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The study focuses on the flow of hybrid nanofluid, induced by magnetic and radiation effects, across an exponentially stretched sheet. The research examines the impact of temperature-dependent properties of the hybrid nanofluid on the sheet. Water is used as the base fluid, and SWCNT and MWCNT are employed as nanoparticles. The study includes a discussion of the Yamada–Ota, Xue and Tiwari–Das models of hybrid nanofluids. The governing system of flow is presented mathematically, and boundary layer approximations are used to reduce differential equations. The differential equations are transformed into dimensionless ordinary differential equations (ODEs) by using transformations. The dimensionless system of equations is then solved numerically. The results of the flow model are offered in tabular and graphical forms. We observed that Tiwari–Das model of hybrid nanofluid achieved more heat transfer and friction factor values when compared to other models of Xue and Yamada–Ota models of hybrid nanofluid. Temperature curves are noted to be enhanced by enlargement in the nano-concentration factor. If the nano-concentration increased in the fluid which boosted the thermal conductivity of the liquid, then as a result, the temperature of fluid enhanced at surface. [ABSTRACT FROM AUTHOR]

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

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

In this analysis, thermal and solutal stratifications in three-dimensional mixed convection flow of second grade fluid along an irregular cylinder through porous medium is demonstrated. Effect of induced magnetic induction is considered to deal many technological and scientific problems like crude oil purification, plasma confinement, rotating magnetic stars and power generation. The flow narrating continuity, magnetic flux, momentum, magnetic induction, concentration and heat equations are modeled in the form of PDEs. Set of dimensionless conversions are introduced to replace non-linear PDEs into a set of ODEs. To predict numerical solution of considering model, we used an efficient numerical technique Bvp4c. The consequential outcomes are sketched for unlike values of dimensionless parameters. Parameters like mixed convection, second grade parameter, magnetic parameter, porosity parameter and buoyancy ratio parameter are initiated to control the flow field. Further, temperature and solutal stratification parameters, Prandtl, magnetic Prandtl and Schmidt numbers are found to control energy, magnetic induction and concentration distributions. Skin drag coefficients, heat and mass fluxes are investigated for inflating values of some sundry parameters. For justification of the model, we compared present numerical outcomes with previous published results. [ABSTRACT FROM AUTHOR]

The heat transfer characteristics of an unsteady magnetohydrodynamic flow through non-conducting infinite vertical parallel plates are presented in this investigation. The flow is subjected to an induced magnetic field, and the base fluid water contains carbon nanotubes (CNTs), in particular multi-wall carbon nanotubes, to present the behaviour of the nanofluid. The aim is to examine the effect of the applied magnetization and CNT concentration on the heat transport performance of the system. However, suitable transformation rules are adopted for the re-designing of the proposed design model into its non-dimensional form. This transformed system is then solved analytically following the standard transformations. The influence of key parameters, including the Hartmann number (Ha), the angle of inclination of the magnetic field, thermal buoyancy, heat source, and the concentration of CNTs in the nanofluid, on the flow phenomena is analysed. The consequences reveal that the occurrence of the inclined magnetic field affects the flow and heat transfer characteristics significantly. Additionally, the introduction of CNTs to the nanofluid enhances the heat transfer performance due to their unique thermal properties. The study demonstrates that enhanced Ha and CNT concentration augments the heat transfer rate.

In order to study the characteristics of the wake magnetic anomaly when multiple ships are sailing at the same time, based on the basic theoretical knowledge of ship wake, the waveform, velocity, and distribution of the induced magnetic field of the ship wake were studied, and the variation characteristics and distribution patterns of the induced magnetic field of the multi-ship wake were obtained. By taking the formation of three ships as an example, the distribution of the induced magnetic field and the distribution of the magnetic field in the directions of x and y during the movement of the ships were analyzed. The magnetic field distribution characteristics of the wake formed when the three ships sail at the same time were solved, and the abnormal induced magnetic field generated during various ship combination operations was analyzed. The experimental results obtained from the simulation were consistent with the existing measurement results. APP Design tools were used for magnetic anomaly simulation system software development of multi-ship wake. The system not only could accurately, intuitively, and quickly simulate and set the magnetic induction intensity and variation patterns of the wake of three ships in any direction but also had the advantages of simple operation and cost saving, which provided a theoretical reference and a more effective simulation platform for ship wake experiment.

The present objective is to numerically analyze the induced magnetic field (IMF) effect of an unsteady MHD flow of Casson fluid through two infinite vertical plates. The effect of radiative heat has been scrutinized. Governing non-dimensional PDEs of the flow are discretized by the finite difference method to some algebraic system of equations, which is then numerically solved concerning the boundary conditions. The effects of the radiations, magnetic Prandtl number, Prandtl number, Hartmann number, and Casson parameter on temperature profile, velocity profile, and induced magnetic field have been depicted through graphs. The radiative effect and Prandtl number have considerable influence on the surface drag force and also on the rate of heat transfer.

The research on entropy generation in a mechanical system is quite imperative owing to its immense applications in the production of advanced cooling devices and medical appliances. The basic need on this research is how to optimize the irreversibilities within the systems and channelize that energy towards the benefit. This study elucidates the entropy generation analysis of a Casson nanofluid near a stagnation point over a lubricated vertical wall. A thin film of shear-thinning liquid with power law index of 0.5 is employed on the wall to ensure the lubrication. The effect of induced magnetic field and the chemical reaction stimulated by the activation energy is also incorporated within the flow. The non-linear PDEs of the substantive problem along with the compatible interfacial and boundary conditions are reverted into ODEs with the aid of suitable similarity transformation, and then cracked numerically using the sixth-order Runge Kutta method assisted with Nachtsheim–Swigert shooting practice. One of the significant findings reveals that the fluid friction irreversibilities in the entropy generation are diminished with the magnetic parameter and the Casson parameter, whereas the thermal irreversibility predominates over the total entropy generation for the escalating values of the activation energy parameter. [ABSTRACT FROM AUTHOR]

