Differential transform solution for Hall and ion‐slip effects on radiative‐convective Casson flow from a stretching sheet with convective heating

Magnetohydrodynamic (MHD) materials processing is becoming increasingly popular in the 21st century as it offers significant advantages over conventional systems, including improved manipulation of working fluids, reduction in wear, and enhanced sustainability. Motivated by these developments, the present work develops a mathematical model for Hall and ion‐slip effects on non‐Newtonian Casson fluid dynamics and heat transfer toward a stretching sheet with a convective heating boundary condition under a transverse magnetic field. The governing conservation equations for mass, linear momentum, and thermal (energy) are simplified with the aid of similarity variables and Ohm's law. The emerging nonlinear‐coupled ordinary differential equations are solved with an analytical technique known as the differential transform method. The impact of different emerging parameters is presented and discussed with the help of graphs and tables. Generally, aqueous electroconductive polymers are considered, for which a Prandtl number of 6.2 is employed. With increasing Hall parameter and ion‐slip parameter, the flow is accelerated, whereas it is decelerated with greater magnetic parameter and rheological (Casson) fluid parameter. Skin friction is also decreased with greater magnetic field effect, whereas it is increased with stronger Hall parameter and ion‐slip parameter values.     

Effects of chemical reaction,Soret and Lorentz force on Casson fluid flow past an exponentially accelerated vertical plate: A comprehensive analysis

The aim of the current study is to explore the effects of heat and mass transfer on unsteady chemically reacted Casson liquid flow over an exponentially accelerated vertical plate in a porous medium. It is assumed that the bounding plate has varying temperatures as well as concentrations in a porous medium under a uniform magnetic field. This phenomenon is modeled in the form of a system of partial differential equations (PDEs) with boundary conditions. The governing dimensionless PDEs are solved using Laplace transform method for velocity, temperature, and concentration. The impact of nondimensional parameters, which are controlling the flow like Casson parameter, Soret number, magnetic parameter, heat generation parameter, Prandtl number, radiation parameter, and Schmidt number is analyzed through graphs. The incremental values of the Casson fluid parameter lead to a reduction in velocity and discovered that for large values of the Casson parameter, the fluid is near to the Newtonian fluid. Also, the Sherwood number increases with enhancing dissimilar estimators of the Schmidt and Soret numbers. A comparison has been made with the published work (Kataria et al.) for a particular case, which was in good agreement.     

Influences of Soret and Dufour numbers on mixed convective and chemically reactive Casson fluids flow towards an inclined flat plate

The purpose of this study is to examine the magnetohydrodynamic mixed convection Casson fluid flow over an inclined flat plate along with the heat source/sink. The present flow problem is considered under the assumption of the chemical reaction and thermal radiation impacts along with heat and mass transport. The leading nonlinear partial differential equations of the flow problem were renovated into the nonlinear ordinary differential equations (ODEs) with the assistance of appropriate similarity transformations and then we solved these ODEs with the employment of the bvp4c technique using the computational software MATLAB. The consequences of numerous leading parameters such as thermophoretic parameter, local temperature Grashof number, solutal Grashof number, suction parameter, magnetic field parameter, Prandtl number, chemical reaction parameter, Dufour number, Soret number, angle of inclination, radiation parameter, heat source/sink, and Casson parameter on the fluid velocity, temperature, and concentration profiles are discoursed upon  and presented through different graphs. Some important key findings of the present investigation are that the temperature of the Casson fluid becomes lower for local temperature Grashof number and solutal Grashof number. It is initiated that the Casson fluid parameter increases the velocity of the fluid whereas the opposite effect is noticed in the temperature profile. Higher estimation of Prandtl number and magnetic parameter elevated the Casson fluid concentration. Finally, the skin friction coefficient, Nusselt number, and Sherwood number are calculated and tabulated. It is also examined that the Nusselt number is weakened for both the Dufour number and Soret number but the skin fraction coefficient is greater for both the Dufour number and Soret number.     

Magnetized squeezed flow of time‐dependent Prandtl‐Eyring fluid past a sensor surface

The present numerical investigation describes the influence of a transverse magnetic field on the heat and mass transfer characteristics of time‐dependent squeezed flow of Prandtl‐Eyring fluid past a horizontal sensor surface. The current physical problem is modeled based on the considered flow configuration. Also, the present problem is analyzed under the influence of Lorentz forces, to explore the impact of a magnetic field on the flow behaviour. The considered physical problem in the present study gives highly nonlinear coupled time‐dependent, two‐dimensional partial differential equations. The governing flow equations are reduced to the system of nonlinear ordinary differential equations by imposing the suitable similarity transformations on the laws of motion. Due to the inadequacy in the analytical methods, the present problem is solved by using the Runge‐Kutta fourth order integration scheme with shooting method. The flow and heat transfer behaviour of various control parameters are studied and presented in terms of graphs and tables. From the current investigation it is noticed that, the increasing magnetic parameter enhances the velocity field and diminishes the temperature profile in the flow region. Also, the magnifying permeable velocity parameter decreases the temperature field. The present similarity solutions are found to be in good agreement with previously published results.     

