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The present investigation describes the flow of a copper (Cu) and cobalt ferrite (CoFe2O4) hybrid nanofluid with water as base fluid across a curved surface stretched with nonlinear power-law velocity in the presence of Lorentz forces. The influence of Joule heating and heat source/sink on fluid flow has also been studied. Using a similarity structure, nonlinear partial differential equations are converted into ordinary differential equations which are numerically computed using the ODE analyzer. Skin friction, Sherwood number and Nusselt number are computed in addition to the momentum, mass and energy profiles. A comparison is analyzed through graphs, tables and results for linear and nonlinear surfaces. The heat sink lowers the temperature profile and the heat source elevates the energy field, which serves a purpose in the petrochemical industries for heating and cooling fluids. When the chemical reaction parameter expands, the concentration profile gets less molded, but the opposite tendency is noticed for a decrease in the chemical reaction parameter, which is advantageous for biological applications. The major finding of the study is that nonlinear surfaces exhibit more drag force, mass and heat rate than linear surfaces. Additionally, there was a decent agreement between our results and prior findings for surface drag force under restricted conditions.

It is very significant and practical to explore a triple hybrid nanofluid flow across the stuck zone of a stretching/shrinking curved surface with impacts from stuck and Lorentz force factors. The combination (Ag–TiO2–Al2O3/blood) hybrid nanofluid is studied herein as it moves across a stagnation zone of a stretching/shrinking surface that curves under the impact of pressure and Lorentz force. Exact unsolvable nonlinear partial differential equations can be transformed into ordinary differential equations that can be solved numerically by similarity transformation. It was discovered that predominant heat transfers and movement characteristics of quaternary hybrid nanofluids are dramatically affected. Numerous data were collected from this study to illustrate how parameters of flow affect the temperature, velocity, heat transmission, and skin friction characteristics. The axial and radial velocities for both fluids (Newtonian and ternary hybrid nanofluid) are increased due to the increasing function of the curvature parameter, magnetic field, and suction parameter. Additionally, the direct relationship between the temperature and heat transfer decreases the heat transfer rate by the curvature parameter, magnetic field, suction parameter, Prandtl number, and heat source/sink. The higher the values of the curvature parameter, the higher the shear stress and velocity.

In most of practical situation multiple slips (velocity, temperature and concentration) has importance in manufacturing, medicinal, imaging processes and design of materials. In view of this, the present work considered the multiple slips on Magneto hydrodynamic (MHD) dissipative non-Newtonian fluid (Casson fluid) above a curved type of a stretching surface are studied. Multiple slips with Casson fluid have significance in controlling the blood flow distribution in human and animal bodies. The R–K fourth-order via shooting technique is used to convert the nonlinear governing equations. The impact of governing parameters is shown and explored graphically. The present investigation explores the multiple slip effects in governing equations under the influence of the magnetic field; the fluid's temperature and velocity have reverse characteristics. In a few unique situations, the current findings have been in reasonable agreement with the current results. As opposed to when viscous dissipation is absent, the temperature distribution is higher when viscous dissipation is present. It helps us to decide depending on the industrial and manufacturing processes, whether dissipation has to be applied or not. The stretching parameter enhances the Skin friction coefficient and rate of heat transfer, while decreases the rate of mass transfer. Also, the fluid's temperature decreases because an increase in Casson fluid parameter enhances the plastic dynamic viscosity, which creates resistance in the fluid motion. [ABSTRACT FROM AUTHOR]

This paper discusses two-dimensional heat flow of an incompressible non-Newtonian hydromagnetic fluid over a power-law stretching curved sheet. The energy equation of the flow problem considers a radiative flux influenced by viscous dissipation and surface frictional heating. Lorentz force and Joule heating are taken in the consequence of applied variable magnetic field satisfying solenoidal nature of magnetism. The governing equations are reduced to boundary-layer regime using dimensionless quantities and the resulting PDEs are converted into ODEs by suitable similarity variables. The flow fields; velocity and temperature are computed numerically by implementing Keller-Box shooting method with Jacobi iterative technique. Error analysis is calculated to ensure solutions' convergence. Interesting flow parameters are examined and plotted graphically. Results show that velocity is increased for large number of fluid rheology and opposite effects are recorded for increasing curvature, Lorentz force, and stretching power. Flow past a flat and curved surfaces are substantial in validation of this present work. [ABSTRACT FROM AUTHOR]