AbstractHollow cylinder structures play a crucial role in scientific experiment and industrial production, and are widely used in various fields, including pipeline transportation of gases and liquids, high-speed engines, porous combustors, and other engineering equipments. As a result, they have garnered considerable academic interest over the years. However, as science and technology progress, studying hollow cylinders under a single physical field is no longer sufficient for real-world applications. Additionally, the classical viscoelastic model has become inadequate in accurately describing complex materials with properties that fall between elasticity and viscosity. Therefore, this article investigates the electro-magneto-thermoviscoelastic coupling behavior of an infinitely long rotating multilayer homogeneous hollow cylindrical conductor. In this study, based on the fractional-order three-phase lag thermoelasticity theory, the fractional-order viscoelastic system and the two-temperature theory are introduced to further increase the accuracy of the model. To solve the corresponding equations, the Laplace transform technique is employed, resulting in solutions with dimensionless physical quantities. Graphs and tables are used to make relevant comparisons and assess the effects of time, material layering properties, different thermoelastic theoretical models, fractional-order parameters and angular velocity on the considered physical quantities. Finally, the numerical results are discussed to reveal the dynamic response of a homogeneous multilayered hollow cylinder under the complex coupling of multiple physical fields. [ABSTRACT FROM AUTHOR]

This study deals with numerical modeling and mathematical analysis, and the investigation specifically delves into peristaltic blood flow characterized by a non-Newtonian six-constant Jeffrey fluid model in a uniform channel under multiple slip boundaries, which has not been explored so far in the literature. The model incorporates double diffusion convection, thermal radiation, viscous dissipation, and induced magnetic flux. Applying the conditions of a low but finite Reynold number, utilizing a long-wavelength approximation, and neglecting the wave number, the study drives numerical solutions for various parameters, including magnetic force function, heat, velocity, nanoparticle volume fraction, concentration, and streamline equations. The obtained results show that the fluid speed diminishes as the Brickman number and velocity slip parameter values increase. Further, thermal curves exhibit an expansion with the increase in the Prandtl number and thermophoresis parameter. The study's findings may be valuable in medical treatments such as cancer cells via a nanoparticle-based drug delivery mechanism. [ABSTRACT FROM AUTHOR]

The present work examines the convective Casson fluid flow over a stretching sheet with viscous dissipation and porous medium. The impact of thermal and mass transport is examined in terms of Soret and Dufour effects. The flow behaviour and heat transfer are investigated by subjecting the fluid to an induced magnetic field and suction/injection. The governing equations describing the flow problem are formulated using partial differential equations (PDEs). Similarity transformations are utilized to transform the governing equations into a system of ordinary differential equations (ODEs). Following that, the MATLAB solver bvp5c is utilized to grasp the results. Graphs serve as a function to display the consequences of flow on attributed parameters. Furthermore, the engineering properties such as skin friction, Nusselt number, and Sherwood number are represented through tables and graphs. Besides, the results of the present study are validated with the existing results, whereas a fine correspondence has been noticed. The findings show that the velocity of the fluid decreases by 8%, when the parameter of the induced magnetic field rises from 0.1 to 0.2. Similarly, a 3% decrement in the velocity profile is observed, while increasing the suction/injection parameter from 1.2 to 1.4. The temperature of the fluid is escalated for the increasing values of the Eckert number. Our analysis indicates a positive correlation between the Nusselt number and increasing Dufour number values. Similarly, the Sherwood number exhibits enhancement with a rise in the chemical reaction parameter. This combination has some applications in designing cooling systems for microfluidic devices, optimizing drag reduction in magnetohydrodynamics (MHD) devices, and developing novel separation processes. [ABSTRACT FROM AUTHOR]

Entropy generation with time periodic thermal boundary conditions have numerous applications in heat exchangers, electronic devices, automatic and thermal control systems. The present research focuses on mixed convective hydromagnetic electrically conducting fluid flow in a vertical annulus using thermodynamic concepts, in the presence of induced magnetic field along with entropy generation and time periodic boundary conditions. The governing equations related to the present model are solved using finite element method. Also to predict heat transport features in the vertical annulus, artificial neural network – backpropogated Levenberg Marquardt algorithm is adopted. The steady and periodic profiles of velocity, skin friction, temperature and induced magnetic field are illustrated graphically for specific range of pertinent parameters to demonstrate significant aspects of the results. It is noted that increase in Hartmann number enhances the entropy generation near the outer cylinder, which illustrates that the fluid friction and magnetic field influence is maximum at the outer cylinder surface. The Bejan number in the annulus reduces with increase in viscous heating parameter. Results indicate that raise in the Prandtl number diminishes the thermal boundary layer thickness. As a result of decrease in the intensity of heating the boundary walls, a raise in Strouhal number lowers the fluid temperature profile. The generalized correlation is expressed to predict heat transport features in the annulus using artificial neural network – backpropogated Levenberg Marquardt algorithm. [ABSTRACT FROM AUTHOR]

The application of mathematical modeling to biological fluids is of utmost importance, as it has diverse applications in medicine. The peristaltic mechanism plays a crucial role in understanding numerous biological flows. In this paper, we present a theoretical investigation of the double diffusion convection in the peristaltic transport of a Prandtl nanofluid through an asymmetric tapered channel under the combined action of thermal radiation and an induced magnetic field. The equations for the current flow scenario are developed, incorporating relevant assumptions, and considering the effect of viscous dissipation. The impact of thermal radiation and double diffusion on public health is of particular interest. For instance, infrared radiation techniques have been used to treat various skin-related diseases and can also be employed as a measure of thermotherapy for some bones to enhance blood circulation, with radiation increasing blood flow by approximately 80%. To solve the governing equations, we employ a numerical method with the aid of symbolic software such as Mathematica and MATLAB. The velocity, magnetic force function, pressure rise, temperature, solute (species) concentration, and nanoparticle volume fraction profiles are analytically derived and graphically displayed. The results outcomes are compared with the findings of limiting situations for verification. [ABSTRACT FROM AUTHOR]

The present study investigates the heat and flow characteristics of mixed convective peristaltic transport of nanofluids containing magnetite γAl2O3 nanomaterials dispersed in conventional liquids, namely, ethylene glycol (C2H6O2) and water (H2O). The research provides a comprehensive analysis, considering various factors such as induced magnetic field, variable viscosity, buoyancy force, viscous dissipation, and porous media effects. The mathematical model is formulated based on a set of governing equations encompassing continuity, temperature, momentum, and induction, which are subsequently transformed into dimensionless form through appropriate scaling. A numerical method is employed to solve the resulting nonlinear differential equations. Results indicate that the velocity profile exhibits substantially higher magnitudes in the case of the γAl2O3-C2H6O2 nanoliquid when compared to the γAl2O3-H2O nanoliquid. Increasing the magnetic Reynolds number leads to a higher magnitude of the axial-induced magnetic field. An observed reduction in system entropy is associated with an increase in the permeability parameter.

