Spectral Homotopy Analysis Method Research Articles

Enhanced numerical resolution of the Duffing and Van der Pol equations via the spectral homotopy analysis method employing chebyshev polynomials of the first kind

Enhanced numerical resolution of the Duffing and Van der Pol equations via the spectral homotopy analysis method employing chebyshev polynomials of the first kind

Numerical Study of Chemical Reaction and Magnetic Field Effects on MHD Boundary Layer Flow over a Flat Plate

This investigation explores the combined effects of magnetic fields and chemical reactions on the movement of a boundary layer toward a flat plate. The study considers the influence of viscous dissipation on the energy distribution. By utilizing partial differential equations (PDEs), the flow phenomenon is modeled. Through the application of suitable similarity transformations, the system of PDEs is transformed into a system of total differential equations. These modified equations are then solved using the spectral homotopy analysis method (SHAM), which incorporates the combination of the CSCM and HAM procedures. The analysis reveals that magnetohydrodynamic (MHD) fluxes generate a Lorentz force, and a higher magnetic parameter intensifies this effect, resulting in a flattened velocity profile. Furthermore, the velocity profile improves with an increase in the chemical interaction variable. The study also shows that as the Eckert number increases, the ambient temperature of the dense dissipative fluid rises. The findings have potential applications in various engineering fields, such as petroleum pipeline flow improvement. The spectral homotopy method used in this study offers a numerical solution for analyzing the problem. The results contribute to the understanding of heat and mass transfer phenomena and can guide future research in this area.

Dynamics of micropolar-Walters B fluids under the influence of thermal radiation and Soret–Dufour mechanisms

PurposeThe purpose of this study is to investigate the Dynamics of micropolar – water B Fluids flow simultaneously under the influence of thermal radiation and Soret–Dufour Mechanisms.Design/methodology/approachThe thermal radiation contribution, the chemical change and heat generation take fluidity into account. The flow equations are used to produce a series of dimensionless equations with appropriate nondimensional quantities. By using the spectral homotopy analysis method (SHAM), simplified dimensionless equations have been quantitatively solved. With Chebyshev pseudospectral technique, SHAM integrates the approach of the well-known method of homotopical analysis to the set of altered equations. In terms of velocity, concentration and temperature profiles, the impacts of Prandtl number, chemical reaction and thermal radiation are studied. All findings are visually shown and all physical values are calculated and tabulated.FindingsThe results indicate that an increase in the variable viscosity leads to speed and temperature increases. Based on the transport nature of micropolar Walters B fluids, the thermal conductivity has great impact on the Prandtl number and decrease the velocity and temperature. The current research was very well supported by prior literature works. The results in this paper are anticipated to be helpful for biotechnology, food processing and boiling. It is used primarily in refrigerating systems, tensile heating to large-scale heating and oil pipeline reduction.Originality/valueAll results are presented graphically and all physical quantities are computed and tabulated.

Numerical scrutinization of micropolar and Walters-B non-Newtonian fluids motion under the influence of thermal radiation and chemical reaction

Purpose The purpose of this study is to explore numerical scrutinization of micropolar and Walters-B non-Newtonian fluids motion under the influence of thermal radiation and chemical reaction. Design/methodology/approach The two fluids micropolar and Walters-B liquid are considered to start flowing from the slot to the stretching sheet. A magnetic field of constant strength is imposed on their flow transversely. The problems on heat and mass transport are set up with thermal, chemical reaction, heat generation, etc. to form partial differential equations. These equations were simplified into a dimensionless form and solved using spectral homotopy analysis method (SHAM). SHAM uses the basic concept of both Chebyshev pseudospectral method and homotopy analysis method to obtain numerical computations of the problem. Findings The outcomes for encountered flow parameters for temperature, velocity and concentration are presented with the aid of figures. It is observed that both the velocity and angular velocity of micropolar and Walters-B and thermal boundary layers increase with increase in the thermal radiation parameter. The decrease in velocity and decrease in angular velocity occurred are a result of increase in chemical reaction. It is hoped that the present study will enhance the understanding of boundary layer flow of micropolar and Walters-B non-Newtonian fluid under the influences of thermal radiation, thermal conductivity and chemical reaction as applied in various engineering processes. Originality/value All results are presented graphically and all physical quantities are computed and tabulated.