This study explores the effects of thermal and magnetohydrodynamics (MHD) on Powell–Eyring fluid with the Cattaneo–Christov heat flux over a curved surface. The mathematical framework regarding the physical problem turn out to a set of nonlinear partial differential equation. The set of governing equations are first reduced into nonlinear ordinary differential equations via appropriate transformations and then analytical solutions of resulting nonlinear differential equations have been obtained by optimal homotopy asymptotic method. The influence of involved parameters such as magnetic parameter, fluid parameter, thermal relaxation parameter, curvature parameter, relaxation parameter, Grashof number, material parameter and Prandtl number are discussed and analyzed in tabular as well as in pictorial form. Finally, a comparison with the existing literature is prepared and an excellent agreement is seen. [ABSTRACT FROM AUTHOR]

The convective–radiative magnetohydrodynamic non‐Newtonian second‐grade fluid boundary layer flow from a curved stretching surface has been scrutinized in the present study. The Reiner–Rivlin second‐grade viscoelastic model is deployed which provides a good approximation for certain magnetic polymers. High temperature invokes the presence of radiative heat transfer, which is simulated with the Rosseland diffusion approximation. Viscous dissipation and Joule heating are also featured in the model and hydrodynamic (velocity) slip at the wall is also incorporated in the boundary conditions. The emerging nonlinear coupled dimensionless transport equations are solved with a Runge–Kutta method and a shooting numerical scheme. The influence of emerging multiphysical flow parameters on the dimensionless profiles is examined with the help of plots for comparative analysis of both non‐Newtonian fluid and Newtonian fluid. The numerical solutions are validated for special cases with existing works. The velocity declines for a higher magnetic field, whereas the reverse trend is noted for the temperature function. The augmentation in the thermal field is noted with increments in radiation parameters. Furthermore, the fluid temperature of the second‐grade fluid is higher with increasing Brinkmann number. The wall slip induces deceleration. Contour plots for streamlines and isotherms are also visualized and analyzed. [ABSTRACT FROM AUTHOR]

This paper discusses the flow of magnetohydrodynamic (MHD) viscous fluid driven by non-linear stretching curved surface. The relevant system of the flow configuration is considered using orthogonal curvilinear geometry in presence of radially varying magnetic field. The governing partial differential equations of the flow problem are reduced into boundary layer regime which are then transformed using similarity variables into ordinary differential equations. The resulting equations of the curved case are not amenable to analytic solutions due to non-linearity of the system. Thus a computational approach through Runge-Kutta fourth order together with the shooting technique is adopted for the numerical solution. The existing solution for flat surface is recovered in validating the present models. The novelty of this work contains the correctness and analytical solution of the existing models over flat surface. The results are interesting and can be useful in polymer dynamics.

This study investigates the flow of heat and mass transport of an incompressible MHD Cross fluid over a nonlinear curved stretching sheet. Heat transport incorporates viscous dissipation, radiative flux, and surface heating, whereas the fluid concentration is distressed with the first-order chemical reaction. A radially varying applied magnetic field is considered to examine the effect of Lorentz force and Ohmic heating. The rheology of the fluid is theoretically modeled and constitute a novel work for the completeness of shear thinning and thickening fluids over curved structure. Similarity method is utilized to reduce the governing system of PDE’s into ODE’s. Numerical computation through Runge-Kutta fourth order with shooting technique is implemented by the first initialized higher-order system into the first ODEs. The behaviors of the flow quantities—velocity, temperature, and concentration—are graphically analyzed against the parameters, including radius of curvature, fluid rheology, radiation, and rate of reactions. The numerical results are validated in comparison with the published results. Studies of Newtonian fluids on flat and curved surfaces are the special cases of this work. The results are useful in material processing and polymer dynamics involving stretchable materials.

This paper discusses the flow of magnetohydrodynamic (MHD) viscous fluid driven by non-linear stretching curved surface. The relevant system of the flow configuration is considered using orthogonal curvilinear geometry in presence of radially varying magnetic field. The governing partial differential equations of the flow problem are reduced into boundary layer regime which are then transformed using similarity variables into ordinary differential equations. The resulting equations of the curved case are not amenable to analytic solutions due to non-linearity of the system. Thus a computational approach through Runge-Kutta fourth order together with the shooting technique is adopted for the numerical solution. The existing solution for flat surface is recovered in validating the present models. The novelty of this work contains the correctness and analytical solution of the existing models over flat surface. The results are interesting and can be useful in polymer dynamics. [ABSTRACT FROM AUTHOR]

A 2-D boundary-layer flow induced by non-linear (quadratic) stretching of a curved surface of an incompressible MHD viscous fluid is investigated. Heat transfer analysis is presented including viscous dissipation and thermal radiation. A radially variable magnetic field is applied that satisfies Maxwell's equation and incorporates the curvature effects. A new similarity variable and similarity transformation are introduced to reduce the governing PDE's into ODE's. A numerical procedure is adopted to find the solution of momentum and energy equations. The numerical scheme is validated with the existing data. The results are illustrated graphically and discussed physically. Comparison with the literature shows a significant improvement compared to existing studies.