This work investigates the heat transmission and boundary layer (BL) slip flow of a power-law fluid induced by stretching surfaces. The power-law fluid, induced magnetic field, and finite thermal relaxation have significant applications in a variety of industrial settings, including thin-layer growth, cooling systems, the extrusion process, and coating and shaping operations in a heat transfer mechanism. With these significant industrial applications, the current study explores BL flow and heat transfer in the context of the of the Cattaneo-Christov theory against the backdrop of an induced magnetic field over a stretching surface. The shear-thinning and thickening features are captured by the power-law fluid model, while the Cattaneo-Christov theory solves the deficiencies of Fourier's law. The BVP4c technique is used to construct and solve BL equations numerically. The surface drag and heat transmission rates at the wall are studied using statistical multi-regression analysis. The findings clarify that the magnetic and power law indices have a favorable effect on the Nusselt number, while their influence on skin friction is conflicting. A lower heat transmission is predicted with thermal relaxation as compared to Fourier's law in the energy equation. The accumulated thermal relaxation parameter produces a non-equilibrium state, delaying the internal thermal processes.

The induced magnetic field is used to control the fluid motion and heat transfer in a variety of applications, such as in MHD devices, microfluidics, electrically conducting fluids in channels and in circular pipes, and clinical applications such as drug delivery and cooling of nuclear reactors. Henceforth this investigation aims to elucidate the behavior of viscoelastic (second-grade fluid) ternary nanofluid flow through a permeable stretching sheet with an induced magnetic field. The stretching surface is subjected to the Cattaneo-Christov heat and mass flux model to investigate heat and mass transfer properties. Solutions of reduced governing equations are obtained numerically via the shooting method and computed using the bvp-4c algorithm. The impacts of diverse active parameters such as porous medium, magnetic parameter, reciprocal magnetic Prandtl parameter, stretching parameter, HSS parameter, and relaxation time parameter for heat and mass flux are studied graphically. In addition, the values of significant engineering factors are calculated and comparative analysis is presented through bar graphs. It is seen that regular heat sink/source promotes thermal distribution and relaxation time for mass flux enhances the mass transfer rate between fluid flow and solid surface.

Abstract In this study, we investigate the profound impact of the Pöschl–Teller double-ring-shaped Coulomb (PTDRSC) potential to induce persistent currents within the S-states of the hydrogenic atom. The confinement of the system is achieved through an impenetrable spherical boundary. Leveraging first-order perturbation theory, we quantify the charge current across various states induced by the PTDRSC potential with its inherent angular and azimuthal dependence, leading to angular and azimuthal distortion, respectively. Notably, persistent currents are observed within S-states without external excitation mechanisms. The magnitude of the induced current is intricately linked to the strength of the PTDRSC potential parameters. These results underscore the prospect of manipulating persistent currents and their associated induced magnetic fields within S-states by tailoring the potential strength and confining boundary size. This discovery presents a compelling avenue for the controlled generation and experimental verification of induced S-state magnetism, opening new possibilities for innovative applications.

Peristaltic flows of non-Newtonian fluids with heat and mass transfer have several applications in physiology and industry, which provide motivation for analysis of such flows. This article provides analysis of a two-dimensional peristaltic flow of a non-Newtonian fluid whose rheological characteristics are depicted by the Johnson–Segalman (J–S) model. Heat and mass transfer attributes considering heat generation/absorption and the Soret and Dufour effects are studied for present flow. A novel aspect of this study is Magnetohydrodynamics, accounting interactions between fluid and applied as well as induced magnetic fields based on of Maxwell's equations. Mathematical model incorporating such effects is then simplified using the lubrication approach. The resulting equations, adhering to no-slip conditions for velocity, temperature, and concentration, are solved numerically, and the graphical results are meticulously examined. The study reports significant findings and introduces a mechanism to obtain outcomes under the influence of a constant applied magnetic field at various stages, particularly within the scope of a low magnetic Reynolds number. The results indicate that by adjusting pertinent parameters, the behavior of a Newtonian fluid under hydrodynamic conditions can be replicated. In these conditions, the velocity of the Newtonian fluid surpasses that of the J–S fluid affected by the applied magnetic field. Furthermore, increasing the Hartman number diminishes the magnetic field's impact. Moreover, higher Reynolds numbers result in augmented current density near the midpoint of the channel, with larger Weissenberg and Hartman numbers resulting in a reduced trapped bolus size. [ABSTRACT FROM AUTHOR]

The present objective is to numerically analyze the induced magnetic field (IMF) effect of an unsteady MHD flow of Casson fluid through two infinite vertical plates. The effect of radiative heat has been scrutinized. Governing non-dimensional PDEs of the flow are discretized by the finite difference method to some algebraic system of equations, which is then numerically solved concerning the boundary conditions. The effects of the radiations, magnetic Prandtl number, Prandtl number, Hartmann number, and Casson parameter on temperature profile, velocity profile, and induced magnetic field have been depicted through graphs. The radiative effect and Prandtl number have considerable influence on the surface drag force and also on the rate of heat transfer. [ABSTRACT FROM AUTHOR]

The induced magnetic field is used to control the fluid motion and heat transfer in a variety of applications, such as in MHD devices, microfluidics, electrically conducting fluids in channels and in circular pipes, and clinical applications such as drug delivery and cooling of nuclear reactors. Henceforth this investigation aims to elucidate the behavior of viscoelastic (second-grade fluid) ternary nanofluid flow through a permeable stretching sheet with an induced magnetic field. The stretching surface is subjected to the Cattaneo-Christov heat and mass flux model to investigate heat and mass transfer properties. Solutions of reduced governing equations are obtained numerically via the shooting method and computed using the bvp-4c algorithm. The impacts of diverse active parameters such as porous medium, magnetic parameter, reciprocal magnetic Prandtl parameter, stretching parameter, HSS parameter, and relaxation time parameter for heat and mass flux are studied graphically. In addition, the values of significant engineering factors are calculated and comparative analysis is presented through bar graphs. It is seen that regular heat sink/source promotes thermal distribution and relaxation time for mass flux enhances the mass transfer rate between fluid flow and solid surface. [ABSTRACT FROM AUTHOR]