Statistical Analysis of MHD Flow of an Electrically Conducting Tangent Hyperbolic Fluid over a Stretching Cylinder with Convective Boundary Condition

The dynamics of MHD non-Newtonian fluid flow past a cylinder with slip boundary condition and magnetic field is addressed in this study. The non-Newtonian fluid (tangent hyperbolic) considered in this study are nail polish and whipped cream. This article investigates the statistical analysis of two-dimensional MHD tangent hyperbolic fluid flow over a cylinder with slip condition. The partial differential equations describing the problem are later transformed into the ordinary differential equation by similarity variables. The derived model is solved by the spectral homotopy analysis method (SHAM). The characteristics of the parameters of the flow are demonstrated by the velocity of the flow. The skin friction coefficient is computed and presented with the aid of a tables. The slope of the linear regression is obtained through the data points while bar charts for engineering quantities of interest are presented. The findings indicated that an increase in magnetic parameters builds a resistance to the flow. Also, it was discovered that the radius of curvature decreases when the curvature parameter increases.

Magneto-Rotational Augmentation of Bioconvective Transport in Plasma-Nanofluid Flowing through a Penetrable Spinning Disc

The phenomenon of bioconvective transport through the manipulation of motile microorganisms is considered a promising process control technique in several biological processes and microdevices. Inducing convective transport in self-propelling microbes could be tailored to improve mixing, reaction propensity, and concentration transport within the media. This paper examined the combined effect of magnetic and rotational fields on the argumentation of bioconvective transport in the nanofluid-mediated plasma flow. A detailed analysis of the transport and dynamics of reactive forces during bioconvection in a rotary disc-like microchannel is presented. The physics of the problem was described by coupled nonlinear ordinary differential equations, which were numerically computed using the spectral relaxation scheme of the spectral homotopy analysis method. It was observed that the imposition of a magnetic field constituted viscous drag in the plasma-nanofluid media, which consequently increases the thermophoretic parameter in the bioconvective flow. It was ascertained that coupled magnetic and rotational effects significantly augmented the motility of microorganisms and translated to growth in momentum and concentration fields which is noticeable in the generation of stretching effect on the bacterium-containing plasma-nanofluid flow. The findings of this study could provide an essential basis for the design of bioreactors, centrifugal microfluidics technologies, and microdevices for use in a broad spectrum of biotechnology.

Numerical simulation of heat and mass transfers radiative–convective fluid flow on a stretching porous surface with temperature‐dependent thermophysical properties

AbstractThis paper is focused on the analysis of heat and mass transfer radiative–convective fluid flow using quadratic multiple regression and numerical approach. The physical phenomenon is analyzed by utilizing partial differential equations (PDEs). Thermophysical properties, such as viscosity, thermal conductivity, and mass diffusivity, are varied and temperature‐dependent. This study is unique because of its applications in magnetohydrodynamic power accelerators, drilling operators, and bioengineering. The governing PDEs are transformed into coupled nonlinear ordinary differential equations (ODEs). The transformed ODEs are solved numerically using the spectral homotopy analysis method. Also, a quadratic multiple regression analysis is performed on quantities of engineering interest to show the significance of the flow parameters. It is observed that the heat and mass transfer process is affected by nonlinear buoyancy impact. The Lorentz force produced by the imposed magnetic field decline the thickness of the hydrodynamic boundary layer. Findings revealed that the nonlinear convective parameter and variable thermophysical properties are greatly affected by the rate of heat and mass transfer. Previously published work was used to validate the present one, which conformed with it. The slope of linear regression through data points is adopted to show the rate of change in skin friction, Nusselt, and Sherwood numbers during the flow phenomenon.

