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The present work is focused on the stagnation point flow over a Jeffery fluid flow through a stretching/shrinking sheet. The nanoparticles namely Cu are considered by exploiting water-based fluid. The governing nonlinear system of partial differential equations is converted into a system of highly nonlinear ordinary differential equations via a similarity transformation. Therefore, it is quite significant to assimilate the analytical extension of heat transfer and mass transfer fluid in the presence of porous under the influence of slip velocity. The analytical solution available for nondimensional momentum, heat transfer, and concentration profiles across the boundary layer is examination is done by checking the various values of physical parameters viz., Prandtl number, Radiation parameter, stretching/shrinking parameter, and mass transpiration for the flow and heat transfer which are obtainable through graphs. The present work on nanofluids flowing through stretching/shrinking surfaces has numerous applications in biomedicine, solar energy, cooling, nuclear system cooling, etc. [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 research article, explores the influence of an inclined magnetic field on the fluid flow over a permeable stretching/shrinking surface with heat transfer. The study use water as a conventional base fluid, with graphene oxide (GO) and Aluminum oxide (Al2O3) nanoparticles submerged to create a nanofluid, the system of governing nonlinear partial differential equations converted into ordinary differential equations via suitable similarity conversions. This allow for the unique solution for stretching sheet/shrinking sheets to be obtained, along with the corresponding temperature solution in terms of the hypergeometric function, several parameters are included in the investigation and their contribution is graphically explained to examine physical characteristics such as radiation, inclined magnetic field, solution domain, volume fraction parameter, and temperature jump. Increasing the volume fraction and thermal radiation increases the thermal boundary layer, increasing the magnetic field parameter and inverse Darcy number increases the temperature and decays the velocity profile. The present work has many useful applications in engineering, biological and physical sciences, as well as in cleaning engine lubricants and thrust-bearing technologies. [ABSTRACT FROM AUTHOR]

The exclusive behaviour of nanofluid has been actively emphasized due to the determination of improved thermal efficiency. Hence, the aim of this study is to highlight the laminar boundary layer axisymmetric stagnation point flow of Casson nanofluid past a stretching plate/cylinder under the influence of thermal radiation and suction/injection. Nanofluid comprises water and Fe3O4 as nanoparticles. In this article, a novel casson nanofluid model has been developed and studied on stretchable flat plate or circular cylinder. Adequate rational assumptions (velocity components) are employed for the transformation of the governing partial-differential equations into a group of non-dimensional ordinary-differential formulas, which are then solved analytically. The momentum and energy equations are solved through the complementary error function method and scaling quantities. Using various figures, the effects of essential factors on the nanofluid flow, heat transportation, and Nusselt number, are determined and explored. From obtained results, it is observed that the velocity field diminishes owing to magnification in stretching parameter B and Casson fluid parameter Λ . The temperature field increases by amplifying radiation N r , and solid volume fraction parameter ϕ . The research is applicable to developing procedures for electric-conductive nanomaterials, which have potential applications in aircraft, smart coating transport phenomena, industry, engineering, and other sectors. [ABSTRACT FROM AUTHOR]

The current studies analytically summarize the impact of magnetohydrodynamic and thermal radiation on the non-Newtonian continuous uniform motion of viscid non-compressible nanofluid across a penetrable stretching/shrinking sheet, even though accomplish Navier's first and second order slips along mass transpiration. Blood-bearing silver and copper nanomaterials have distinct flow and heat transfer properties when exposed to heat. Silver (Ag) as well as copper (Cu) nanoparticles are assumed to be present in blood as the non-Newtonian liquid; this fluid serves as the base. We anticipate that the current study will be useful in fields including food, petrochemical products, and medicines, as well as blood circulation, and highly beneficial for patients who are dealing with blood clotting in the uterus, which may result in infertility or cancer, to evaluate the blood flow in the tube. Employing the similarity conversion technique, the ruling partial differential equations are modified into a couple of non-linear ordinary differential equations. Then the transformed ordinary differential equations are analytically solved with the Laplace transformation and expressed in terms of an incomplete gamma function. The current analytical results are compared to previous studies. It is addressed how several physical features such as magnetic field M, Navier's first and second order slip, permeability, Prandtl number Pr, and radiation parameter affect non-dimensional velocity as well as temperature patterns through graphs. The results obtained reveal that there is an enhancement in the rate of heat transfer with the rise in nanoparticle volume fraction and radiation. The temperature distribution is also influenced by the presence of Prandtl numbers, radiation, solid volume fraction, permeability, and slip conditions. This shows that the solid volume fraction of nanoparticles can be used to control the behaviour of heat transfer and nanofluid flows. [ABSTRACT FROM AUTHOR]