• The velocity profiles decay for the higher magnetic factor while augmenting for the higher curvature. • The temperature profiles are enhanced by the higher thermal Biot and Eckert numbers and heat source. • The concentration profiles enhance with the increasing curvature, activation energy, and heat source factors. • The hybrid nanofluid performs better in terms of surface drag, concentration, velocity, and rate of heat transfer. • The velocity and temperature of the Newtonian model are better on a flat surface than they are on a curved one. Scientists are paying close attention to Casson fluids due to their remarkable industrial and technical applications. Among the non-Newtonian substances, Casson fluid is one of the most significant types. Generally, the viscosity becomes zero at infinity shear rate for a shear-diminishing substance with zero-shear rate. In this work, the flow of a sodium alginate–based Casson hybrid nanofluid composed of copper and aluminum oxide nanoparticles is studied. The hybrid nanofluid flow is considered to be magnetically influenced and chemically reactive. Additionally, the effects of the heat source, non-Newtonian heating, thermophoretic, Brownian motion, and activation energy are considered. It is anticipated that stretching curved surface is thermally convective and that there is no mass flow. The mathematical formulation is given in the form of PDEs, which are then converted into ODEs by using suitable similarity variables. The HAM and bvp4c MATLAB function is applied on the converted ODEs to accomplish the semi-analytical and numerical solutions of the modeled equations. By contrasting the new data with those that have already been published, the correctness of current model is confirmed. According to the findings, the hybrid nanofluid over a flat surface resulted in enhancements in velocity, temperature, and concentration compared to its performance on a curved surface. The hybrid nanofluid demonstrated superior performance in terms of temperature, surface drag, concentration, and rate of heat transfer. Moreover, the velocity and temperature of the classical Newtonian model were observed to be higher on the flat surface in contrast to the curved surface. The streamlines become closer with the increasing magnetic factor, while the streamlines become farther apart with the increasing curvature parameter. [ABSTRACT FROM AUTHOR]

This analysis addresses the impact of heat generation and MHD on nanofluid flow near a nonlinear curved surface. For an inclusive and representative analysis most common fluids like ethylene glycol and water are chosen as base fluids and alumina particles are treated as nanoparticles. The alumina particles are considered due to their high conductivity. The mathematical model of nanofluid flow under different assumptions are generated using curvilinear coordinates which gives set of ordinary differential equations. Computational analysis is performed by using "Bvp4c" on computational software MATLAB. It is found that the velocity profile increases by increasing the values of curvature parameter, power law index and volume fraction of nanoparticles for two cases without and with effective of P r numbers. Moreover, the base flow temperature decreases for effective P r number corresponding to both nanofluids while an opposite behaviour occurs for without effective Prandtl number. Furthermore, the graphs are drawn for velocity and temperature for two different cases (with and without effective Prandtl numbers). • Viscous fluid flow near the non-linear curve surface are investigated. • Viscosity at initial steady state is constant considered. • Heat generation is considered energy equation. • Alumina particles are considered due to their high conductivity. • Relationship between kinematic viscosity and intermolecular force is described. [ABSTRACT FROM AUTHOR]

This work presents a numerical investigation of viscous nanofluid flow over a curved stretching surface. Single-walled carbon nanotubes were taken as a solid constituent of the nanofluids. Dynamic viscosity was assumed to be an inverse function of fluid temperature. The problem is modeled with the help of a generalized theory of Eringen Micropolar fluid in a curvilinear coordinates system. The governing systems of non-linear partial differential equations consist of mass flux equation, linear momentum equations, angular momentum equation, and energy equation. The transformed ordinary differential equations for linear and angular momentum along with energy were solved numerically with the help of the Keller box method. Numerical and graphical results were obtained to analyze the flow characteristic. It is perceived that by keeping the dynamic viscosity temperature dependent, the velocity of the fluid away from the surface rose in magnitude with the values of the magnetic parameter, while the couple stress coefficient decreased with rising values of the magnetic parameter. [ABSTRACT FROM AUTHOR]