Dynamics of MHD Convection of Walters B Viscoelastic Fluid through an Accelerating Permeable Surface Using the Soret–Dufour Mechanism

The MHD convective Walters-B memory liquid flow past a permeable accelerating surface with the mechanism of Soret-Dufour is considered. The flow equation constitutes a set of partial differential equations (PDEs) to elucidate the real flow of a non-Newtonian liquid. The radiation thermo-physical parameters were employed based on the use of Roseland approximation. This implies the fluid employed in this exploration is optically thick. Utilizing suitable similarity terms, the flow equation PDEs were simplified to become total differential equations. The spectral homotopy analysis method (SHAM) was utilized to provide outcomes to the model. The SHAM involves the addition of the Chebyshev pseudospectral approach (CPM) alongside the homotopy analysis approach (HAM). The outcomes were depicted utilizing graphs and tables for the quantities of engineering concern. The mechanisms of Soret and Dufour were separately examined. The imposed magnetism was found to lessen the velocity plot while the thermal radiation term elevates the temperature plot because of the warm particles of the fluid.

Contributions of variable viscosity and thermal conductivity on the dynamics of non-Newtonian nanofluids flow past an accelerating vertical plate

The present study is focused on the contributions of variable viscosity and thermal conductivity on the dynamics of non-Newtonian nanofluids flow with nonlinear buoyancy force. A constant magnetic field is applied transversely to the flow direction. The nonlinear couples partial differential equations (PDEs) and the boundary conditions were reduced into system of ordinary differential equations by using appropriate transformation. The transformed equations were solved by utilizing spectral homotopy analysis method (SHAM) and spectral relaxation method (SRM). A higher value of Casson parameter was noticed to decrease the velocity profile. The outcome of this paper was compared with previously published works and was in good agreement.

Spectral methods to solve nonlinear problems: A review

The study is intended to give a brief overview of recent papers on spectral methods in different types of fluid flow especially nanofluid flow. The survey does not presume to be exhaustive; hence some selection is necessary. The papers reviewed herein relate to the recent use of some spectral based algorithms, notably the spectral relaxation method, the spectral local linearization method, the spectral quasi-linearization method, the successive linearization method, the piecewise successive linearization method and the spectral homotopy analysis method, etc. We review the important papers and problems where these methods have been used. The paper is divided into sections related to the use of each method. In addition to reviewing the journal articles in the main body of the paper, we also give details of important books published on spectral methods in fluid dynamics.

Heat and mass transfer effects on MHD mixed convection flow of viscoelastic fluid with constant viscosity and thermal conductivity

AbstractThe present exploration is based on the contributions of heat and mass transport on the non‐Newtonian viscoelastic liquid motion under the impact of magnetism, Soret and Dufour numbers. The model equations that describe the flow mechanism of heat and mass transport are partial differential equations (PDEs). The PDEs were simplified using suitable similarity functions to obtain coupled nonlinear total ordinary differential equations. The simplified equations are numerically solved utilizing the spectral homotopy analysis method. Findings show that the process of heat transport is because of thermal radiation. The velocity, as well as temperature distributions, enhances due to a higher viscoelastic term. The present analysis is examined closely with past works and was discovered to concord.

Heat and mass transfer effects on MHD non-Newtonian fluids flow through an inclined thermally-stratified porous medium

PurposeThis paper aims to analyze heat and mass transfer of magnetohydrodynamic (MHD) non-Newtonian fluids flow past an inclined thermally stratified porous plate using a numerical approach.Design/methodology/approachThe flow equations are set up with the non-linear free convective term, thermal radiation, nanofluids and Soret–Dufour effects. Thus, the non-linear partial differential equations of the flow analysis were simplified by using similarity transformation to obtain non-linear coupled equations. The set of simplified equations are solved by using the spectral homotopy analysis method (SHAM) and the spectral relaxation method (SRM). SHAM uses the approach of Chebyshev pseudospectral alongside the homotopy analysis. The SRM uses the concept of Gauss-Seidel techniques to the linear system of equations.FindingsFindings revealed that a large value of the non-linear convective parameters for both temperature and concentration increases the velocity profile. A large value of the Williamson term is detected to elevate the velocity plot, whereas the Casson parameter degenerates the velocity profile. The thermal radiation was found to elevate both velocity and temperature as its value increases. The imposed magnetic field was found to slow down the fluid velocity by originating the Lorentz force.Originality/valueThe novelty of this paper is to explore the heat and mass transfer effects on MHD non-Newtonian fluids flow through an inclined thermally-stratified porous medium. The model is formulated in an inclined plate and embedded in a thermally-stratified porous medium which to the best of the knowledge has not been explored before in literature. Two elegance spectral numerical techniques have been used in solving the modeled equations. Both SRM and SHAM were found to be accurate.