This article focuses on MHD flow and heat transfer of Jeffrey fluid due to a stretching/shrinking surface with carbon nanotubes, considering the effects of thermal radiation, heat source/sink parameters, and Navier's slip. Generally, solids offer higher thermal conductivity than fluids. To offer higher thermal conductivity, a new type of nanofluid is formed by suspending two types of carbon nanotubes (CNTs), i.e. single-wall carbon nanotubes (SWCNTs) and multi-wall carbon nanotubes (MWCNTs), which act as nanoparticles, into the base fluid, water. It is intended to enhance the thermal conductivity and mechanical properties of the base fluid. The structure of the problem is an equation of momentum and temperature, which are then converted into a set of ODEs to imitate the MHD flow of carbon nanotubes. The magnetic parameter, radiation parameter, and Navier slip effect significantly affect the structure of the solution to the problem. Carbon nanotubes act as nanoparticles that enhance the heat performance and mechanical properties more than the base fluid, so they have many applications in electronics and transportation. The velocity and temperature profiles, skin friction coefficient, and Nusselt number are observed and discussed through graphs. The results reveal that for stretching case, velocity profile increases with increasing the magnetic field, while the opposite trend observed in shrinking case. We notice that the SWCNT Nanofluids are better nanofluids than the MWCNT Nanofluids. We study from these final results that the usage of CNTs in most cancerous therapies can be more useful than all sorts of nanoparticles. [ABSTRACT FROM AUTHOR]

In this paper, the three-dimensional Casson flow of a ternary hybrid nanofluid over a porous linearly stretching/shrinking surface in the presence of an external magnetic field is considered. The surface deformation process is described by introducing two parameters of stretching/shrinking in the lateral directions. Using similarity transformations, the basic set of nonlinear partial differential equations is converted into ordinary differential equations. An exact analytical solution to this boundary value problem is obtained. The influence of the Casson parameter, magnetic field, porosity medium, and stretching/shrinking parameter, taking into account mass transpiration, on the velocity profiles and the skin friction coefficients is considered in detail. It has been established that the results obtained in some limited cases are in excellent agreement with the available data. Tables show the new results for the skin friction coefficients in the lateral directions (x and y) for different variants of surface deformation. [ABSTRACT FROM AUTHOR]

The current work shows an incline MHD and Casson fluid flow with a mixed convective boundary layer with hybrid nanofluid Cu–Al2O3/water flow over a stretching/shrinking sheet. The present study is analyzed using an Al2O3–Cu/H2O hybrid nanofluid with a fixed Prandtl number of 6.8. The governing equation of highly nonlinear partial differential equations is converted into ordinary differential equations using exact similarity transformations. Moreover, the radiation effects are also permitted with help of Rosseland's approximation. The subsequent system of equations is then investigated analytically with appropriate boundary conditions. The outcomes of this topic can be addressed using a graphical representation with many parameters like radiation, heat source/sink, stretching/shrinking mass transpiration so on. The research shows that the solution depicts a unique explanation for stretching/shrinking sheets and that the explanation demonstrates the dual flora focused on some stretching/shrinking sheet parameters. The nanoparticles are disseminated in water, which serves as the base fluid. Graphs are also used to study the effects of the magnetic parameter, mass transpiration, and heat source/sink parameter on the velocity profile. It has a wide range of uses in the polymer sector, power generators, flow meters, and pumps, among others. The results indicate that the solution illustrates an inimitable solution for the stretching sheet and that the explanation manifests the dual flora aimed at some parameters for the stretching/shrinking sheet. The hybrid nanofluid has significant features improving the heat transfer process and is extensively developed for manufacturing industrial uses. It was found that the basic similarity equations admit two phases for both stretching/shrinking surfaces. [ABSTRACT FROM AUTHOR]

Hybrid nanofluids (HNFs) comprise combinations of different nanoparticles suspended in base fluid. Applications of such nanofluids are rising in the areas of energy and biomedical engineering including smart (functional) coatings. Motivated by these developments, the present article examines theoretically the magnetohydrodynamic coating boundary layer flow of HNFs from a stretching sheet under the transverse magnetic field in porous media with chemically reactive nanoparticles. Darcy's law is deployed. Momentum slips of both first and second order are included as is solutal slip. The transformed boundary value problem is solved analytically. Closed form solutions for velocity are derived in terms of exponential functions and for the concentration field in terms of incomplete Gamma functions by the application of the Laplace transformation technique. The influence of selected parameters e.g. suction/injection, magnetic field and slips on velocity and concentration distributions are visualized graphically. Concentration magnitudes are elevated with stronger magnetic field whereas they are suppressed with greater wall solutal slip. Magnetic field suppresses velocity and increases the thickness of the hydrodynamic boundary layer. The flow is accelerated with reduction in inverse Darcy number and stronger suction direct to reduce in skin friction. The concentration magnitudes are boosted with magnetic field whereas they are depleted with increasing solutal slip. The analysis provides a good foundation for further investigations using numerical methods. [ABSTRACT FROM AUTHOR]

