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.     

Magnetohydrodynamic flow of a micropolar nanofluid in association with Brownian motion and thermophoresis: Irreversibility analysis

This investigation was carried out with the purpose of presenting the flow of micropolar fluid flowing in the microchannel placed parallel to the ground. The prime aim of the work was to study the behavior of micropolar fluid and the response of the microrotation component when the two significant mechanisms namely Brownian movement and thermophoresis are accounted for, as these effects are mainly concerned with the motion of the particles of nano-dimensions. For the flow of micropolar, we account for the extra kinematics variables combined with the classical continuum mechanics namely microinertia moment tensor and gyration tensor. Magnetic effect and suction/injection of the fluid through the channel walls are also facilitated. The influence on the fluid concentration due to the presence of activation energy was accounted in the present examination. On considering all of these effects, equations are carefully modeled and the solution was attained with the aid of Runge–Kutta Fehlberg 4–5th order method using a shooting scheme. The results have deciphered that the presence of material parameter elevates the microrotation component on the upper half of the channel and depletes it at the lower half. The microinertia parameter shows the opposite behavior of the material parameter. Brownian motion parameter is found to enhance the thermal profile and concentration profile. Lesser entropy was generated when the material parameter was high.     

Thermophoresis and Brownian motion effects on Williamson nanofluid flow past a stretching surface with thermal radiation and chemical reaction

The heat transfer mechanism of nanofluids has numerous industrial applications owing to the non-Newtonian behavior and has been exercised as a thermophysical phenomena in presence of thermal radiation. The present paper deals with the thermal transfer characteristics of time-independent magnetohydrodynamics Williamson fluid past a stretching surface in presence of the reaction of chemical equilibrium is dealt. The flow constitutive nonlinear partial differential coupled equations are transmitted into ordinary differential equalities by employing relevant similarity transmutations. These deduced equations are determined by using the Runge–Kutta numerical technique with a shooting approach with the aid of MATLAB software. Influences of distinct pertinent flow parameters like an inclined uniform magnetic field, Soret number, heat generation/absorption, and Schmidt number constrained to convective boundary condition is displayed through graphs with relevant physical interpretations. Computed numerical values for the friction factor coefficient, local Nusselt parameter, and Sherwood number are tabulated.      

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.     

A mathematical simulation of unsteady MHD Casson nanofluid flow subject to the influence of chemical reaction over a stretching surface: Buongiorno's model

In this study, unsteady boundary layer flow with Casson nanofluid within the sight of chemical reaction toward a stretching sheet has been analyzed mathematically. The fundamental motivation behind the present examination is to research the influence of different fluid parameters, in particular, Casson fluid $\beta (0.2\le \beta \le 0.4)$, thermophoresis $Nt(0.5\le Nt\le 1.5)$, magnetohydrodynamic $M(3.0\le M\le 5.0)$, Brownian movement $Nb(0.5\le Nb\le 2.0)$, Prandtl numberty, unsteadiness parameter $A(0.10\le A\le 0.25)$, chemical reaction parameter $\gamma (0.1\le \gamma \le 0.8)$, and Schmidt number $Sc(1.0\le Sc\le 3.0)$ on nanoparticle concentration, temperature, and velocity distribution. The shooting procedure has been adopted to solve transformed equations with the assistance of Runge–Kutta Fehlberg technique. The impact of different controlling fluid parameters on flow, heat, and mass transportation are depicted in tabular form and are shown graphically. Additionally, values of skin friction coefficient, Nusselt number, and Sherwood number are depicted via tables. Present consequences of the investigation for Nusselt number are related with existing results in writing by taking $Nb=0$ and $Nt=0$ where results are finding by utilization of MATLAB programming. Findings of current research help in controlling the rate of heat and mass aspects to make the desired quality of final product aiding manufacturing companies and industrial areas.     

Dynamics of Brownian motion and flux conditions on naturally unsteady thermophoretic flow with variable fluid properties

This work examines the boundary flow difficulties of the past and the heat transfer properties of Blasius and Sakiadis flows under prescribed concentration flux and prescribed heat flux. The nanofluid is also taken into account in this model, along with impacts from Brownian motion and thermophoresis. The modified system governing partial differential equations is numerically solved by using the R-K method along with the shooting technique. Various values of physical quantities like thermophoresis parameter, Brownian motion parameter, Eckert number, thermal radiation parameter, heat source parameter, and magnetic field parameter along with the $C_f,N{u}_x,\text{and}S{h}_x$ were calculated using the temperature, concentration, and velocity profiles. Finally, we demonstrated how the Brownian motion, radiation, and thermophoresis parameters can significantly increase the temperature distributions. The concentration distributions were decelerated with an increase in Brownian motion parameters for both Blasius and Sakiadis cases.     