Influence of homogeneous‐heterogeneous reactions and induced magnetic field on the nonlinear thermal convective radiative Jeffrey liquid flow with heat source/sink

An analysis has been carried out to investigate the effect of homogeneous‐heterogeneous reactions and induced magnetic field on the unsteady two‐dimensional incompressible nonlinear thermal convective velocity slip flow of a Jeffrey fluid in the presence of nonlinear thermal radiation and heat source/sink. We assumed that the flow is generated due to injection at the lower plate and suction at the upper plate. We obtained a numerical solution for the reduced nonlinear governing system of equations via the shooting technique with fourth‐order Runge‐Kutta integration. We plotted the graphs for various nondimensional parameters, like Deborah number, heat source/sink parameter, nonlinear convection parameter, nonlinear radiation parameter, magnetic Reynolds number, Strommer's number, velocity slip parameter, strengths of homogeneous, heterogeneous reaction parameters and skin friction over the nondimensional flow, temperature, concentration profiles and magnetic diffusivity fields. Also, we calculated the numerical values of boundary properties, such as the skin friction and heat transfer rate. We noticed that the temperature of the fluid is enhanced with the radiation parameter, whereas the concentration decreases with increase of the magnetic Reynolds number. The present results have good agreement with published work for the Newtonian case.     

Dissipative heat for the Casson fluid flow past an expanding cylindrical surface

A non-Newtonian model is developed by considering the flow of non-Newtonian Casson fluid past an expanding cylinder embedded in a porous medium. The novelty arises because of the conjunction of dissipative heat, and the additional heat source that enriches the heat transport phenomenon significantly. The application of the study is vital due to the flow of blood through the artery, a physiological study. Therefore, the study of Casson fluid plays an important role. The nonlinear partial differential equations that appeared in the formulation are now renovated to the coupled nonlinear ordinary differential equations. However, a numerical technique associated with shooting-based followed by Runge–Kutta fourth-order is employed for the solution of these transformed equations. The uniqueness of diverse pertinent parameters on the flow phenomena is scrutinized through graphs and numerically simulated results presented in tables. The important observations are as follows; the magnetic parameter and permeability augment the shear rate coefficients, whereas the Casson parameter rendered the opposite impact. Furthermore, the non-Newtonian Casson parameter retards the fluid temperature, and the curvature parameter significantly enhances it.     

Unsteady squeezed Casson nanofluid flow by considering the slip condition and time-dependent magnetic field

The present flow problem investigates the incompressible and squeezed flow between two parallel plates. The mathematical formulation includes the constitutive equations of Casson nanofluid, which is treated as a lubricant. Brownian movement, slip condition, and thermophoretic mechanisms are also considered. The formulated model is tackled by Runge-Kutta-Fehlberg fourth- and fifth-order numerical scheme joint with shooting criteria. Momentum, thermal, and mass species behavior is executed by plots of distinct physical constraints values. It is found that the velocity component is boosted for the larger squeezed parameter whereas the temperature component shows the same behavior for Brownian motion and thermophoresis parameter. Near the lower half of the plate, velocity increases for the slip parameter whereas it decreases for magnetic and Casson parameters.     

Simulation of unsteady natural convection flow of a Casson viscoplastic fluid in a square enclosure utilizing a MAC algorithm

Non‐Newtonian fluids are increasingly being deployed in energy systems and materials processing. Motivated by these developments, in the current study, a numerical simulation is performed on two‐dimensional, unsteady buoyancy‐driven flow in a square cavity filled with non‐Newtonian fluid (Casson liquid). The enclosure geometry features vertical isothermal walls (with one at higher temperature than the other) and thermally insulated horizontal walls. The conservation equations for mass, momentum, and energy are normalized via appropriate transformations and the resulting dimensionless partial differential boundary value problem is solved computationally with a marker and cell algorithm, which features a finite difference scheme along with a staggered grid system. The projection method is employed to evaluate the pressure term. Extensive visualizations of the impact of emerging physical parameters (Rayleigh number and Casson viscoplastic parameter) on streamline and isotherm distributions in the cavity are presented for fixed Prandtl number. Nusselt number, that is, heat transfer rate, is increased with rising values of the Casson viscoplastic fluid parameter for any value of Rayleigh number. The density of streamlines increases with increasing values of Casson viscoplastic fluid parameter upto 1. Overall, the Casson fluid parameter plays a vital role in controlling the convective heat transfer within the enclosure. The computations are relevant to hybrid solar collectors, materials fabrication (polymer melts), etc.     

