Spectral Quasi-linearization Method Research Articles

Spectral Simulation to Investigate the Effects of Active Passive Controls of Nanoparticles on the Radiative Nanofluidic Transport Over a Spinning Disk

AbstractThe present investigation deals with the flow dynamics and heat transport of the nanofluid flow over a rotating disk. The flow is considered to be laminar and steady. Active–passive controls of tiny nanoparticles influenced by the Brownian motion and thermophoretic migration are included to reveal the variations in the hydrothermal behaviour. Thermal radiation, velocity slip, and thermal slip are also introduced to model the flow. The foremost governing equations are converted into its dimensionless form after applying the requisite similarity transformation. The spectral quasi-linearization method (SQLM) has been employed to extract the numeric outcomes of the flow. Effects of the underlying parameters on the flow and heat-mass transport are revealed through graphs and tables. Several three-dimensional (3D) and streamlines plots are depicted to enrich the Result and Discussion section. Results assured that the velocities in every direction reduce for velocity slip parameter and magnetic parameter. Temperature increases for thermophoresis and Brownian motion, but reduces for velocity and thermal slip parameter. Active flow reveals high temperature than passive flow. The Brownian motion and thermophoresis provide dual scenario for concentration profile. Heat and mass transport always sustain high magnitude for passive flow.

Dissipative Power-law fluid flow using spectral quasi linearization method over an exponentially stretchable surface with Hall current and power-law slip velocity

The present article aims to reports laminar, incompressible, electrically conducting two-dimensional non-Newtonian (power-law) liquid flow via exponentially stretching sheet with power-law slip velocity conditions. Transverse magnetic field, Hall current, viscous dissipation and radiative flux effects are incorporated in the formulation. Rosseland's diffusion model is defined for the radiation heat transfer. The non-linear partial derivation formulations satisfying the flow are transformed to the non-linear derivative equations by employing the local similarity quantities and then solved analytically through spectral quasi-linearization method (SQLM). The resultant solution is computed for different parameters in tables and graphical representation for clear understanding of the thermo-physical terms. Extensive visualization of primary and secondary velocities, temperature distributions for various emerging parameters presented for n = 0.7 (pseudo-plastic fluid) and n = 1,3 (dilatant fluid). The results are verified for limiting cases by comparing with various investigations and found excellent accuracy for Newtonian case. It is interesting to note that secondary flow rate is more dominant for both the cases of pseudo plastic and dilatant fluids for Hall parameter and Eckert number. Increasing Hall current leads suppress the fluid temperature but as Eckert number grows it leads grow the fluid temperature. Further, it is observed that as Hall parameter increases local Nusselt number strongly elevates.

Numerical Investigation of Natural Convection Viscoelastic Jeffrey’s Nanofluid Flow from a Vertical Permeable Flat Plate with Heat Generation, Thermal Radiation, and Chemical Reaction

The boundary layer flow of an incompressible viscoelastic Jeffrey’s nanofluid from a vertical permeable flat plate is investigated. We consider the effects of heat generation, thermal radiation, and chemical reaction on the fluid flow. The nonlinear transformed coupled differential equations that describe the transport processes are solved numerically using a multidomain bivariate spectral quasilinearization method (MD-BSQLM). This innovative method involves blending the quasilinearization idea with the bivariate Lagrange interpolation. The solutions of the resulting system of equations are then obtained sequentially on multiple intervals using the Chebyshev spectral collocation method. The method is shown to give accurate solutions for boundary layer-type equations. The influence of various physical parameters on velocity, temperature, and nanoparticle concentration fields, as well as on the skin friction and heat and mass transfer coefficients, is shown and discussed in detail. The range of the values of the governing parameters considered in this study is between 0 , 4 . For qualitative validation of the results and the numerical method used, calculations were carried out to graphically obtain the velocity, temperature, and nanoparticle concentration fields for selected physical parameter values. The results obtained were found to correlate with the results from published literature. For quantitative verification of our findings, the MD-BSQLM numerical solutions were again confirmed against published results reported in the literature, and the results were observed to be in perfect agreement. This study’s findings indicate that the Deborah number and suction parameter have related effects on the velocity profile, which is to suppress both the flow velocity and the momentum boundary layer thickness. Increasing the heat generation and thermal radiation parameters enhances both the temperature and thermal boundary layer depths. In contrast, an increase in the chemical reaction parameter causes a decrease in the fluid concentration.