This work is focused on Magneto hydrodynamic unsteady flow of Newtonian fluid flow over a perpendicular porous plate along with chemical reaction, heat, and mass transfer. The induced magnetic field and viscous and magnetic dissipation properties are considered throughout the porous plate. Heat source is the added effect in the model to observe the nature of flow in this work. This study finds its applications in understanding the storage of flues, disposal of radioactive waste materials, flow in water purifies, etc. The nonlinear behavior of the governing equation motivates us to use a finite difference approach for solving equations. The major resolution of this research is to work on how the physical elements affect velocity, temperature, concentration, and magnetic field. Fascinating facts are noticed as the unsteady fluid velocity rises with the heat source parameter because as the heat of a material increases, the movement of the fluid particle will be fast. Due to the presence of a magnetic field high thermal radiation is observed at high temperature and concentration. As the magnetic parameter and magnetic field are inversely proportional according to an induced magnetic field, it is noticed that their magnetic field declines for higher values of magnetic Prandtl number & magnetic parameter. This work has dynamic prominence in the field of medicine and engineering, which develops interest among young researchers. [ABSTRACT FROM AUTHOR]

An analysis is presented for the stagnation-point two-dimensional fluid flow of hybrid nanofluid towards an expanding surface characterized by the induced magnetic field. Further, the consideration of thermal buoyancy and additional heat source enhances the flow phenomena with various physical parameters involved in it. This work has significant novelty due to the behavior of the convective boundary conditions. Besides, due to the convective term the nonlinear differential equations designed in this problem are incorporated and are resolved numerically by executing the Runge–Kutta–Fehlberg method. Additionally, three different classes of nanosized particle configurations named brick, cylinders, and platelets shapes are examined for the implementation of the Hamilton–Crosser thermal conductivity model. In the end, the influences characterizing the local Nusselt number and the coefficient of skin friction profiles have been discussed for unalike shapes of nanosized particles are discussed. In the above study, it is found that the platelet-shaped nanosized particle is more efficient in comparison to the other shapes considered herein. Further, particle concentration and particle shape are also favorable in enhancing fluid temperature in hybrid nanofluids in contrast to pure fluid. [ABSTRACT FROM AUTHOR]

In this study, we investigate the profound impact of the Pöschl–Teller double-ring-shaped Coulomb (PTDRSC) potential to induce persistent currents within the S-states of the hydrogenic atom. The confinement of the system is achieved through an impenetrable spherical boundary. Leveraging first-order perturbation theory, we quantify the charge current across various states induced by the PTDRSC potential with its inherent angular and azimuthal dependence, leading to angular and azimuthal distortion, respectively. Notably, persistent currents are observed within S-states without external excitation mechanisms. The magnitude of the induced current is intricately linked to the strength of the PTDRSC potential parameters. These results underscore the prospect of manipulating persistent currents and their associated induced magnetic fields within S-states by tailoring the potential strength and confining boundary size. This discovery presents a compelling avenue for the controlled generation and experimental verification of induced S-state magnetism, opening new possibilities for innovative applications. [ABSTRACT FROM AUTHOR]

Steady flow of incompressible Maxwell–Sutterby fluid at stretching sheet is discussed in the presence of stagnation point region. The magnetic Reynolds number is considered very high and induced magnetic and electric fields are applied to the fluid flow. Temperature-dependent properties with radiation influence are considered in this analysis. The heat source or sink and melting impact are also debated in this analysis. A differential model of mathematics is developed by employing a governing constitutive equation. The differential equations' model is condensed and becomes ordinary differential equations by implementing the appropriate transformations. Furthermore, these equations are elucidated by the numerical scheme. The physical influence of physical parameters is exhibited in the graphs and tabular form. The escalating values of M cause a shear thinning attitude in the fluid; as a result, devaluation in the velocity is detected in the case of a / c = 0. 5 , while it depicted the counter behavior for a / c = 1. 5. The skin friction is heightened with improving values of Re because R e boosted which improved the viscosity of liquid as well as heightened the friction at sheet. The enhancing values of M p cause a decrement in skin friction. The melting parameter is enriched which reduces the viscosity of fluid due to temperature boosting as well as friction reduction. The diminution in skin friction is found for enhancing the values of β. [ABSTRACT FROM AUTHOR]

AbstractThis research scrutinizes the impact of the Thompson and Troian slip effect on a two-dimensional flow of ternary nanoliquid induced by an extending sheet near a stagnation point. Nanoparticles Iron oxide (Fe2O3), Nickle Zinc ferrite (NiZnFe2O4), and Magnesium zinc iron oxide (MnZnFe2O4) are dispersed in Ethylene glycol (C2H6O2) to establish ternary nanofluid. The induced magnetic field influences the flow, and the analysis of heat and mass transfers takes into account the Cattaneo–Christov (C–C) heat flux with homogenous–heterogeneous (H–H) reactions, respectively. To expedite the reaction, a surface-catalyzed process is introduced to efficiently control both (H–H) reactions within a reduced time frame. Utilizing the Tiwari and Das framework, the fluid flow characteristics are elucidated. Appropriate transformations are applied to derive ordinary differential equations (ODEs), which are then numerically deciphered via the bvp4c scheme. Graphs are portrayed to highlight the consequence of non-dimension quantities on the flow and temperature profiles. The surface drag coefficient and heat flux rate are also assessed and summarized. Outcomes revealed that for large estimates of the velocity slip parameter, the surface drag coefficient is enhanced while the heat flux rate is reduced. It is also interesting to note that because of the high estimations of ferromagnetic nanoparticles, the rate of heat transfer is elevated significantly. The validation of the proposed model is also included. [ABSTRACT FROM AUTHOR]

Purpose: Several graphs, streamlines, isotherms and 3D plots are illustrated to enlighten the noteworthy fallouts of the investigation. Embedding flow factors for velocity, induced magnetic field and temperature have been determined using parametric analysis. Design/methodology/approach: Ternary hybrid nanofluids has outstanding hydrothermal performance compared to classical mono nanofluids and hybrid nanofluids owing to the presence of triple tiny metallic particles. Ternary hybrid nanofluids are considered as most promising candidates in solar energy, heat exchangers, electronics cooling, automotive cooling, nuclear reactors, automobile, aerospace, biomedical devices, food processing etc. In this work, a ternary hybrid nanofluid flow that contains metallic nanoparticles over a wedge under the prevalence of solar radiating heat, induced magnetic field and the shape factor of nanoparticles is considered. A ternary hybrid nanofluid is synthesized by dispersing iron oxide (Fe3O4), silver (Ag) and magnesium oxide (MgO) nanoparticles in a water (H2O) base fluid. By employing similarity transformations, we can convert the governing equations into ordinary differential equations and then solve numerically by using the Runge–Kutta–Fehlberg approach. Findings: There is no fund for the research work. Social implications: This kind of study may be used to improve the performance of solar collectors, solar energy and solar cells. Originality/value: This investigation unfolds the hydrothermal changes of radiative water-based Fe3O4-Ag-MgO-H2O ternary hybrid nanofluidic transport past a static and moving wedge in the presence of solar radiating heating and induced magnetic fields. The shape factor of nanoparticles has been considered in this study. [ABSTRACT FROM AUTHOR]