Slip Flow of Casson Rheological Fluid Under Variable Thermal Conductivity with Radiation Effects

This paper investigates the radiation and chemical reaction effects on Casson non‐Newtonian fluid towards a porous stretching surface in the presence of thermal and hydrodynamic slip conditions. The governing boundary layer conservation equations are normalized into nonsimilar form using similarity transformations. A numerical approach is applied to the resultant equations. The behavior of the velocity, temperature, concentration, as well as the skin friction coefficient, Nusselt number, and Sherwood number for various governing physical are discussed. Increasing the radiation parameter decreases the temperature. An increase in the rheological parameter (Casson parameter) induces an elevation in the skin friction coefficient, the heat and mass transfer rates. The larger the β values the closer the fluid is in behavior to a Newtonian fluid and further departs from plastic flow. Temperature of the fluid was found to decrease with increasing values of the Casson rheological parameter. The most important non‐Newtonian fluid possessing a yield value is the rheological Casson fluid, which finds significant applications in polymer processing industries, biomechanics, and chocolate food processing.     

Impact of aligned MHD flow with inclined outer velocity for a casson nanofluid over a stretching sheet

The scope of the introduced study focuses on the analysis of heat as well as flow transportation in an oblique Casson nanofluid in the presence of an aligned magnetic field. The fluid is supposed to impinge obliquely on a sheet that stretches in both directions of the x‐axis with heat generation. The moulded partial differential equations computed numerically with the shooting procedure by adopting the Runge Kutta Fehlberg method. The change in the behaviour of the emerging fluid parameters are described graphically and their results are shows in tables. The outcomes disclosed that the fluid velocity declined for Casson fluid parameter and the aligned angle of the magnetic field. In addition, with the increase in the Casson fluid parameter and aligned angle of magnetic field, the fluid temperature and concentration rise. The outcomes of this study may be beneficial to control the rate of heat and mass transportation as well as controlling fluid velocity in industry to obtain a final product of the desired quality.     

Heat Transfer in a Casson Rheological Fluid from a Semi‐infinite Vertical Plate with Partial Slip

The laminar boundary layer flow and heat transfer of Casson non‐Newtonian fluid from a semi‐infinite vertical plate in the presence of thermal and hydrodynamic slip conditions is analyzed. The plate surface is maintained at a constant temperature. Increasing velocity slip induces acceleration in the flow near the plate surface and the reverse effect further from the surface. Increasing velocity slip consistently enhances temperatures throughout the boundary layer regime. An increase in thermal slip parameter strongly decelerates the flow and also reduces temperatures in the boundary layer regime. An increase in the Casson rheological parameter acts to elevate considerably the skin friction (non‐dimensional wall shear stress) and this effect is pronounced at higher values of tangential coordinate. Temperatures, however, are very slightly decreased with increasing values of Casson rheological parameter. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21115     

Zero‐mass flux and Cattaneo–Christov heat flux through a Prandtl non‐Newtonian nanofluid in Darcy–Forchheimer porous space

The Darcy–Forchheimer Prandtl fluid flow due to moving sheet is described here. The familiar energy transfer model, namely, the Cattaneo–Christov model of heat transportation, is adopted under thermal radiation phenomenon. The Prandtl non‐Newtonian nanofluid is accounted as a functioning fluid. The functioning fluid flows in Darcy–Forchheimer porosity space. The boundary‐layer and similarity variables are executed to reframe the mathematical expressions into simplified and single independent variable. Numerical solutions of nonlinear dimensionless expressions are calculated. The variations of distinct constraints on important quantities are demonstrated through tabular and pictorial forms. It is visualized that the velocity of non‐Newtonian nanofluid is enhanced significantly by incrementing the elastic parameter. Improving the thermophoretic and Brownian movement parametric values leads to higher profile of Prandtl nanofluid temperature.     