Spectral quasi-linearization for MHD nanofluid stagnation boundary layer flow due to a stretching/shrinking surface

This article concentrates on the effect of MHD heat mass transfer on the stagnation point nanofluid flow over a stretching or shrinking sheet with homogeneous-heterogeneous reactions. The flow analysis is disclosed in the neighborhood of stagnation point. Features of heat transport are characterized with Newtonian heating. The homogeneous-heterogeneous chemical reaction between the fluid and diffusing species is included in the mass diffusion equation. The MHD stagnation boundary layer flow is explored in the presence of heat generation/absorption. Numerical convergent solutions are computed via the spectral quasi-linearization method (SQLM). The physical aspects of different parameters are discussed through graphs.

MHD bioconvective radiative flow of chemically reactive Casson nanofluid from a vertical surface with variable transport properties

ABSTRACT In this paper, we analyse magnetohydrodynamic bioconvective flow of Casson nanofluid comprising gyrotactic microorganisms from a vertical surface with variable thermo-physical features, nonlinear radiation, chemical reaction, Hall and ion-slip currents. The Casson fluid model incorporates zero nanoparticle mass flux at the boundary along with aspects of Brownian motion and thermophoresis to improve the motion of nanoparticles. The inclusion of motile microorganisms is considered to be beneficial for the stability of the nanoparticles. The model equations are first reduced into dimensionless form and then solved numerically using overlapping multi-domain bivariate spectral quasilinearisation method. Numerical analysis of the residual error and convergence properties of the method are discussed. For validation, our numerical results were compared with those available in the literature, and an excellent agreement was found. The impact of significant parameters on the flow fields, skin friction coefficients, heat, mass and motile microorganism transfer rates are analysed. We found that the flow fields improve due to enhancement of variable thermal conductivity, whereas retard with increment in variable viscosity and Casson fluid parameter. The inclusion of variable thermal conductivity and nonlinear radiative heat flux augments the fluid temperature, heat and mass transfer rates. An increment in variable fluid viscosity and Casson fluid parameter enhances heat and motile microorganism transfer rates, whereas diminishes the mass transfer rate. The reported observations find applications in enrobing processes for electric-conductive nano-materials, can be used in aerospace, smart coating transport situation, polymer processing and other industries. This type of flow can efficiently be utilised in solar energy system, enhancement of extrusion systems, and improvement of heat transfer devices as well as microbial fuel cells.

Spectral approach to study the entropy generation of radiative mixed convective couple stress fluid flow over a permeable stretching cylinder

The present literature illustrates the radiative couple stress fluid runs over a permeable stretched cylinder. The problem has been modelled mathematically introducing the mixed convective condition and magnetic effect. Additionally, the analysis of entropy generation provides the fine points of the flow. The leading PDE equations of the system have been framed non-dimensionally using proper transformation. The resulting ODEs are tackled using by Spectral quasi-linearization method (SQLM). A convergence schematic was obtained graphically. Consequence of various parameters on the flow features has been delivered via graphs and tables. Result signifies that Bejan number declines due to magnetic source. The entropy generation escalates for magnetic parameter, Reynolds number, but couple stress factor discloses the dual effect. The couple stress parameter allows Nusselt number to reduce at the rate 19.05%, whereas heat transport enhances for radiation at the rate 1.67%. Skin friction enhances for couple stress factor at the rate 8.45%.

MHD mixed convective radiative flow of Eyring‐Powell fluid over an oscillatory stretching sheet using bivariate spectral method on overlapping grids

AbstractThe bivariate spectral quasilinearization method (BSQLM) on overlapping grids is presented and applied in the analysis of unsteady magnetohydrodynamic mixed convection flow of Eyring‐Powell fluid over an oscillatory stretching sheet embedded in a non‐Darcy porous medium with nonlinear radiative heat flux and variable thermophysical properties. The fluid properties, namely the fluid viscosity, thermal conductivity, and mass diffusivity, are assumed to vary with temperature. It is assumed that the first‐order chemical reaction with heat generation/absorption takes place in the flow. The flow domain is subject to uniform transverse magnetic field perpendicular to the stretching surface. The transformed flow equations are solved numerically using BSQLM on overlapping grids. The convergence properties and accuracy of the method are assessed. The proposed method is computationally efficient, and it gives stable and highly accurate results after few iterations and using few grid points in each subinterval. The improved accuracy rests upon the use of the overlapping grid, which produces sparse coefficient matrices that are easy to invert and have small condition numbers. The effects of physical parameters on the flow fields, local skin friction, the Nusselt number, and the Sherwood number are exhibited through graphs and tables. Amongst other findings, we found that the amplitude of the fluid flow along with flow characteristics may efficiently improve through the utilization of variable fluid viscosity. Heat and mass transportation processes enhance with the inclusion of nonlinear radiative heat flux, temperature‐dependent thermal conductivity, and mass diffusion coefficient, whereas they diminish with the increase in the local inertia coefficient. The current flow analysis can be useful in various engineering applications including paper production, polymer solution, glass blowing, extrusion of thermal system manufacturing process, and heat transportation enhancement.