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

AbstractThis 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.

Soret, viscous dissipation, and thermal radiation effects on MHD free convective flow of Williamson liquid with variable viscosity and thermal conductivity

AbstractThe flow model of heat and mass transport of a Williamson liquid through a porous stretching sheet with radiation, viscous dissipation, Soret effect, and chemical reaction has been explored. The motion starts from the slot to the free stream. The present study is unique, because it examines the flow of a Williamson fluid under the influence of variable viscosity and thermal conductivity. The Williamson fluid term as added to the momentum and energy equation is considered in a nonlinear form as compared with other studies in literature. The flow model is a set of coupled highly nonlinear partial differential equations that are simplified and lead to coupled nonlinear total differential equations by employing sufficient similarity variables. The simplified equations are later solved by utilizing the spectral homotopy analysis method. Our experiment shows that the injected variable viscosity, together with thermal conductivity, has a great impact on the fluid profiles. An increase in the Williamson parameter (β) leads to a decrease in the thickness of the hydrodynamic thermal layer. Our numerical calculations were compared with earlier published work, and they were discovered to be correct.

Effects of Cattaneo–Christov heat flux analysis on heat and mass transport of Casson nanoliquid past an accelerating penetrable plate with thermal radiation and Soret–Dufour mechanism

AbstractIn this analysis, the effect of Catteneo–Christov model on heat alongside mass transport magnetohydrodynamics of a Casson nanoliquid with thermal radiation and Soret–Dufour mechanism is considered. The fluid flow is considered through porous media as the thermophysical attributes such as viscosity along with thermal conductivity are considered to be constant. Suitable similarity transformations were employed on the governing coupled flow equation to yield total differential equations (ODE). An accurate and newly developed spectral method called spectral homotopy analysis method (SHAM) was employed to provide solution to the simplified equations. The numerical method of homotopy analysis method (HAM) is SHAM. SHAM portrays the division of nonlinear equations into linear as well as nonlinear parts. The findings in this study show that an increment in the Casson parameter is seen to elevate the velocity plot at the wall and lessen the velocity far away from the plate. An increase in the Brownian motion and thermophoresis term is observed to speed up the local skin friction coefficient.

A Laguerre spectral method for quadratic optimal control of nonlinear systems in a semi-infinite interval

This paper presents a Laguerre homotopy method for quadratic optimal control problems in semi-infinite intervals (LaHOC), with particular interests given to nonlinear interconnected large-scale dynamic systems. In LaHOC, the spectral homotopy analysis method is used to derive an iterative solver for the nonlinear two-point boundary value problem derived from Pontryagin's maximum principle. A proof of local convergence of the LaHOC is provided. Numerical comparisons are made between the LaHOC, Matlab BVP5C generated results and results from the literature for two nonlinear optimal control problems. The results show that LaHOC is superior in both accuracy and efficiency.

Variable thermal conductivity and viscosity effects on non-Newtonian fluids flow through a vertical porous plate under Soret-Dufour influence