Influence of radiation and viscous dissipation on MHD heat transfer Casson nanofluid flow along a nonlinear stretching surface with chemical reaction

The present article investigates the influence of Joule heating and chemical reaction on magneto Casson nanofluid phenomena in the occurrence of thermal radiation through a porous inclined stretching sheet. Consideration is extended to heat absorption/generation and viscous dissipation. The governing partial differential equations were transformed into nonlinear ordinary differential equations and numerically solved using the Implicit Finite Difference technique. The article analyses the effect of various physical flow parameters on velocity, heat, and mass transfer distributions. For the various involved parameters, the graphical and numerical outcomes are established. The analysis reveals that the enhancement of the radiation parameter increases the temperature and the chemical reaction parameter decreases the concentration profile. The empirical data presented were compared with previously published findings.     

Joule heating impacts on MHD pulsating flow of Au/CuO-blood Oldroyd-B nanofluid in a porous channel

This article deals, the pulsating flow of blood carrying Au/CuO Oldroyd-B nanofluid through a porous channel with the effects of viscous dissipation, thermal radiation, and Joule (Ohmic) heating, and applied magnetic field. The perturbation technique is employed to get analytic solutions for flow variables. A comparison between analytical and numerical results shows a good agreement. The effect of various parameters is addressed extensively aided by pictorial results. The obtained results present that the velocity is reduced with the higher values of Hartmann number and volume fraction of nanoparticles. The temperature of nanofluid is enhanced with an enhancement of Eckert number and radiation parameter while it reduces with a rise in Hartmann number. Furthermore, the rise of the volume fraction of nanoparticles boosts up the rate of heat transfer.     

Unsteady nanofluid flow between two spinning expanding disks with continuous vertical motion under the influence of modified Hall effect

The principle aim of this article is to detect the effects of externally applied magnetic force in the nanofluid flow, flowing between two co-axially rotating and expanding disks where the upper disk is continuously moving vertically upward and downward. Also, the modified Hall Effect has been considered as an effective factor of the flow. The lower disk is vertically static. The rotation and vertical motion of the disks create a three-dimensional flow of nanofluid. Heat and mass density along with the motion of the flow has been analyzed under the variation in magnetic and Hall parameters. The findings have been compared with the results in Von Karman flow of nanofluid between two rotating and stretching disks. The velocity components have been largely influenced by magnetic and Hall parameters in case of downward movement of the upper disk. The fluid temperature is detected higher in case of upward velocity and lower in case of the downward motion of the upper disk. The heat transferability of the disks is effected differently at two different disks with the influence of magnetic force and Hall effect.     

Effects of the viscous dissipation and chemical reaction on Casson nanofluid flow over the permeable stretching/shrinking sheet

A steady two‐dimensional Casson nanofluid flow over the permeable stretching/shrinking sheet along the viscous dissipation and the chemical reaction is studied in this article. The convective boundary condition is incorporated in energy equation. Similarity variables are applied to convert the governing partial differential equations into ordinary differential equations. The numerical solutions of the equations are obtained by using the shooting method with Maple implementation. The numerical findings indicate occurrence of the dual solutions for a certain range of stretching/shrinking and suction parameters. Therefore, a stability analysis is done to find the solution that is stable and physically realizable. The effects of the pertinent physical parameters on velocity, temperature, and concentration profiles are investigated graphically. Numerical results of various parameters involved for skin friction coefficient, the local Nusselt as well as Sherwood numbers are determined and also discussed in detail. The Casson and suction parameters decrease the velocity in the first solution, whereas they increase it in the second solution. The rate of heat transfer increases in both solutions with an increment in Eckert number, Biot number, thermophoresis, and Brownian motion parameters. Thermophoresis and Brownian motion parameters show opposite behavior in the nanoparticle's concentration. The nanoparticle concentration decreases in both solutions with increment in Schmidt number, Brownian motion, and chemical reaction parameters.     