In this research article, we intend to perform a numerical investigation of the thermal features of MHD Williamson hybrid nanofluid flow over a linearly stretching surface with viscous dissipation and nonlinear thermal radiation effects. An external magnetic field exists in the vicinity of stagnation point along with the creation of induced magnetic field due conducting fluid. A thin film of viscous and incompressible base fluid, engine oil (E O) , encumbered with titanium alloy (T i 6 A l 4 V) and zinc oxide (Z n O) nanoparticles is examined taking pure nanofluid and hybrid nanofluid cases simultaneously in a single frame in Cartesian coordinates. The governing equations are first transformed to ordinary differential equations employing similarity transformations and then simulated by successive over-relaxation method. Approximate solutions are assessed through graphs for velocity, temperature and induced magnetism corresponding to the prominent parameters. A significant improvement in wear resistance, lubrication and thermal features of the engine oil has been observed due to titanium alloy and zinc oxide hybrid nanocomposite. [ABSTRACT FROM AUTHOR]

The current article deals with a novel idea of a suspension of spherical silver Ag , cylindrical aluminium oxide Al 2 O 3 and platelet aluminium Al nanoparticles in water–ethylene glycol as a conducting fluid through a convective stretching surface. The effects of induced magnetic field, heat sink or source, thermal radiation and slip condition aspect are also incorporated during ternary hybrid nanofluid flow. The significance of the current investigation lies in enhancing heat transfer efficiencies, high-temperature processes, electronic devices where heat is generated or cooling systems and metal casting. The numerical solutions of nonlinear ordinary differential are obtained by employing a finite difference approach via the bvp4c solver (MATLAB package). The obtained results pointed out that the spherical silver nanoparticles provide a higher rate of heat transfer followed by cylindrical alumina nanoparticles and platelet aluminium nanoparticles, respectively. Moreover, the velocity profile and induced magnetic profile decrease with increasing volume fraction of spherical Ag nanoparticles, cylindrical Al 2 O 3 alumina nanoparticles, platelet Al nanoparticles and induced magnetic parameter. The ternary hybrid nanofluid's heat transfer rate is greatly increased by larger values of the radiative parameter, Biot number and slip parameter. Additionally, the temperature profile is improved when the heat source parameter grows while the heat sink parameter decreases. [ABSTRACT FROM AUTHOR]

The analysis focuses on investigating the phenomenon of double-diffusive convection using the Sisko nanofluid model. It particularly highlights the impact of induced magnetic flux, viscous dissipation, and heat radiation within an asymmetric geometry having multiple slip conditions. To ascertain the salient of the Brownian diffusion coefficient and thermophoresis, we have incorporated viscous dissipation, heat radiation, and the Buongiorno model. The Soret and Dufour parameters describe the convective double diffusion phenomenon. The mathematical formulation is constructed through equations governing magnetic force function, concentration, temperature, momentum, and continuity. These formulations yield nonlinear partial differential equations to explain the designated flow. To simplify the nonlinear partial differential equations, the lubrication paradigm of mathematical simulations is employed. The subsequent system of coupled nonlinear differential equations is calculated numerically through the NDSolve function, which is a built-in program of Mathematica. Numerical results and graphs give evidence that supports the significance of different flow quantities in physiological contexts. The findings from this investigation are anticipated to contribute to the development of intelligent magneto-peristaltic pumps, particularly in thermal and drug administration applications. The current investigation suggests that the distribution of temperature reduces as the coefficient of radiation increases due to a system’s high heat emission and consequent effects of cooling. Furthermore, the increased influence of heat radiation raises the concentration profile. It is also highlighted that heat radiation has the potential to raise a fluid’s temperature, which raises the volume fraction of nanoparticles.

Aiming at the difficulty in detecting concealed geological isomers using conventional geophysical method in ultra-wide coal working face, the electromagnetic response mechanism of mine transient electromagnetic (TEM) perspective detection with opposite side emission and reception is revealed in this study. The electromagnetic field diffusion characteristics, data influence mechanism and detection capability of transient electromagnetic perspective detection technology are studied in detail by means of theoretical research, numerical simulation and analysis of measured data. The results show that the transient electromagnetic field diffusion of the full-space elongated emission loop is different from that of the half-space electromagnetic field diffusion due to the boundary between ground and air. In the full-space state, the extreme value of the induced electromotive force (EMF) is located in the center of the emission coil for a long time, which cannot be interpreted directly by using the ground ‘smoke ring effect’. The early transient electromagnetic perspective data transmitted and received on the opposite side are mainly affected by the primary magnetic field and have high resolution and detection ability of left and right low resistance anomalies. The late data and the same-side transmitting and receiving data have the same generation mechanism, both them are formed by mutual induction and diffusion of secondary fields generated near the transmitting loop, and their resolution and detection ability are relatively weak. Compared with the transient electromagnetic method, this technology can distinguish the spatial position of the low-resistance anomaly relative to the transmitting loop and the receiving point by combining early and late data. The closer the low resistivity anomaly body is to the transmitter loop, the greater the impact on the early data received at the opposite side, and the impact time period of the late data increases, but the degree of influence is smaller. On the contrary, the closer it is to the receiving point in the roadway, the opposite the impact characteristics are. Therefore, the approximate position of the low-resistance anomaly body along the working face can be roughly determined. The transient electromagnetic perspective detection technology, which combines early and late data, can more accurately interpret the spatial information of hidden water inrush geological isomers which are inside and near the working face.

