Narrow Results

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.

The heat transfer through the thermal radiation is very significant in many industrial processes, biomedical engineering, technological devices and thermal therapeutic process. These comprise nuclear power plants, propulsion of rockets, missiles, satellites and space vehicles, photochemical reactors, solar collector performance, heat exchangers. The boundary layer flow and the heat transport of dusty liquid over a stretching cylinder are discussed. The impact of nonlinear thermal radiation is explored. Cattaneo–Christov heat flux model is considered to formulate the energy equation. The resulting equations of the physical system are converted into a system of nonlinear ordinary coupled differential equations with the help of suitable similarity transformations and numerically solved by using Runge–Kutta–Fehlberg’s method along with shooting technique. The influence of nondimensional parameters is analyzed and interpreted graphically. The heat transfer rate and local coefficient of skin friction are also calculated for diverse nondimensional constraints and plotted.

This paper aims to investigate the time-dependent stagnation point flow of an Oldroyd-B fluid subjected to the modified Fourier law. The flow into a vertically stretched cylinder at the stagnation point is discussed. The heat flux model of a non-Fourier is intended for the transfer of thermal energy in fluid flow. The study is carried out on the surface heating source, namely the surface temperature. The developed nonlinear partial differential equation for regulating fluid flow and heat transport is transformed via appropriate similarity variables into a nonlinear ordinary differential equation. The development and analysis of convergent series solutions were considered for velocity and temperature. Prandtl number numerical values are computed and investigated. This study’s findings are compared to the previous findings. By making use of the bvp4c Matlab method, numerical solutions are obtained. Besides, high buoyancy parameter values are found to increase the fluid velocity for the stimulating approach. By improving the thermal relaxation time parameter values, heat transfer in the fluid flow decreases. The temperature field effects are displayed graphically.

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.

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.

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 4^th order (RK-4) method with shooting technique. MAPLE-2019 software is used to simulate the system with a degree of precision of $10^{-6}$. 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.

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.

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.

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.

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.

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.

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.

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.

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.