Hydromagnetic mixed convection unsteady radiative Casson fluid flow towards a stagnation-point with chemical reaction,induced magnetic field,Soret effect,and convective boundary conditions

This article presents the two-dimensional mixed convective MHD unsteady stagnation-point flow with heat and mass transfer on chemically reactive Casson fluid towards a vertical stretching surface. This fluid flow model is influenced by the induced magnetic field, thermal radiation, viscous dissipation, heat absorption, and Soret effect with convective boundary conditions and solved numerically by shooting technique. The calculations are accomplished by MATLAB bvp4c. The velocity, induced magnetic field, temperature, and concentration distributions are displayed by graphs for pertinent influential parameters. The numerical results for skin friction coefficient, rate of heat, and mass transfer are analyzed via tables for different influential parameters for both assisting and opposing flows. The results reveal that the enhancement of the unsteadiness parameter diminishes velocity and induced magnetic field but it rises temperature and concentration distributions. Moreover, higher values of magnetic Prandtl number enhance Nusselt number and skin friction coefficient, but it has the opposite impact on Sherwood number. We observe that the amplitude is higher in assisting flow compared to opposing flow for skin friction coefficient and Nusselt number whereas opposite trends are noticed for Sherwood number. Our model will be applicable to various magnetohydrodynamic devices and medical sciences.     

Gyrotactic microorganisms bioconvection in combined convective magnetohydrodynamic Casson nanofluid flow over a vertically surfaced saturated porous media with variable viscosity

The current article focuses on mass and thermal transfer analysis of a two-dimensional immovable combined convective nanofluid flow including motile microorganisms with temperature-dependent viscosity on top of a vertical plate through a porous medium, and a model has been developed to visualize the velocity slip impacts on a nonlinear partial symbiotic flow. The governed equations include all of the above physical conditions, and suitable nondimensional transfigurations are utilized to transfer the governed conservative equations to a nonlinear system of differential equations and obtain numerical solutions by using the Shooting method. Numerical studies have been focusing on the effects of intricate dimensionless parameters, namely, the Casson fluid parameter, Brownian motion parameter, thermophoresis parameter, Peclet number, bioconvection parameter, and Rayleigh number, which have all been studied on various profiles such as momentum, thermal, concentration, and density of microorganisms. The concentration boundary layer thickness and density of microorganisms increased as the Casson fluid parameter, Brownian and thermophoresis parameters increased, whereas the bioconvection parameter, Peclet number, and Rayleigh number increased. The thermal boundary layer thickness, concentration boundary layer thickness, and density of microorganisms all decreased. The velocity distribution decreases as the Peclet number, bioconvection, and thermophoresis parameters rise but rises as the Rayleigh number, Brownian motion parameter, and Casson fluid parameter rise. These are graphed via plots along with divergent fluid parameters.     

Radiative flow of micropolar nanofluid accounting thermophoresis and Brownian moment

This article describes the Brownian motion and thermophoresis aspects in nonlinear flow of micropolar nanoliquid. Stretching surface with linear velocity creates the flow. Energy expression is modeled subject to consideration of thermal radiation phenomenon. Effect of Newtonian heating is considered. The utilization of transformation procedure yields nonlinear differential systems which are computed through homotopic approach. The important features of several variables like material parameter, conjugate parameter, Prandtl number, Brownian motion parameter, radiation parameter, thermophoresis parameter and Lewis number on velocity, micro-rotation velocity, temperature, nanoparticles concentration, surface drag force and heat and mass transfer rates are discussed through graphs and tables. The presented analysis reveals that the heat and mass transfer rates are enhanced for higher values of radiation and Brownian motion parameters. Present computations are consistent with those of existing studies in limiting sense.     

Radiation and slip effects on MHD point flow of nanofluid towards a stretching sheet with melting heat transfer

In the present paper, the melting heat transfer of a nanofluid over a stretching sheet is investigated. Magnetohydrodynamic stagnation point flow with thermal radiation and slip effects is considered for this study. The governing model of the flow is solved by Runge–Kutta fourth-order method using appropriate similarity transformations. Temperature and velocity fields are presented for various flow pertinent parameters. Nondimensional physical parameters such as Prandtl number, radiation parameter, Brownian motion parameter, Lewis number, thermophoresis parameter, magnetic parameter, and melting parameter on fluid velocity, heat, concentration, skin friction, Sherwood number, and Nusselt number are presented graphically and discussed numerically. Heat transfer rate can be increased by increasing slip, melting, or radiation parameter. Mass transfer increases for greater values of melting parameter or slip parameter while radiation parameter shows the opposite impact on mass transfer.     

