayed by graphs and tables. Results are compared considering both slip and without slip conditions, whereas the concentration profile is described under active and passive control conditions. Mass transfer decreases for Brownian motion but reverse effect is found for thermophoresis parameter under passive control of flow. Mass transfer is changed by 10.1% in case of passive control condition for the Reynolds number parameter. Nusselt number is diminished by 6.16% under passive control provision for magnetic parameter. [ABSTRACT FROM AUTHOR]

In the current analysis, steady incompressible Sutterby fluid flows over a stretching cylinder are studied. The influence of variable thermal conductivity is considered in the presence of thermal slip, Darcy resistance, and sponginess. The impact of the induced magnetic field is considered to analyze the results at the cylindrical surface. The governing equations are established as partial differential equations using the boundary layer approximation. Appropriate transformations are used to convert partial differential equations into ordinary differential equations. The numerical technique, namely (bvp4c), is applied to ordinary differential equations to develop the results. The numerical results, such as heat transfer rate and skin friction, are revealed by tabular form to demonstrate the physical impact of governing factors. The physical impact of governing factors on induced magnetic hydrodynamic, velocity, and temperature profiles is presented through various graphs. The velocity function deteriorated due to the augmentation of the Sutterby fluid parameter.

The current study reveals the impact of MHD heat transfer properties of an incompressible viscous fluid were numerically solved across a continuously expanding horizontal cylinder immersed in a porous material in the existence of internal heat production/sink. The partial differential equations which govern the fluid flow with boundary constraints were converted to a collection of non-linear ODE’s with the aid of similarity variables and then numerically solved by using Keller-Box approach. The components of fluid velocity, temperature, as well as friction factor, and rate of heat transfer were all calculated numerically. Graphs and tables illustrate the fluid velocity and heat transfer properties for several Prandtl numbers, and magnetic parameters. The main goal of the current findings is to examine how the magnetic field M, Pr, and the heat absorption/generation factor Q influence the velocity and temperature gradients along a stretching cylinder. It is projected that the rise in the curvature parameter and the porosity factor would contribute to the enhancement of the temperature gradient in the boundary layer area around the cylinder.