The paper studies effect of induced magnetic field on laminar convection flow of a viscous electrically conducting incompressible fluid between two parallel porous plates at constant temperature gradient in presence of a uniform inclined magnetic field. An angle (θ) is formed with the vertical line by applying a magnetic field in that direction and field is strong enough to induce another field along the line of flow. Using the proper similarity transformations, the flow equations are converted into ordinary differential equations, which are then numerically solved by using MATLAB's bvp4c solver. Plotting of the graphs allows one to examine the effects of several critical parameters such as Hartmann number, Darcy number, Magnetic Reynolds number, Prandtl number, and Field inclination on velocity field, induced magnetic field, temperature field at the plates. The acquired results demonstrate that the flow system is effectively influenced by the field inclination, the magnetic parameter, and the plate porosity. The rise in field inclination leads to an increase in magnetic drag force.

This research offers an analysis of the mixed convective transient boundary film Casson fluid stream and thermal distribution through a vertical sheet. Viscous dissipation and the Soret effect are introduced to support the flow in stimulating heat capacity. Unlike typical investigations, the present flow-formulated model is done to capture an induced magnetic field. The Boussinesq approximation is used to describe the nonlinear formulated partial derivatives governing the heat transfer fluid that is non-dimensionalized using suitable dimensionless quantities. The transformed partial derivative model is numerically solved via the spectral Chebyshev technique and the results of shear stress, current density, Nusselt number, and mass gradient are tabulated. The role of numerous terms on dimensionless flow rate, induced velocity, and heat transfer with species distribution is discussed in a very effective way. Velocity and temperature of liquid decline as boosting the material parameter. Enhancing values G r , G r m favor the flow momentum and oppose the temperature profile. [ABSTRACT FROM AUTHOR]

The physiological system loses heat energy through the bloodstream to nearby cells. Such energy loss can lead to a quick death, anemia, severe hypothermia and high or low blood pressure to heart surgery. As a result, biomedical engineers and physicians are increasingly attracted to the study of entropy production to calculate the energy loss of biological systems. Furthermore, the thermodynamic state of entropy production is used to access cancer cells during chemotherapy treatment and heat transfer in tissues. The current model intends to explore the significance of the non-Fourier heat flux model on Eyring–Powell/Maxwell hybrid nanofluid (Fe3O4–CuO/blood) flow in a linear extending sheet with induced magnetic field and entropy generation. Suitable self-similarity variables are performed to convert momentum and thermal equations determined using the homotopy perturbation method into ordinary differential equations. The significance of distinct physical parameters such as thermal relaxation parameter, volume fraction, fluid parameter, magnetic Prandtl number, Biot number, Brinkman number, heat source, Eckert number, radiation and heat source on velocity, temperature, skin friction coefficient, Nusselt number, entropy production, streamlines and isotherm are represented through figures. It is recognized that the fluid friction irreversibility is comparatively higher than thermal irreversibility and highly dominates the total entropy generation. The nanoparticle volume fraction diminishes the velocity and induced magnetic field of both Eyring–Powell and Maxwell hybrid nanofluid. Fluid friction irreversibility is more in Maxwell fluid compared to the Eyring–Powell fluid. [ABSTRACT FROM AUTHOR]

AbstractIn the present investigation, the onset of Marangoni convection in the flow of self-rewetting fluid over a stretching disk has been discussed. The self-rewetting fluid is considered to be electrically conducting and the flow problem is discussed under the influence of an induced magnetic field. The fluid flow is mainly induced due to two different mechanisms: (i) onset of Marangoni convection due to presence of temperature gradient along the liquid-gas interface and (ii) induction of magnetic field due to presence of an external magnetic field, which modifies the original field. The governing partial differential equations are written, following Navier-stokes equations and Prandtl boundary layer equation. With the use of similarity transformations, the governing equations are turned into a system of ordinary differential equations. Nonlinear systems of ordinary differential equations are solved by the bvp4c technique. The reciprocal of the magnetic Prandtl number diminishes the induced magnetic profile. [ABSTRACT FROM AUTHOR]

Ternary hybrid nanoparticles require infected blood cell base fluid flow. Blood vessels feature ciliated walls and peristaltic waves. Anemia comes from cancer treatment-induced red blood cell destruction. This study reproduces Jeffrey model blood flow through a ciliary peristaltic artery using ternary hybrid nanoparticles of gold, iron oxide, and copper. This work examines ternary hybrid nanofluid MHD ciliary peristaltic motion using Jeffrey curves. A nonlinear PDE system has heat and induced magnetic force equations. The Adomian Decomposition Method solved this system without long-wavelength approximation. Visualize how essential biological and physical elements affect velocity, temperature, trapping, magnetic force contours, induced magnetic field components, axial pressure, and normal pressure. Flow, temperature, magnetic features, and other important properties are plotted and discussed against biological and biomedical parameters. We discovered full consistency with modest scenario efforts. The increase in nanoparticles gives ternary hybrid nanofluid a larger friction force than hybrid, so its axial pressure gradient at the wall is stronger, decays at hybrid, decays further from nanofluid to base fluid, and reverses at the intermediate area. Peristaltic ciliary activity alters magnetic force contours, shrinks loops, and forms four contour groups with different implications. [ABSTRACT FROM AUTHOR]

AbstractThe current study investigates the influence of induced magnetic field and convective boundary condition on the behavior of a magnetohydrodynamic (MHD) Maxwell fluid including nanoparticles flowing through a stretching sheet. Furthermore, the analysis considers the existence of radiation. Numerical solutions to the basic governing equations are achieved using the Runge–Kutta–Fehlberg technique. The impact of various physical parameters on concentration, velocity, and temperature profiles is deployed through graphs. The primary conclusions of this study are that increasing the Magnetic parameter decreases the Induced Magnetic field while increasing the Deborah parameter improves the velocity profile. Temperature distribution is growing due to increased estimates of the Radiation, Biot number, and Deborah number values. When the Lewis number values are raised, the concentration profiles get smaller but there is an opposite scenario deployed as the Thermophoresis parameter upsurges. The findings of this study are consistent with those that have been previously reported. The phenomenon of flow induced by a stretched surface finds several applications in various industrial and technological domains, including copper wire production, polymer extrusion, article manufacturing, and fiber synthesis. Induced magnetic fields are extremely prominent in many areas of science and technology, including electromagnetism, magnetic materials, and magnetic resonance imaging (MRI). [ABSTRACT FROM AUTHOR]