Comparative analysis of a Sisko nanofluid over a stretching cylinder through a porous medium

The present article examines the Sisko nanofluid flow and heat transfer through a porous medium due to a stretching cylinder using Buongiorno's model for nanofluids. Suitable similarity transformations are used to transform the governing boundary layer equations of fluid flow into nonlinear ordinary differential equations. The finite difference method is used to solve coupled nonlinear differential equations with MATLAB software. The impact of different parameters viz., the Sisko material parameter, porosity parameter, curvature parameter, thermophoresis parameter, and Brownian diffusion parameter on the velocity and temperature distribution are presented graphically. Moreover, the effect of the involved parameters on the heat transfer rate is also studied and presented through table values. It is noticed from the numerical values that the porosity parameter reduces the velocity while enhancing the temperature. The curvature parameter enhances the velocity throughout the fluid regime and reduces the temperature near the surface while enhancing the temperature far away from the surface. The study reveals that the thermophoresis and Brownian diffusion parameters that characterize the nanofluid flow reduce the wall heat transfer rate, while the curvature parameter enhances it. This investigation of wall heating/cooling has essential applications in solar porous water absorber systems, chemical engineering, metallurgy, material processing, and so forth.     

MHD Eyring–Powell nanofluid past over an unsteady exponentially stretching surface with entropy generation and thermal radiation

This study's primary objective is to analyze the entropy generation in an unsteady magnetohydrodynamics (MHD) Eyring–Powell nanofluid flow. A surface that stretched out exponentially induced flow. The influences of thermal radiation, thermophoresis, and Brownian motion are also taken into consideration. The mathematical formulation for the transport of mass, momentum, and heat described by a set of partial differential equation is used, which is then interpreted by embracing the homotopy analysis method and with a fourth-order precision program (bvp4c). Graphical results display the consequences of numerous parameters on velocity, temperature, concentration, and entropy generation. Moreover, escalating amounts of the magnetic parameter, thermal radiation parameter, Reynolds number, and Brinkman number improve the entropy profile of the nanofluid. The rate of heat flux and the mass flux conspicuously improves for non-Newtonian fluid as compared to Newtonian fluid.     

Heat and Mass Transfer Flow of a Nanofluid over an Inclined Plate under Enhanced Boundary Conditions with Magnetic Field and Thermal Radiation

This article presents the magnetohydrodynamic boundary layer flow, heat and mass transfer characteristics of a nanofluid over an inclined porous vertical plate with thermal radiation and chemical reaction. The new enhanced concentration boundary condition on the surface of the wall is considered in this analysis. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations using the similarity variables and are solved numerically using the finite element method. The effect of key parameters such as magnetic parameter (M), buoyancy ratio (Nr), Prandtl number (Pr), thermal radiation (R), Brownian motion (Nb), thermophoresis (Nt), Lewis number (Le), and chemical reaction parameter (Cr) on velocity, temperature, and concentration distributions is discussed in detail and the results are shown graphically. Furthermore, the impact of these parameters on skin‐friction coefficient, Nusselt number, and Sherwood number is also investigated and the results are shown in tabular form. The developed algorithm is validated with works published previously and was found to be in good agreement. The thermal boundary layer thickness is elevated, whereas the solutal boundary layer thickness retards with the improving values of the Brownian motion parameter (Nb). The rates of nondimensional temperature and concentration both decelerate with higher values of the thermophoresis parameter (Nt).     

Second law analysis of pseudo-plastic nanofluid stream past a stretching sheet with a sliding consequence

The entropy generation (second law of thermodynamics) analysis of gyrotactic microorganism flow of power-law nanofluid with slip effects and combined effect of heat and mass transfer past a stretching sheet has been studied. The flow is maintained with Lorentz force and thermal radiation. The governing nonlinear partial differential equations are transformed into ordinary differential equations using similarity transformations. The impact of different physical parameters, such as convective bouncy parameter, power-law parameter, Brownian motion parameter, thermophoresis parameter, and slip parameter for velocity and temperature on the entropy generation number (Ns) are plotted graphically with the help of MATLAB built in bvp4c solver technique. Further, the uniqueness of this study is to find out the ratios of various irreversibilities due to thermal and mass diffusions, momentum diffusion, and microorganism over the total entropy generation rate. Our results showed that the power-law parameter and Brownian motion parameter influenced entropy generation positively. The slip parameter for velocity and temperature and the thermophoresis parameter helps to reduce the entropy production.     