A multivariate spectral quasi-linearization method for the solution of (2+1) dimensional Burgers’ equations

AbstractIn this paper, we introduce the multi-variate spectral quasi-linearization method which is an extension of the previously reported bivariate spectral quasi-linearization method. The method is a combination of quasi-linearization techniques and the spectral collocation method to solve three-dimensional partial differential equations. We test its applicability on the (2 + 1) dimensional Burgers’ equations. We apply the spectral collocation method to discretize both space variables as well as the time variable. This results in high accuracy in both space and time. Numerical results are compared with known exact solutions as well as results from other papers to confirm the accuracy and efficiency of the method. The results show that the method produces highly accurate solutions and is very efficient for (2 + 1) dimensional PDEs. The efficiency is due to the fact that only few grid points are required to archive high accuracy. The results are portrayed in tables and graphs.

Framing the Impacts of Highly Oscillating Magnetic Field on the Ferrofluid Flow Over a Spinning Disk Considering Nanoparticle Diameter and Solid–Liquid Interfacial Layer

Abstract This article communicates on the ferrofluid flow over a spinning disk in the presence of highly oscillating magnetic field. The flow is presumed to be unsteady. Ferrous nanoparticles are suspended within base medium water. This investigation reveals how presence and absence of oscillating magnetic field influence the hydrothermal basis of the flow. Also, the effects of particles diameter and solid–liquid interfacial layer have been precisely incorporated to reveal the thermal integrity of the system. Shliomis theory is introduced to frame the leading equations of the system. Resulting equations have been solved using innovative spectral quasi-linearization method (SQLM). Residual error analysis is included to explore the advantage of such computational scheme. The influence of dynamic parameters on the velocities and temperature is deliberated through graphs and tables. Several 3D pictures and contour plots are depicted to extract the key points of the flow. The results exhibit that heat transfer is reduced for nanoparticle diameter but amplifies for base liquid nanolayer conductivity ratio and elevated field frequency enhances the temperature. Relative magnetization reduces for high field frequency, but increases for angular displacement. SQLM exhibits an accurate computational scheme with fast convergence.

On Numerical Analysis of Carreau–Yasuda Nanofluid Flow over a Non-Linearly Stretching Sheet under Viscous Dissipation and Chemical Reaction Effects

This work reports the Carreau–Yasuda nanofluid flow over a non-linearly stretching sheet viscous dissipation and chemical reaction effects. The coupled system of non-linear partial differential equations are changed into a system of linear differential equations employing similarity equations. The spectral quasi-linearization method was used to solve the linear differential equations numerically. Error norms were used to authenticate the accuracy and convergence of the numerical method. The effects of some thermophysical parameters of interest in this current study on the non-dimensional fluid velocity, concentration and temperature, the skin friction, local Nusselt and Sherwood numbers are presented graphically. Tables were used to depict the effects of selected parameters on the skin friction and the Nusselt number.

Effect of Cattaneo-Christov Heat Flux on Radiative Hydromagnetic Nanofluid Flow between Parallel Plates using Spectral Quasilinearization Method

In this paper, we numerically solve the equations for hydromagnetic nanofluid flow past semi-infinite parallel plates where thermal radiation and a chemical reaction are assumed to be present and significant. The objective is to give insights on the important mechanisms that influence the flow of an electrically conducting nanofluid between parallel plates, subject to a homogeneous chemical reaction and thermal radiation. These flows have great significance in industrial and engineering applications. The reduced nonlinear model equations are solved using a Newton based spectral quasilinearization method. The accuracy and convergence of the method is established using error analysis. The changes in the fluid properties with various parameters of interest is demonstrated and discussed. The spectral quasilinearization method was found to be rapidly convergent and accuracy is shown through the computation of solution errors.