The study of nanoliquid characteristics and their heat performance have attracted the interest of engineers. These engineered fluids have high thermal conductivity due to which such liquids are reliable for different engineering applications including heating/cooling of buildings, thermal and mechanical engineering, etc. Therefore, the current research design provides a new ternary nanoliquid model for the heat transport process under induced magnetic field effects, mixed convection, heating source and thermal radiations. The modeling has been done by implementing the ternary fluid characteristics and supportive transformations and then for results simulation; bvp4c is coded successfully. It is scrutinized that a higher inductive magnetic field (0.1–0.4) and nanoparticles amount (0.01–0.07) are better to resist the movement while the wedge parameter (λ1) promotes it. By promoting the heating source, Eckert and Rd, the heat transfer process is observed rapidly while the mixed convective number α controls it. Further, the particular used ternary nanoliquid is examined and found to be good for cooling purposes. [ABSTRACT FROM AUTHOR]

In the present study, we introduce a new method with a high-accurate to solve a system of equations of boundary value problems. This method is a mixture of numerical methods (Runge-Kutta and finite difference) and exact methods (Laplace transforms), each having a role in studying. The novelty of the present method is converting boundary value problems to initial value problems using accurate numerical methods and then using Laplace transforms method to find an approximate to the exact solution. Approximate to exact method (AEM) is a new algorithm, with a very strong accuracy that approaches the exact solution. (AEM) applied in studying radiative steady MHD heat and mass transfer flow past a vertical porous plate. (AEM) applied in a system of four non-dimensional equations using suitable dimensional quantities on the governing equations. The new technique's uniqueness, convergence, and stability are verified and tested by comparisons with the previous exact solution. The present governing equations which solved using (AEM) designed by using the Wolfram Mathematica algorithms version 12.3. [ABSTRACT FROM AUTHOR]

AbstractThe main objective of this framework is to formulate a model and carry out simulations on the thermally radiative biological fluid of Sisko nanofluid in the non-uniform channel under the combined effects of induced magnetic field and double diffusion convection. Additionally, the effect of viscous dissipation is also considered. The formulation and simplification of the governing equations for a non-Newtonian fluid with nanoparticles and double diffusion convection is done under the assumption of a long wavelength and low Reynolds number. The numerical solution of the proposed problem is calculated by utilizing built in commands in Matlab and Mathematica software’s. The equation solving is done in Mathematica using the integrated program NDSolve. The framework provides expressions for temperature, nanoparticle fraction, velocity, pressure rise, stream functions, pressure gradient, magnetic force function, and concentration. The impact of relevant parameters on various physical quantities is then analyzed through graphical representations, considering both non-Newtonian and viscous fluid behavior. The present analysis suggests that an increase in heat radiation may cause a drop in the temperature distribution strengthening the cooling effects. It is also found that as Brinkman number rise, buoyancy-driven flows have a greater impact on fluid motion. The concentration of nanoparticles may fluctuate and maybe decrease in specific locations in accordance with the dispersion and advection phenomena. Furthermore, this finding has important ramifications for the field of biomechanics too. Examples include comprehending chyme movements in the digestive system and the prospective use in operations to regulate blood flow by adjusting the magnetic field’s strength. [ABSTRACT FROM AUTHOR]

The axisymmetric stagnation point flow of brick and blade-shaped Silver and Copper nanoparticles immersed in an ethylene glycol base fluid under the influence of an induced magnetic field over an unsteady radial stretching surface is investigated in this study. The unsteady phenomenon is considered because most flow issues in practice are unsteady. The fundamental laws of mass, momentum, and energy conservation are used to present the physical model. Heat transmission is also examined under the effects of magnetohydrodynamics, Joule heating, viscous dissipation, and convective boundary conditions to give a realistic physical investigation. Scaling analysis transforms the flow-governing issue into a collection of higher-order nonlinear ODEs. These are, then, solved numerically using the fourth-order Runge–Kutta and shooting techniques. Moreover, the numerical technique is validated by calculating residual error. It is concluded that, compared to the Ag–EG nanofluid, the Cu–EG nanofluid had the highest IMF, lowest temperature, minimum surface drag, and maximum heat flux, making it the ideal choice for creating a radial module. [ABSTRACT FROM AUTHOR]

The issue of Jeffrey nanofluid peristaltic flow in an asymmetric channel being affected by an induced magnetic field was studied. In addition, mixed convection and viscous dissipation were considered. Under the supposition of a long wave length and a low Reynolds number, the problem was made simpler. The system and corresponding boundary conditions were solved numerically by using the built-in package NDSolve in Mathematica software. This software ensures that the boundary value problem solution is accurate when the step size is set appropriately. It computes internally using the shooting method. Axial velocity, temperature distribution, nanoparticle concentration, axial induced magnetic field, and density distribution were all calculated numerically. An analysis was conducted using graphics to show how different factors affect the flow quantities of interest. The results showed that when the Jeffrey fluid parameter is increased, the magnitude of axial velocity increases at the upper wall of the channel, while it decreases close to the lower walls. Increasing the Hartmann number lads to increases in the axial velocity near the channel walls and in the concentration of nanoparticles. Additionally, as the Brownian motion parameter is increased, both temperature and nanoparticle concentration grow. [ABSTRACT FROM AUTHOR]

In this article, the Caputo Fabrizio fractal fractional order derivatives operator with an exponential kernel was employed to examine the radiative heat and mass transfer characteristics of time dependent flow with variable fluid viscosity, induced magnetic field, Soret and Dufour effects. The local mathematical model for the flow problem is formulated by take into account the impacts of thermal radiation, heat source, and viscous dissipation. The governing equations in-terms of fractal fractional model with an exponential kernel were solved numerically using finite difference method. The influence of flow variables such as induced magnetic field, concentration field, entropy rate, thermal field, and velocity field profiles against the pertinent parameters are discussed through graphs. Increase the values of magnetic Prandtl number results to rises of induced magnetic field. Higher Dufour number significantly grows the thermal field. The fractal fractional parameters enhance the velocity field, thermal field, Bejan number, entropy rate, concentration field and induced magnetic field profiles. The velocity field profiles recede with higher values of fluid variable viscosity parameter whereas the thermal field and induced magnetic field has an opposite effect. Larger Soret number amplifies the concentration field. Increase of Brinkman number, thermal radiation parameter, and magnetic Prandtl number intensifies the entropy generation rate. Increases of Brinkman number, magnetic Prandtl number, Soret number and Dufour number leads to a decrease of Bejan number whereas Bejan number rises with an increase of thermal radiation parameter and heat source. [ABSTRACT FROM AUTHOR]