Homogeneous–heterogeneous reactions in flow past a horizontal circular cylinder with an induced magnetic field and nonlinear thermal radiation

In this study, we investigate the steady, two‐dimensional, incompressible viscous boundary layer flow of an electrically conducting Casson fluid over a horizontal circular cylinder. The cylinder is impermeable and the flow is assumed to be subject to homogeneous–heterogeneous reactions. The homogeneous–heterogeneous reactions are also assumed to have unequal diffusion coefficients. The novelty in this study is in the consideration of a nonlinear radiative flux together with Joule heating and an induced magnetic field. The magnetodynamic pressure gradient in induced magnetic flows is important as it gives insights into the boundary layer characteristics. The flow velocity and the magnetic field in the free stream are assumed to be uniform and directed vertically over the cylinder. The partial differential equations are solved using the bivariate spectral quasi‐linearization method. An analysis and comparison of results with existing literature are provided. Among the findings, we show, inter alia, that the reactants dominate while the autocatalysts have a negligible impact on the flow progression. The skin friction coefficient decreases with an increase in the Casson parameter and increases when the Joule heating parameter is increased. The rate of heat transfer increases with increasing the Casson parameter and decreases when the Joule heating parameter is increased.     

Thermosolutal convective non-Newtonian radiative Casson fluid transport over a vertical plate propagated by Arrhenius kinetics with heat source/sink

In the current study, a mathematical formulation is developed by combining the non-Newtonian (Casson) fluid model to simulate the thermosolutal free convection radiative flow over a vertical surface. The current flow model is formulated with a heat sink/source and radiation driven by Arrhenius kinetics. The basic flow equations are transmuted into a nondimensional form via similarity transformations for which numerical simulations are performed utilizing the Runge-Kutta-Fehlberg method with shooting technique. The results obtained for velocity, energy, and species mass concerning various flow parameters are presented graphically. Computed results for skin friction, Nusselt number, and Sherwood number are tabulated. The results have been verified for limited cases by comparing with various investigations, revealing excellent accuracy. The detailed geometry reveals that an increase in the activation energy enhances the flow velocity and heat transport in the Casson fluid system due to exothermic heat reaction. With the increase of the Frank-Kamenetskii term, there is a substantial rise in temperature distribution and a decrease in concentration profiles due to high Arrhenius exothermic process, which revealed that the presence of Arrhenius kinetics is more effective to improve heat transportation phenomenon. Enhancement of the heat source/sink term completely boosts heat distribution. Rise in Radiation parameter, temperature field increases by reducing heat dissipation to the ambient.     

Effect of nonlinear partial slip and thermal radiation on Oldroyd 8‐constant fluid in a channel with convective boundary condition

This investigation deals with the effects of nonlinear slip, nonlinear thermal radiation, and non‐Newtonian flow parameters on heat transfer of an incompressible magnetohydrodynamic steady flow of an Oldroyd 8‐constant fluid through two parallel infinite plates with convective cooling. The Rosseland approximation is adopted to simulate the radiation effects. Heat exchange with the surrounding at the surfaces is assumed to obey Newton's law of cooling. The system of coupled and highly nonlinear ordinary differential equations governing the model is solved numerically using the method of weighted residual. The combined effects of non‐Newtonian flow parameters, velocity slip parameter, magnetic field parameter, Biot numbers, thermal radiation on the fluid velocity, temperature distributions, skin friction, and the Nusselt number are presented graphically and discussed. It is found that the velocity slip has an increasing effect on the fluid velocity and temperature profiles. For larger values of the thermal radiation parameter, the temperature profile and the Nusselt number are noticed to be increased.     

Hydromagnetic non‐Newtonian nanofluid transport phenomena from an isothermal vertical cone with partial slip: Aerospace nanomaterial enrobing simulation

In this article, the combined magneto‐hydrodynamic heat, momentum, and mass (species) transfer in external boundary layer flow of Casson nanofluid from a vertical cone surface with convective conditions under an applied magnetic field is studied theoretically. The effects of Brownian motion and thermophoresis are incorporated in the model in the presence of both heat and nanoparticle mass transfer convective conditions. The governing partial differential equations (PDEs) are transformed into highly nonlinear, coupled, multidegree, nonsimilar PDEs consisting of the momentum, energy, and concentration equations via appropriate nonsimilarity transformations. These transformed conservation equations are solved subject to appropriate boundary conditions with a second‐order, accurate finite difference method of the implicit type. The influences of the emerging parameters, that is, magnetic parameter (M), Casson fluid parameter (β), Brownian motion parameter (Nb), thermophoresis parameter (Nt), Lewis number (Le), Prandtl number (Pr), velocity slip (S_f) and thermal slip (S_T) on velocity, temperature, and nanoparticle concentration distributions is illustrated graphically and interpreted at length. Validation of solutions with a Nakamura tridiagonal method has been included. The study is relevant to enrobing processes for electrically conductive nanomaterials, of potential use in aerospace and other industries.     