Spectral quasi linearization simulation of radiative nanofluidic transport over a bended surface considering the effects of multiple convective conditions

This article enlightens on the hydrothermal performance of radiative nanofluid flow over a curved stretched surface. The curved surface is coiled inside a circular segment of radius R. The surface has been presumed to be permeable and slippery. Effects of multiple convective conditions i.e. convective conditions at the surface caused by both heat and mass transport are incorporated to explore the outcomes. The permeability characteristic of the surface that affects the hydrothermal integrity of the flow has been discussed in detail. The leading equations are renovated into its non-dimensional form by applying similarity conversion. After then, the spectral quasi linearization method (SQLM) is introduced to solve those foremost nonlinear ordinary differential equations (ODEs). Residual error analysis is depicted to show the convergence rate of SQLM. The impact of the pertinent factors on the flow is illustrated through graphs and tables. Several streamlines and three-dimensional plots are provided to enrich the result section. Results assured that temperature reduces for curvature parameter, but intensifies for both thermal and mass Biot numbers. Nanofluidic motion increases for curvature parameter and declines for slip factor. Curvature parameter and Lewis number provide reduction in mass transfer, whereas thermal and mass Biot numbers, slip parameters provide the enhancement. Heat transfer is enhanced for curvature parameter, thermal and mass Biot number.

On the Numerical Analysis of Unsteady MHD Boundary Layer Flow of Williamson Fluid Over a Stretching Sheet and Heat and Mass Transfers

A thorough and detailed investigation of an unsteady free convection boundary layer flow of an incompressible electrically conducting Williamson fluid over a stretching sheet saturated with a porous medium has been numerically carried out. The partial governing equations are transferred into a system of non-linear dimensionless ordinary differential equations by employing suitable similarity transformations. The resultant equations are then numerically solved using the spectral quasi-linearization method. Numerical solutions are obtained in terms of the velocity, temperature and concentration profiles, as well as the skin friction, heat and mass transfers. These numerical results are presented graphically and in tabular forms. From the results, it is found out that the Weissenberg number, local electric parameter, the unsteadiness parameter, the magnetic, porosity and the buoyancy parameters have significant effects on the flow properties.

Magnetohydrodynamic micropolar fluid flow in a porous medium with multiple slip conditions

Theoretically, micropolar fluids are used in the biomedical investigations. This study analyzes the flow, heat and mass transfer in a magneto-micropolar reactive fluid over a nonlinear stretching sheet in a saturated non-Darcy porous medium. The impact of velocity, thermal and concentration slips with prescribed surface temperature and concentration boundary conditions are examined. Mathematical models are formulated and solved using an iterative technique spectral quasi-linearization method. The results of numerical simulations are depicted graphically. The present results when cross-checked with earlier reported data in the literature for limiting conditions exhibit good agreement. The results show that the momentum and thermal boundary layer thicknesses fall as the nonlinear stretching parameter increases while the opposite occur with a rise in the thermal conductivity parameter.

ENTROPY GENERATION IN MHD FLOW OF VISCOELASTIC NANOFLUIDS WITH HOMOGENEOUS-HETEROGENEOUS REACTION, PARTIAL SLIP AND NONLINEAR THERMAL RADIATION

We investigate the combined effects of homogeneous and heterogeneous reactions in the boundary layer flow of a viscoelastic nanofluid over a stretching sheet with nonlinear thermal radiation. The incompressible fluid is electrically conducting with an applied a transverse magnetic field. The conservation equations are solved using the spectral quasi-linearization method. This analysis is carried out in order to enhance the system performance, with the source of entropy generation and the impact of Bejan number on viscoelastic nanofluid due to a partial slip in homogeneous and heterogeneous reactions flow using the spectral quasi-linearization method. Various fluid parameters of interest such as entropy generation, Bejan number, fluid velocity, shear stress heat and mass transfer rates are studied quantitatively, and their behaviors are depicted graphically. A comparison of the entropy generation due to the heat transfer and the fluid friction is made with the help of the Bejan number. Among the findings reported in this study is that the entropy generation has a significant impact in controlling the rate of heat transfer in the boundary layer region.

Double dispersed bioconvective Casson nanofluid fluid flow over a nonlinear convective stretching sheet in suspension of gyrotactic microorganism

AbstractMicroorganisms play a vital role in understanding the ecological system. The motions of micororganisms are self‐propelled while the impact of thermophoresis and Brownian motion property of nanoparticle shows more challenges in biotechnological and medical applications. The present problem is based on the understanding of double‐dispensed bioconvection for a Casson nanofluid flow over a stretching sheet. Suction phenomenon is introduced at the surface of the stretching sheet along with the convective boundary condition. The convection and movement of the microorganisms are assisted by an applied magnetic field, nonlinear thermal radiation, and first‐order chemical reaction. The governing equations are highly coupled and thus we used the spectral quasilinearization method to solve the governing equations. The study of the residual errors on the systemic parameters had given a confidence with the present results. The final outcomes are displayed through graphs and tables. The thermal dispersion coefficient shows a positive response in the temperature while a similar response is observed for the concentration with solutal dispersion coefficient. The response is reversible for the heat transfer rate at the surface with thermal dispersion coefficient. The density of the motile microorganism at the surface decreases with increase in the Casson number, thermal dispersion coefficient, and solute dispersion coefficient, while an opposite phenomenon was observed with increase in the density ratio of the motile microorganism.