Thermal analysis of buoyancy-motivated Casson fluid flow with time-independent chemical reaction under Lorentz forces

The present research study examines the magneto-hydrodynamic natural convection visco-elastic boundary layer of Casson fluid past a nonlinear stretching sheet with Joule and viscous dissipation effects under the influence of chemical reaction. To differentiate the visco-elastic nature of Casson fluid with Newtonian fluids, an established Casson model is considered. The present physical problem is modeled by utilizing the considered geometry. The resulting system of coupled nonlinear partial differential equations is reduced to a system of nonlinear ordinary differential equations by applying suitable similarity transformations. Numerical solutions of these reduced nondimensional governing flow field equations are obtained by applying the Runge-Kutta integration scheme with the shooting method (RK-4). The physical behavior of different control parameters is described through graphs and tables. The present study describes that the velocity and temperature profiles decreased for increasing values of Casson fluid parameter. Velocity field diminished for the increasing nonlinear parameter whereas velocity profile magnified for increasing free convection parameter. Thermal field enhanced with increasing magnetic parameter in the flow regime. The concentration profile decreased for the rising values of the chemical reaction parameter. The magnitude of the skin-friction coefficient enhanced with increasing magnetic parameter. Increasing Eckert number increases the heat transfer rate and increasing chemical reaction parameter magnifies the mass transfer rate. Finally, the similarity results presented in this article are excellently matched with previously available solutions in the literature.     

Numerical analysis of MHD nanofluid flow over a wedge,including effects of viscous dissipation and heat generation/absorption,using Buongiorno model

The key purpose of this article is to examine magnetohydrodynamics flow, generative/absorptive heat, and mass transfer of nanofluid flow past a wedge in the presence of viscous dissipation through a porous medium. The investigation is completely theoretical, and the present model expresses the influence of Brownian motion and thermophoresis using the nanofluid Buongiorno model. The fundamental model of partial differential equations is reframed into the structure of ordinary differential equations implementing the nondimensional similarity transformation, which are tackled through the fourth–fifth-order Runge–Kutta–Fehlberg algorithm together with the shooting scheme. The analysis of sundry nondimensional controlling parameters, such as magnetic parameter, Eckert number, heat generation/absorption parameter, porosity parameter, Brownian motion parameter, and thermophoresis parameter on velocity, temperature, and concentration profiles are discussed graphically. The effects of the physical factors on the rate of momentum and heat and mass transfer are also determined with appropriate analysis in terms of skin friction, Nusselt number, and Sherwood number. The outcomes illustrate that the local Nusselt number and local Sherwood number are reduced for higher values of the thermophoresis parameter. Besides, it is found that higher estimations of heat generation/absorption and viscous dissipation parameters increase temperature. Moreover, it is found that the temperature profile increases with the involvement of the Brownian motion parameter, while an opposite trend is observed in the concentration profile. A comparison is also provided for limiting cases to authenticate our obtained results.     

Heat and mass transfer in MHD Casson nanofluid flow past a stretching sheet with thermophoresis and Brownian motion

The foremost objective of the current article is to explore the impact of Brownian motion on magnetohydrodynamic Casson nanofluid flow toward a stretching sheet in the attendance of nonlinear thermal radiation. The combined heat and mass transfer characteristics are investigated. The influence of chemical reaction, nonuniform heat source/sink, Soret, and Dufour is deemed. The convective boundary condition is taken. The appropriate transformations are utilized to transform the flow regulating partial differential equations into dimensionless ordinary differential equations (coupled). The numerical outcomes of the converted nonlinear system are solved by the Runge-Kutta based Shooting procedure. Results indicate that the temperature is an increasing function of both thermophoresis and Brownian motion parameters. The concentration of the fluid and the corresponding boundary layer thickness reduces with an enhancement in Lewis number.     

Squeezing flow of Casson hybrid nanofluid between parallel plates with a heat source or sink and thermophoretic particle deposition

The investigations on the flow of non-Newtonian fluids are becoming one of the major topics in the research field. These liquids have substantial applications in industrial and engineering fields such as drilling rigs, food processing, paint and adhesives, nuclear reactors and cooling systems. On the other hand, hybrid nanofluids play a major role in the heat transfer process. Keeping this in mind, the motion of Casson hybrid nanofluid squeezing flow between two parallel plates with the effect of heat source and thermophoretic particle deposition is examined here. The partial differential equations that govern fluid flow are converted into ordinary differential equations using appropriate similarity variables and those equations are numerically solved using the Runge–Kutta–Fehlberg fourth–fifth-order method by implementing the shooting scheme. The graphs depict the effects of a number of key parameters on fluid profiles in the absence and presence of the Casson parameter. These graphs show that fluid velocity enhances with the augmentation of the local porosity parameter. Thermal dispersal upsurges for enhancement of heat source/sink parameter and the concentration profile escalates for an upsurge of the thermophoretic parameter. Skin friction enhances with enhancement in the local porosity parameter.     