Generalized differential quadrature analysis of unsteady three‐dimensional MHD radiating dissipative Casson fluid conveying tiny particles

It is worth remarking that little is known about generalized differential quadrature analysis of three‐dimensional flow of non‐Newtonian Casson fluid in the presence of Lorentz force, thermal radiation, haphazard motion of tiny particles, thermomigration of these tiny particles due to temperature gradient, heat source, significant conversion of kinetic energy into internal energy, first‐order chemical reaction, convectively heated horizontal wall, and zero nanoparticles mass flux at the stretching surface. The revised form of Buongiorno's nanofluid model accounted for significant influences of Brownian motion and thermophoresis. The similarity solution was complemented with a powerful collocation procedure based on the generalized differential quadrature method and Newton–Raphson iterative scheme to achieve accuracy and convergent outcomes. The numerical effects disclose that the Casson nanofluid parameter slows down the axial velocities in both directions. Also, the unsteadiness parameter tends to decline generally the temperature throughout the medium and decrease particularly the concentration profile away from the stretching surface. These examinations are applicable in the field of biomechanics, polymer processing, and for characterizing the cement slurries.     

MHD,thermal radiation,thermophoresis and Soret–Dufour mechanism contributions on unsteady motion of Casson fluid over a semi-infinite porous vertical plate

This paper examined the contribution of MHD, thermal radiation, thermophoresis and Soret–Dufour mechanism on unsteady motion of Casson non-Newtonian fluid. The flow model which resulted in partial differential equations (PDES) was transformed into a dimensionless form of PDES using suitable quantities. The contributions of controlling flow parameters were graphically presented for velocity, temperature, and concentration. The quantities of engineering interest were calculated for flow parameters and presented using table. A considerable value of Soret parameter was noticed to elevate the skin friction and Sherwood number. Impact of the magnetic parameter has great impact on the motion of Casson fluid by lowering its motion. This is because as the value of magnetic parameter increases the Lorentz force added more strength and hereby slow down the motion of an electrically conducting fluids. The present outcomes were examined with previously published work and was in conformity with each other.     

Numerical modelling of second‐grade fluid flow past a stretching sheet

The present numerical study reports the chemically reacting boundary layer flow of a magnetohydrodynamic second‐grade fluid past a stretching sheet under the influence of internal heat generation or absorption with work done due to deformation in the presence of a porous medium. To distinguish the non‐Newtonian behaviour of the second‐grade fluid with those of Newtonian fluids, a very popularly known second‐grade fluid flow model is used. The fourth order momentum equation with four appropriate boundary conditions along with temperature and concentration equations governing the second‐grade fluid flow are coupled and highly nonlinear in nature. Well‐established similarity transformations are efficiently used to reduce the dimensional flow equations into a set of nondimensional ordinary differential equations with the necessary conditions. The standard bvp4c MATLAB solver is effectively used to solve the fluid flow equations to get the numerical solutions in terms of velocity, temperature, and concentration fields. Numerical results are obtained for a different set of physical parameters and their behaviour is described through graphs and tables. The viscoelastic parameter enhances the velocity field whereas the magnetic and porous parameters suppress the velocity field in the flow region. The temperature field is magnified for increasing values of the heat source/sink parameter. However, from the present numerical study, it is noticed that the flow of heat occurs from sheet to the surrounding ambient fluid. Before concluding the considered problem, our results are validated with previous results and are found to be in good agreement.     

Steady MHD Casson Ohmic heating and viscous dissipative fluid flow past an infinite vertical porous plate in the presence of Soret,Hall, and ion‐slip current

In the present study, the influence of Hall and ion‐slip current on steady magnetohydrodynamics mixed convective, Ohmic heating, and viscous dissipative Casson fluid flow over an infinite vertical porous plate in the presence of Soret effect and chemical reaction are investigated. The modeling equations are transformed into dimensionless equations and then solved analytically through the multiple regular perturbation law. Computations are performed graphically to analyze the behavior of fluid velocity, temperature, concentration, skin friction, Nusselt number, and Sherwood number on the vertical plate with the difference of emerging physical parameters. This study reflects that the incremental values of Casson fluid parameter and Schmidt number lead to reduction in velocity. However, fluid velocity rises due to enhancement of ion‐slip parameter but an opposite effect is observed in case of Hall parameter. In addition, the Sherwood number declines with enhancing dissimilar estimators of the chemical reaction, Schmidt number, as well as Soret number.