MHD Slip Flow of CNT-Ethylene Glycol Nanofluid due to a Stretchable Rotating Disk with Cattaneo–Christov Heat Flux Model

This article deals with carbon nanoliquid flow due to stretchable rotating disk with the effect of Cattaneo–Christov heat flux model. Both SWCNTs and MWCNTs are considered with ethylene glycol as the base fluid. The effects of nanoparticle volume friction, normally applied magnetic field, stretching factor, velocity, and thermal slip factors are examined. The fundamental flow governing equations are transformed into dimensionless system of coupled nonlinear ordinary differential equations, and they are solved numerically using spectral quasi-linearization method (SQLM). Employing graphs and tables, the results of velocity and temperature fields as well as skin friction coefficient and local heat transfer rate are analyzed and presented via embedded parameters. The results reveal that higher velocity fields and lower temperature fields are noticed in the MWCNT nanofluids than SWCNT nanofluids. The higher incidence of magnetic field improves the thermal boundary layer thickness. A growth in velocity slip factor reduces the momentum boundary layer thickness of the nanoliquid flow. Generally, radial stretching of the disk is helpful in improving the cooling process of the rotating disk in practical applications.

Rotational nanofluids for oxytactic microorganisms with convective boundary conditions using bivariate spectral quasi-linearization method

In this study, we considered the three-dimensional flow of a rotating viscous, incompressible electrically conducting nanofluid with oxytactic microorganisms and an insulated plate floating in the fluid. Three scenarios were considered in this study. The first case is when the fluid drags the plate, the second is when the plate drags the fluid and the third is when the plate floats on the fluid at the same velocity. The denser microorganisms create the bioconvection as they swim to the top following an oxygen gradient within the fluid. The velocity ratio parameter plays a key role in the dynamics for this flow. Varying the parameter below and above a critical value alters the dynamics of the flow. The Hartmann number, buoyancy ratio and radiation parameter have a reverse effect on the secondary velocity for values of the velocity ratio above and below the critical value. The Hall parameter on the other hand has a reverse effect on the primary velocity for values of velocity ratio above and below the critical value. The bioconvection Rayleigh number decreases the primary velocity. The secondary velocity increases with increasing values of the bioconvection Rayleigh number and is positive for velocity ratio values below 0.5. For values of the velocity ratio parameter above 0.5, the secondary velocity is negative for small values of bioconvection Rayleigh number and as the values increase, the flow is reversed and becomes positive.

Analysis of exponentially varying viscosity and thermal conductivity on a tangent hyperbolic fluid

We present an analysis of the significance of exponentially varying viscosity and thermal conductivity in the magnetohydrodynamic flow of a tangent hyperbolic fluid. The study assumes the combined impact of viscous dissipation, chemical reaction and variable transport properties on the flow. The model equations are reduced to a system of parabolic partial differential equations using a non-similar solution. We solve the coupled nonlinear partial differential equations using the multi-domain bivariate spectral quasi-linearisation method. Among other findings, the study shows that varying the viscosity reduces fluid flow resistance and this leads to an increase in the fluid velocity while the temperature and species concentration profiles decrease. The flow heat and mass transfer rates increase with the magnetic variable.

MHD mixed convective nanofluid flow about a vertical slender cylinder using overlapping multi-domain spectral collocation approach

This paper investigates the magnetohydrodynamic flow, heat and mass transfer characteristics in a silver water nanofluid about a vertical slender cylinder by considering diffusion-thermal, thermo-diffusion, chemical reaction and Hall effects. The nonlinear partial differential equations modelling the flow problem are non-dimensionalized and the overlapping multi-domain bivariate spectral quasilinearisation method is used to solve the dimensionless equations. The impact of flow parameters on the fluid properties and physical quantities of interest are determined. Amongst other findings, we found that increment in the nanoparticle volume fraction, Hall current and curvature parameter augments the skin friction coefficient and diminishes the heat transfer rate, while the introduction of chemical reaction, silver nanoparticles, Hall current and Soret effect into the system enhances the mass transfer rate. Also, the fluid properties amplifies in the curved surface than in the flat plate.