GFEM analysis of MHD nanofluid flow toward a power‐law stretching sheet in the presence of thermodiffusive effect along with regression investigation

In the current study, we use Galerkin finite‐element simulation to analyze the concept of triple diffusive flow with magnetic field effect toward a power law stretching sheet. The fluid comprises dissolved solutal particles and nanoparticles in the base fluid. The three important mechanisms that are responsible for rise in phenomenon of convective transportation are diffusophoresis, thermophoresis along with Brownian motion have been considered. Recently, the proposed nanoparticles' mass flux and heat flux boundary conditions have been imposed. Nanoparticle mass transportation, solutal mass transportation with heat transportation for prominent physical parameters, such as stretching parameter, magnetic influence parameter, thermophoresis parameter, and Brownian motion parameter are calculated. To further verify and understand the strength of the relationship between heat transportation rate and controlling parameters, the multiple regression process is used. The finite difference approach was adopted to numerically solve the nonlinear governing equations and the linked boundary conditions. In the present study, we used MATLAB software for finding the final outcomes and relating the concluding results for $?{{\theta }_{\delta }}^{\prime }\left(0\right)$ with extant outcomes in the literature as a limiting case in the absence of the magnetic intensity parameter and an excellent agreement was noted. It was observed that the magnetic field has a positive effect on heat and mass transfer. This study also helps in understanding and thus controlling the velocity of the flow along with solutal depositions, which has a significant engineering application in the process of extrusion. The findings of the present study help to control the rate of heat and mass transfer, aiding manufacturing companies in obtaining the desired quality of product.     

Unsteady squeezing flow of water‐based nanofluid between two parallel disks with slip effects: Analytical approach

The squeezing flow of an unsteady water‐based nanofluid between two parallel disks has been analyzed in the current study. Thermal and solutal buoyancy along with heat source enhance the flow phenomena of free convective flow through a porous medium. In addition to that velocity slip and temperature slip are also accounted for in the boundary conditions. The similarity transformation is adopted to formulate the governing equations that convert the complex partial differential equations (PDEs) to nonlinear ordinary differential equations (ODEs). These transformed equations are handled analytically by using the variation parameter method (VPM). For computational purposes, the fixed numeric values of physical parameters are used and their behaviors are shown by means of graphs. The calculated results for the physical quantities of interest are shown in tables. The conformity of the solution is obtained in comparison to an earlier study in a particular case. The major findings are (i) the velocity profile has distinct variations, which are separated by the middle layer of the channel and (ii) enhancement in the heat transfer coefficient is noted due to the interaction of buoyancy parameter.     

Impacts of variable thermal conductivity and mixed convective stagnation‐point flow in a couple stress nanofluid with viscous heating and heat source

The current study examines mixed (combined) convection stagnation‐point couple stress nanofluid over a stretched cylinder of variable thermal conductivity in the presence of viscous dissipation and internal heat source. The basic governing partial differential equations have been converted to coupled nonlinear differential equations by using adequate similarity transformations. By applying semi‐analytic technique (BVPh2.0), the equivalent ordinary differential equations are successfully solved and validated with a bvp4c solver. Graphs are presented to study the impact of various parameters on axial velocity, temperature, and volumetric nanofluid concentration profiles. The coefficient of skin friction (quantifying resistance) and the rate of heat and mass transfer on the surface due to flow variables are computed and explained. The axial velocity and momentum thickness are decreased with increasing couple stress parameter, whereas the reverse trend is noted with mixed convection and buoyancy ratio parameters. The temperature distribution increases for increasing Brownian motion and thermal conductivity parameter, whereas it decreases for increasing stagnation parameter.     

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.     

Transient electromagnetohydrodynamic radiative squeezing flow between two parallel Riga plates using a spectral local linearization approach

This article addresses transient electromagnetohydrodynamic radiative squeezing flow due to convectively heated electromagnetic actuator. The transport analysis of heat and mass is explored considering the heat generation/absorption and destructive species homogeneous reaction. Suitable transformations are applied on the mathematical model developed to convert governing partial differential equations to ordinary differential equations (ODEs). Spectral local linearization method (SLLM) is employed on the resultant nonlinear coupled ODEs to compute the numerical results. Influence of sundry physical quantities on heat mass transfer of squeezing flow characteristics are determined using graphs and tabular results. SLLM results exhibit that momentum and temperature improved with rise in squeezing and heat source parameters correspondingly. Momentum enhances at lower plate and detracts with rise in modified Hartmann number. For improved heat source parameter, the rate of heat transfer diminishes and is more significant for higher Prandtl number values. This investigation has relevance in disk style magnetic clutches, rolling elements, food processing, bearings, squeezing film pressure sensors, and flow rheostats.