The invention of carbon nanotubes (CNT) has a wide range of industrial and medical applications. The notion of boundary layer flow is used in medicine, particularly in nanomedicine, and the use of magnetic fields is used to treat cancer tumour growth. The governing PDEs are altered into ODEs with the help of suitable transformations. The mass transfer of a chemically reactive species and the flow of MHD over a stretching plate subjected to an inclined magnetic field are investigated, and analytical solutions for velocity in terms of exponential function and temperature field in terms of incomplete Gamma function are obtained using the Laplace transformation. We investigate the variation of physically important parameters with varying suction, magnetic field, and slip using the analytical results. The differences in velocity and temperature profiles are explored in relation to a number of physical parameters. MWCNT nanofluids have higher effective velocities than the SWCNT deferred nanofluids, and this might assist in industrial applications and medical benefits. Earlier research tells us that carbon nanotubes are likely quicker than nanoparticles at achieving the same tumour instance. As a result, in the presence of CNTs or nanoparticles, the magnetic field can also act as a source. We found that SWCNTs nanofluids are better nanofluids than MWCNTs nanofluids. [ABSTRACT FROM AUTHOR]

An investigation of 2D laminar magnetohydrodynamics couple stress hybrid nanofluid is performed with inclined magnetic field over the stretching/-shrinking surface embedded in porous media. The quiescent water-based nanofluid is subjected to the external force by pulling the two ends of the sheet with equal magnitude and opposite forces. The governing nonlinear partial differential equations (PDEs) are converted into nonlinear ordinary differential equation (ODE) by adopting the suitable similarity transformation and obtains the analytical solution for velocity. The hydrodynamic characteristics are investigated in the presence of different physical parameters such as couple stress parameter, magnetic parameter, mass transpiration, stretching/shrinking parameter, porosity and magnetic parameter with the help of graphs. The thermal properties are enhanced by adding the copper and alumina nanoparticles to the base fluid. The result of this study has important applications in industrial and scientific are such as polymer extrusion process, liquid crystal solidification, cement artificial foams production, ceramics, metal spinning, and roofing shingles and also have possible technological applications in fluid-based systems involving stretchable/shrinkable materials. [ABSTRACT FROM AUTHOR]

The steady magnetohydrodynamics (MHD) incompressible hybrid nanofluid flow and mass transfer due to porous stretching surface with quadratic velocity is investigated in the presence of mass transpiration and chemical reaction. The basic laminar boundary layer equations for momentum and mass transfer, which are non-linear partial differential equations, are converted into non-linear ordinary differential equations by means of similarity transformation. The mass equation in the presence of chemical reaction is a differential equation with variable coefficients, which is transformed to a confluent hypergeometric differential equation. The mass transfer is analyzed for two different boundary conditions of concentration field that are prescribed surface concentration (PSC) and prescribed mass flux (PMF). The asymptotic solution of concentration filed for large Schmidt number is analyzed using Wentzel-Kramer-Brillouin (WKB) method. The parameters influence the flow are suction/injection, superlinear stretching parameter, porosity, magnetic parameter, hybrid nanofluid terms, Brinkman ratio and the effect of these are analysed using graphs. [ABSTRACT FROM AUTHOR]

In the current work, we have investigated the flow past a semi-infinite porous solid media, after presenting a similarity transformation, governing equations mapped to a system of non-linear PDE. The flow of a dusty fluid and heat transfer through a porous medium have few applications, viz., the polymer processing unit of a geophysical, allied area, and chemical engineering plant. Further, we had the option to get an exact analytical solution for the velocity to the equation that is non-linear. The highlight of the current work is the flow of hybrid dusty nanofluid due to Darcy porous media through linear thermal radiation with the assistance of an analytical process. The hybrid dusty nanofluid has significant features improving the heat transfer process and is extensively developed in manufacturing industrial uses. It was found that the basic similarity equations admit two phases for both stretching/shrinking surfaces. The existence of computation on velocity and temperature profile is presented graphically for different estimations of various physical parameters. [ABSTRACT FROM AUTHOR]