Effects of thermal radiation on micropolar fluid flow and heat transfer over a porous shrinking sheet

The effects of thermal radiation on the flow of micropolar fluid and heat transfer past a porous shrinking sheet is investigated. The self-similar ODEs are obtained using similarity transformations from the governing PDEs and are then solved numerically by very efficient shooting method. The analysis reveals that for the steady flow of micropolar fluid, the wall mass suction needs to be increased. Dual solutions of velocity and temperature are obtained for several values of the each parameter involved. For increasing values of the material parameter K, the velocity decreases for first solution, whereas, for second solution it increases. Due to increase of thermal radiation, the temperature and thermal boundary layer thickness reduce in both solutions and also the heat transfer from the sheet enhances with thermal radiation.     

Significance of thermal radiation on dusty fluid flow over a stretching rotating disk with convective boundary condition

This paper explores the flow of dusty fluid over a stretching rotating disk with thermal radiation. Further, the convective boundary condition is considered in this modeling. The described governing equations are reduced to ordinary differential equations by using apt similarity transformations and then they are numerically solved using Runge–Kutta–Fehlberg-45 scheme. To gain a clear understanding of the current boundary layer flow problem, the graphical results of the velocity and thermal profiles, shear stresses at the disk, and Nusselt number are drawn. Results reveal that the increase in the value of the porosity parameter reduces the velocity of both particle and fluid phases. The increase in the value of the Biot number improves the temperature gradient of both particle and fluid phases. The rise in the value of the radiation parameter advances the heat transference of both phases. The rise in the value of the Biot number improves the rate of heat transfer. Finally, increasing the value of the radiation parameter improves the rate of heat transfer.     

Radiation and slip effects on MHD Maxwell nanofluid flow over an inclined surface with chemical reaction

The numerical solutions of the upper-convected Maxwell (UCM) nanofluid flow under the magnetic field effects over an inclined stretching sheet has been worked out. This model has the tendency to elaborate on the characteristics of “relaxation time” for the fluid flow. Special consideration has been given to the impact of nonlinear velocity slip, thermal radiation and heat generation. To study the heat transfer, the modified Fourier and Fick's laws are incorporated in the modeling process. The mass transfer phenomenon is investigated under the effects of chemical reaction, Brownian motion and thermophoresis. With the aid of the similarity transformations, the governing equations in the ordinary differential form are determined and then solved through the MATLAB's package “bvp4c” numerically. This study also brings into the spotlight such crucial physical parameters, which are inevitable for describing the flow and heat transfer behavior. This has been done through graphs and tables with as much precision and exactitude as is possible. The ascending values of the magnetic parameter, the Maxwell parameter and the angle of the inclined stretching sheet cause decay in the dimensionless velocity while an assisting behavior of the thermal and concentration buoyancy parameters is noticed.     

Significance of heat source/sink on the radiative flow of Cross nanofluid across an exponentially stretching surface towards a stagnation point with chemical reaction

A numerical review on magnetohydrodynamics radiative motion of Cross nanofluid across an exponentially stretchable surface near stagnation point with varying heat source/sink is addressed. Brownian movement and thermophoretic impacts are assumed. The governing equations for this study are first altered as a system of ordinary differential equations by similarity transformation. With an aid of the Runge–Kutta 4th order mechanism together with the shooting procedure, the impacts of several pertinent parameters including chemical reaction on regular profiles (velocity, temperature, and concentration) are explicated. The consequences of the same parameters on surface drag force, transfer rates of heat, and mass are visualized in tables. From the analysis, it was noticed that the magnetic field parameter enhances the temperature and decreases the velocity of the Cross nanofluid. Also, fluid temperature is an increasing function with thermal radiation and nonuniform heat source/sink. The rate of heat transfer is increased with thermophoresis and diminished with Brownian motion. Sherwood's number is diminished with Brownian motion but it was boosted up with thermophoresis. The present results are compared with published results and those are in agreement.     