The purpose of this paper is to consider heat and mass transfer processes on two non-Newtonian fluids (Walters-B viscoelastic and Casson fluid) situated in a hot environment. This study considered concentrated fruit juice and tomato sauce as the type of Casson fluid and polymethyl methacrylate, chromatography, and ceramic processing as the type of Walters-B viscoelastic fluids. The model is governed by systems of partial differential equations. These equations were simplified with the help of appropriate similarity variables to obtain nonlinear couple fourth-order ordinary differential equations. The transformed equations were solved numerically using the spectral homotopy analysis method (SHAM). SHAM is rooted in the homotopy analysis method (HAM) and the Chebyshev spectral collocation method. SHAM is efficient and converges faster than HAM. This paper is unique because it explored variable viscosity and thermal conductivity in the presence of flow parameters such as Soret, Dufour, radiation, viscous dissipation, magnetic field, and so on. The applied magnetic field serves as an opposition to the flow and thereby slows down the motion of an electrically conducting fluid. The influence of pertinent flow parameters is extensively discussed and presented graphically. The permeability parameter is noticed to decrease the velocity profile and increase the temperature profile. The present results were found to be in good agreement with existing works in literature.

Variable viscosity and thermal conductivity effects on Williamson fluid flow over a slendering stretching sheet

PurposeThe purpose of this paper is to consider heat and mass transfer on magnetohydrodynamics (MHD) Williamson fluid flow over a slendering stretching sheet with variable thickness in the presence of radiation and chemical reaction. All pertinent flow parameters are discussed and their influence on the hydrodynamics, thermal and concentration boundary layer are presented with the aid of the diagram.Design/methodology/approachThe governing partial differential equations are reduced into a system of ordinary differential equations with the help of suitable similarity variables. A discrete version of the homotopy analysis method (HAM) called the spectral homotopy analysis method (SHAM) was used to solve the transformed equations. SHAM is efficient, and it converges faster than the HAM. The SHAM provides flexibility when solving linear ordinary differential equations with the use of the Chebyshev spectral collocation method.FindingsThe findings revealed that an increase in the variable thermal conductivity hike the temperature and the thermal boundary layer thickness, whereas the reverse is the case for velocity close to the wall.Originality/valueThe uniqueness of this paper is the exploration of combined effects of heat and mass transfer on MHD Williamson fluid flow over a slendering stretching sheet. The Williamson fluid term in the momentum equation is expressed as a linear function and the viscosity and thermal conductivity are considered to vary in the boundary layer.

Mechanism of Soret‐Dufour, magnetohydrodynamics, heat and mass transfer flow with buoyancy force, and viscous dissipation effects

AbstractThis paper examined the mechanism of both positive and negative effects of Soret‐Dufour with heat and mass transfer processes over an accelerating permeable surface. The partial differential flow equations were simplified using similarity variables, and the resulting equations were solved numerically using the spectral homotopy analysis method (SHAM). The SHAM is used in separating nonlinear equations into linear and nonlinear. The physics of each pertinent flow parameters was used to examine their influence on velocity, temperature, and concentration fields. The effect of Soret‐Dufour was examined separately, and its negative effect was used to determine its influence on velocity, temperature, and concentration fields. The result revealed that positive Soret‐Dufour enhances the boundary layer, whereas negative Soret‐Dufour parameter decreases the boundary layer. The result presented in this paper is in good agreement with existing works in literature.

Effects of thermophoresis, Soret-Dufour on heat and mass transfer flow of magnetohydrodynamics non-Newtonian nanofluid over an inclined plate

Heat together with mass transfer of magnetohydrodynamics (MHD) non-Newtonian nanofluid flow over an inclined plate embedded in a porous medium with influence of thermophoresis and Soret-Dufour is studied. The novelty of this study is the combined effects of Soret, Dufour and thermophoresis with nanofluid flow on heat together with mass transfer. The flow is considered over an inclined plate embedded in a porous medium. Appropriate similarity transformations were used to simplify the governing coupled nonlinear partial differential equations into coupled nonlinear ordinary differential equations. A novel and accurate numerical method called spectral homotopy analysis method (SHAM) was used in solving the modelled equations. SHAM is the numerical version of the well-known homotopy analysis method (HAM). It involves the decomposition of the nonlinear equations into linear and nonlinear equations. The decomposed linear equations were solved using Chebyshev pseudospectral method. The findings revealed that the applied magnetic field gives rise to an opposing force which slows the motion of an electrically conducting fluid. Increase in the non-Newtonian Casson fluid parameter increases the skin friction factor and reduces the rate of heat and mass transfer. The present results are compared with existing work and found to be in good agreement.