AbstractThe major goal of this work is to give a thorough examination of the effect of double diffusion convection (DDC) in addition to a generated magnetic field on peristaltic movement of fourth-grade nanofluid across a vertical sophisticated asymmetrical microchannel using a nondeformable porous media as a basis for intricate pumping systems inspired by biological processes for hazardous waste. The mathematical formulas pertaining to flow, heat/mass transfer under the influence of viscous dissipation, nonlinear heat radiation, and Joule heating were developed using Buongiorno’s framework for nanofluids with combining the thermophoresis and Brownian motion characteristics. Mathematical analysis has been conducted under the suppositions of an extended wavelength and a relatively small Reynolds number. Magnetic field induced axially, density of current, magnetic force function, thermal characteristics, nanoparticles proportion gradient, an additional stress tensor, pressure gradient, and stream function are all given explicit formulas. The constructed function (ND Solve function) within the Wolfram software (Mathematica) is employed to computationally resolve the ensuing system of coupled nonlinear differential equations. Numerical and pictorial evidence is presented to highlight the significance of different physiological characteristics of flow volumes. Further, contour visualizations and circulation bolus have been used to highlight the trapping phenomena, one of among the most noteworthy peristaltic motion occurrences. The main results showed that, despite the dissolvent concentration and the volume percentage of nanoparticles having the opposite effects, the resistance of a substance to heat is shown to climb as the Soret and Dufour numbers rise. At larger levels of the electromagnetic Reynolds number, Strommer’s number, electric field parameter, and thermal Grashof number, stronger axial induced magnetic fields (IMFs) are also provided. [ABSTRACT FROM AUTHOR]

Ternary hybrid nanofluids possess several potential applications in the modern science beyond just the heat transfer efficiency. A continuous research and advancements on binary and ternary hybrid nanofluids might lead towards new developments in many technological and scientific zones. Ongoing research interprets and distinguishes the novel attributes of the sodium alginate (Na.C6H7O6) based unary, binary and ternary nanofluids through a porous medium under induced magnetic field environment. The nano-composition of single-wall carbon nanotubes (SWCNT) with silver (Ag) and molybdenum dioxide (MoS2) gives rise to the binary (SWCNT-Ag/Na.C6H7O6) and ternary hybrid (SWCNT-Ag-MoS2/Na.C6H7O6) nanofluids respectively. A complex and highly nonlinear system of differential equations, obtained via the boundary layer approximations, is tackled numerically. An algorithmic approach, using MATLAB software, is incorporated to determine the iterative solutions. The efficiency as well as validity of the developed algorithm is confirmed by equating the results with the previous ones. The results evidently portray the fact that the magnetic Prandtl number and magnetic interaction parameter not only dissuade the induced magnetic field but also resist the fluids’ speed. With the larger values of activation energy parameter, higher will be the concentration of fluid.

In this study, the influence of induced magnetic field and chemically reacting on hydromagnetic generalized Couette flow of Jeffrey fluid in an inclined channel through a porous medium with variable viscosity and convective cooling has been investigated using the Caputo fractional order derivative operator. The mathematical formulation used for the hydromagnetic Couette flow of Jeffrey fluid takes into account the effects of viscous dissipation, Soret, and Dufour. The system of nonlinear partial differential equations governing the flow were solved numerically using the explicit finite difference method. The numerical results for the behavior of various physical parameter on the flow variables are obtained and represented graphically. Moreover, effects of the flow parameters on heat and mass transfer rates are obtained and discussed numerically through tabular forms. The graphical findings show that velocity, concentration, induced magnetic field, and thermal field profiles decline with progressively increment of Jeffrey parameter. The velocity, and temperature of the fluid decline with higher values of fluid viscosity parameter. An increase in the chemical reaction parameter recede the concentration field profiles while increase with raises the values of Soret number. Increasing Biot, and Dufour numbers significantly grows the thermal field profiles. Induced magnetic field grows with larger values of fluid viscosity parameter. The findings of this study are important due to its application in magnetohydrodynamics pumps, polymer manufacturing, fins designs, and food processing.

The abstract is categorized into the following sections as.Background: There are various challenges in the real life, which are required to deal with the specific intervals. Fuzzification is most appropriate way to find the solutions and can provide the accurate results of uncertain problems in specific intervals. Some conditions and imprecise parameters make the problems based on the fluid flow uncertain.Purpose: This current attempt focuses on the investigation of inclined magnetized Cross fluid flow in fuzzy conditions embedded with the chemical process with fuzzy complex conditions.Formulation: The governing system of modeled PDEs are tackled numerically with the utilization of finite difference method under fuzzy conditions at the boundary surface.Finding: The magnetic parameter intensifies the velocity field and induced magnetic field H. Amplification in viscosity parameter diminishes the velocity.Novelty: α‐cut technique for the case of fuzzified Cross fluid has not been studied in the accessible literature.

The appealing traits of carbon nanotubes (CNTs) encompassing mechanical and chemical steadiness, exceptional electrical and thermal conductivities, lightweight, and physiochemical reliability make them desired materials in engineering gadgets. Considering such stimulating characteristics of carbon nanotubes, our goal in the current study is to scrutinize the comparative analysis of Darcy–Forchheimer nanofluid flows containing CNTs of both types of multi and single-wall carbon nanotubes (MWCNTs, SWCNTs) immersed into two different base fluids over a stretched surface. The originality of the model being presented is the implementation of the induced magnetic field that triggers the electric conductivity of carbon nanotubes. Moreover, the envisioned model is also analyzed with homogeneous-heterogeneous (h-h) chemical reactions and heat source/sink. The second-order slip constraint is assumed at the boundary of the surface. The transmuted high-nonlinearity ordinary differential equations (ODEs) are attained from the governing set of equations via similarity transformations. The bvp4c scheme is engaged to get the numerical results. The influence of different parameters is depicted via graphs. For both CNTs, the rate of heat flux and the surface drag coefficient are calculated using tables. It is highlighted that an increase in liquid velocity is witnessed for a varied counts volume fraction of nanoparticles. Also, Single-wall water-based carbon nanotube fluid has comparatively stronger effects on concentration than the multi-walled carbon nanotubes in water-based liquid. The analysis also indicates that the rate of heat flux and the surface drag coefficient are augmented for both SWCNTs and MWCNTs for different physical parameters. The said model is also validated by comparing it with a published result.