Effects of heat and mass transfer on MHD nonlinear free convection non-Newtonian fluids flow embedded in a thermally stratified porous medium

This communication examines heat alongside mass transport in a nonlinear free convection magnetohydrodynamics (MHD) non-Newtonian fluid flow with thermal radiation and heat generation deep-rooted in a thermally stratified penetrable medium. The Casson and Williamson fluid considered in this communication flos simultaneously across the boundary layer and are mixed together. The model of heat alongside mass transport is set up with chemical reaction and thermal radiation alongside heat generation to form a system of partial differential equations (PDEs). Appropriate similarity variables are used to simplify the PDEs to obtain systems of coupled ordinary differential equations. An efficiently developed numerical approach called the spectral homotopy analysis method was used in providing solutions to the transformed equations. A large value of Casson term is observed to degenerate the velocity plot while the Williamson parameter enhances the velocity profile. The parameter of thermal stratification is found to enhance the rate of heat transport within the boundary layer. An incremental value of the magnetic parameter declines the velocity of the fluid and the entire boundary layer thickness. The present result was compared with previous studies and was seen to be in good agreement.     

Numerical study of activation energy and thermal radiation effects on Oldroyd-B nanofluid flow using the Cattaneo–Christov double diffusion model over a convectively heated stretching sheet

This paper investigates a theoretical model of a mixed convective Oldroyd-B nanofluid with thermal radiation and activation energy effects. A thorough analysis is done by employing the nonhomogeneous Buongiorno model in the presence of velocity slip and suction. The surface is porous in nature, and nanoparticle mass flux is maintained passively at the surface. The thermal and concentration equations are modeled with the Cattaneo–Christov theory of heat and mass flux, respectively. Proper transformations are utilized for the conversion of transport equations and boundary conditions. The similarity solution is obtained through a numerical approach by utilizing the Runge–Kutta–Fehlberg method and shooting technique. The vital outcomes of this study and the influence of controlling parameters on the flow field, temperature, and concentration profiles are discussed graphically and in a tabular manner. Furthermore, a detailed discussion is provided to explain the results physically. The velocity of the nanofluid increases when the porosity parameter is increased, and temperature decreases with increasing thermal relaxation parameter. The outcomes elucidate that the suction parameter, thermal radiation parameter, and thermal relaxation parameter are positively correlated with the heat transfer coefficient. The result of passive control of nanoparticles at the surface is that the Brownian motion parameter has no influence on the temperature of the Oldroyd-B nanofluid flow and rate of heat transfer at the surface.     

Effects of thermal radiation and variable fluid viscosity on free convective flow and heat transfer past a porous stretching surface

Free convective boundary layer flow and heat transfer of a fluid with variable viscosity over a porous stretching vertical surface in presence of thermal radiation is considered. Fluid viscosity is assumed to vary as a linear function of temperature. The symmetry groups admitted by the corresponding boundary value problem are obtained by using a special form of Lie group transformations viz. scaling group of transformations. A third-order and a second-order coupled ordinary differential equations corresponding to the momentum and the energy equations are obtained. These equations are then solved numerically. It is found that the skin-friction decreases and heat transfer rate increases due to the suction parameter. Opposite nature is noticed in case of blowing. With the increase of temperature-dependent fluid viscosity parameter (i.e. with decreasing viscosity), the fluid velocity increases but the temperature decreases at a particular point of the sheet. Due to suction (injection) fluid velocity decreases (increases) at a particular point of the surface. Effects of increasing Prandtl number as well as radiation parameter on the velocity boundary layer is to suppress the velocity field and the temperature decreases with increasing value of Prandtl number. Due to increase in thermal radiation parameter, temperature at a point of the surface is found to decrease.     

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.     

Unsteady problem of magnetohydrodynamic heat plus mass transfer convective flow over a moveable plate with effects of thermophoresis and thermal radiation

This paper investigates the problem of unsteady magnetohydrodynamic heat plus mass transfer convective flow over a moveable vertical plate with the influence of thermophoresis and thermal radiation. The physical problem is governed by a set of partial differential equations. These sets of equations are coupled and are nonlinear. They were transformed into a dimensionless form of equations by introducing appropriate nondimensional quantities. An iterative method called the spectral relaxation method was used to linearize and decouple the set of dimensionless equations. Results were presented both in graphs and tables. It was found out that thermophoresis parameter has a significant effect on velocity and concentration fields. The thermal radiation is seen to have a significant effect on velocity and temperature fields. The skin friction is seen to increase the moment thermal Grashof number is increased. The model of Newtonian fluid flow over a moveable vertical plate is considered. The plate was considered moving toward the $y^{?}$‐direction and the radiative heat flux is only with respect to $y^{?}$. This study considered effects of viscous dissipation, thermophoresis, and radiation on heat plus mass transfer. This, to the best of our knowledge, has not been considered in the literature.     

Multiple characteristics of three-dimensional radiative Cross fluid with velocity slip and inclined magnetic field over a stretching sheet

This article focuses on the three-dimensional Cross fluid flow of a radiative nanofluid over an expanding sheet with aligned magnetic field, chemical reaction, and heat generation phenomenon. The stretching sheet has convective heat and slip boundary conditions. The similarity variables are properly used for the conversion of a dimensional mathematical model into a nondimensional one. The transformed ordinary differential equations are handled for the numerical outcomes of the suggested fluidic model by incorporating the shooting scheme. Furthermore, the numeric investigations are also compared by bvp4c MATLAB built-in package. In a limited case, both the techniques are checked with already published articles, thereby revealing good agreement. Furthermore, the effects of few parameters like Prandtl number, Weissenberg number, heat generation, stretching rate parameter, magnetic parameter, thermal radiation, Brownian and thermophoresis parameters, and Lewis number on concentration, temperature, and velocity profiles have been presented using figures and numerical tables. The strong intensity of the magnetic field across the fluid and increment in the inclination angle (ϑ) result in a lower velocity profile. Temperature is more prominent for the higher slip mechanism. Furthermore, there in an increase in thermophoretic force, which pushes the nanoparticles, and this mixing of nanoparticles helps to increase the concentration profile. A higher Cross fluid index responds to a larger velocity.     

On the analytic solution of MHD flow and heat transfer for two types of viscoelastic fluid over a stretching sheet with energy dissipation,internal heat source and thermal radiation

In this paper we study the magneto-hydrodynamic flow and heat transfer of an electrically conducting, viscoelastic fluid past a stretching surface, taking into account the effects of Joule and viscous dissipation, internal heat generation/absorption, work done due to deformation and thermal radiation. Closed-form solutions for the boundary layer equations of the flow are presented for two classes of viscoelastic fluid, namely, the second-grade and Walters’ liquid B fluids. Thermal transport is analyzed for two types of non-isothermal boundary conditions, i.e. prescribed surface temperature (PST) and prescribed surface heat flux (PHF) varying as a power of the distance from the origin. Results for some special cases of the present analysis are in excellent agreement with the existing literature. The effects of various physical parameters, such as viscoelasticity, magnetic parameter, thermal radiation parameter, heat source/sink parameter, Prandtl number, Eckert number and suction/injection parameter on the velocity and temperature profiles, skin friction coefficient and Nusselt number are examined and discussed in detail.     

A two-component modeling for free stream velocity in magnetohydrodynamic nanofluid flow with radiation and chemical reaction over a stretching cylinder

This analysis explores the influence of magnetohydrodynamic (MHD) nanofluid flow over a stretching cylinder with radiation effect in presence of chemically reactive species. The thermal radiation phenomenon is incorporated in the temperature equation. The mathematical modeling of the physical problem produces nonlinear set of partial differential equations corresponding to the momentum and energy equations that can be transformed into simultaneous system of ordinary differential equations with appropriate boundary conditions by applying similarity transformations. Shooting technique is used to solve the molded equations after adoption of Runge–Kutta–Fehlberg approach and ODE45 solver in MATLAB. A parametric analysis has been carried out to investigate the impacts of physical parameters that are considered in the current study. The attractive pattern studied the consequence of Brownian motion along with thermophoresis parameter. The outcomes of prominent fluid parameters, especially heat radiation, Lewis number, free stream velocity, chemical reaction, thermophoresis, and Brownian motion on the concentration, temperature, as well as velocity have been examined and are displayed through graphs and tables. The present study reveals that the temperature phenomenon enhances with an increase in radiation parameter, while nanoparticle concentration phenomenon reduces with an increase in chemical reaction parameter.