Spectral Local Linearization Method Research Articles

Irreversibility and spectral analysis for nanofluid with melting and higher order slip effects

This work is intended to examine the impacts of first and second-order velocity slips, viscous dissipation, and melting on mixed convective flow of nickel zinc ferrite + SAE 20W-40 motor oil based nanofluid along a stretching or shrinking sheet for the first time. The multigrade 20W-40 motor oil is categorized by Society of Automotive Engineers (SAE). An irreversibility analysis has also been performed using the second law of thermodynamics. The resulting non-dimensional flow-governing equations are modified into ODEs (Ordinary Differential Equations) and then the numerical estimates are provided by adopting the spectral local linearization method. Next, the efficiency of the above-mentioned spectral procedure is verified through the maximum error norms. Finally, the influence of important parameters included in this evaluation on the flow profiles and physical quantities is systematically represented. Based on the findings, the melting effect enhances the heat transference rate by 24.6% and reduces entropy by 38.4%. The use of higher-order velocity slips and viscous dissipation effects results in a lower friction factor. In the presence and absence of ferrite particles, the streamline visualization is clarified. This type of simulation is extremely useful for the readers in considering the rates of cooling or heating at electromagnetic interfaces, industrial devices, orthopedic joint replacements, aircraft turbines, bone plate surgeries, and so on.

Magnetohydrodynamic thermo-bioconvective flow of 3D rotating Williamson nanofluid with Arrhenius activation energy in a Darcy–Forchheimer medium over an exponentially stretching Surface

This paper aims to analyze the heat and mass transfer characteristics of the 3D thermo-bioconvective flow of rotating Williamson nanofluid over an exponentially stretching vertical sheet. The flow distribution considers the influence of nonlinear thermal radiation, Hall and ion-slip currents, joule heating, coupled effects of Dufour and Soret diffusion, internal heat generation, Arrhenius activation energy, Brownian, and thermophoresis diffusion in a Darcy–Forchheimer porous medium. The modeled partial differential equations (PDE) in terms of continuity, momentum, energy, concentration, and density of motile microorganisms are reformed into ordinary differential equations (ODE) forms employing similarity variables. The resulting equations are solved numerically using the spectral local linearization method (SLLM). The successive over-relaxation technique is applied to accelerate and enhance the convergence of the method. The obtained results are graphically and tabularly represented and numerically explored for the effects of pertinent parameters on the velocity, temperature, nanoparticle concentration, and motile microorganism concentration profiles. The rotation and mixed convection parameters dropped the primary velocity curve, while the Williamson and heat source parameters uplifted the microbes density distributions. The temperature field rises with an increase in radiation and microbes Brownian motion and declines with an increase in Hall and ion-slip numbers. Furthermore, with the increase in activation energy from 0.5 to 2 and the mixed convection parameter from 0.6 to 1.3, we observe a respective 3.93% rise and 8.30% fall in mass transfer rates. The current investigation has broad applications, including MHD accelerators, biotechnology, the formation of elastic sheets, the production of polymer solutions, and the synthesis of nanoparticles through microbial processes.

Analysis of irreversibility on nanofluid flow through porous medium considering shape, dispersion and melting effects

This study is conducted to explore the impact of thermal dispersion and melting on the natural convective nanofluid (nickel zinc ferrite + SAE 20W-40 motor oil) flow over a stretching sheet in a Darcy porous medium. An irreversibility analysis has also been performed using the second law of thermodynamics. The fundamental nonlinear partial differential equations (PDEs) are converted into a system of dimensionless nonlinear ordinary differential equations (ODEs) through Lie group similarity transformations and then solved by employing the spectral local linearization method implemented in MATLAB software. It is noteworthy to highlight that the validation results indicate a strong concurrence with existing findings in previously published literature. After simulation, it is specified that the thermal dispersion disrupts the entropy (by 63.7%) and enhances the surface friction. Likewise, the heat transfer rate improves by 1.5% with the melting effect and 58.7% with the Darcy number. The results indicate that the brick-shaped particles exhibit a higher rate of heat transfer and lower entropy production. Further, this work has many uses such as, core, microwave, and biomedical applications like tumor treatments, bone plate surgeries, EMI (electromagnetic interfaces), electronics cooling, and aerodynamic extrusion processes, in the design of passive ventilation systems.

SPECTRAL ANALYSIS FOR ENTROPY GENERATION AND IRREVERSIBILITY ON NiZnFe2O4: ENGINE OIL BASED NANOFLUID IN POROUS MEDIUM

This study aims to investigate the impact of volume fraction on entropy generation in a melting stretching/shrinking sheet scenario, considering both first and second-order velocity slips. The investigation focuses on the mixed convective flow of a nanofluid in a porous medium comprising nickel-zinc ferrite and SAE 20W-40 motor oil, which is characterized by Society of Automotive Engineer. Ferrites possess exceptional resistance properties, a crucial consideration in microwave applications. The solution to the derived nondimensional flow governing differential equations is computed using the spectral local linearization method combined with a local non-similarity technique. An assessment of the error is performed to verify the convergence of the numerical approach utilized. A comparison to existing results for specific cases highlights a strong agreement. Various flow-influencing parameters are considered to investigate entropy production, Bejan number, velocity, temperature, heat transport, and skin friction characteristics. The outcomes are presented in graphical form for different parameter values. After simulation, it is perceived that the melting parameter and Darcy number disrupt the entropy by 35.94 and 2.21%, respectively, and enhance the heat transport rate by 27.71 and 2.72%, respectively. This work can be utilized in designing innovative materials for electronics and textiles, in environmental processes like groundwater movement and pollutant dispersion, and in the biomedical field like hyperthermia treatments, tissue engineering, and regenerative medicine.

Surface dynamics on Jeffrey nanofluid flow with Coriolis effect and variable Darcy regime

AbstractStretching and shrinking application ranges from aerodynamic extrusion of plastic sheets, biological implants, condensation of metallic plates to the design of musical instruments. To emphasize the need for proper fluid flow in the mammalian system, the phenomenon of stretching or shrinking suppresses muscle strains and cramps, and also prevents stroke and heart disease. For further insight into the dynamics of blood with Prandtl number of 21.0 in a rotating system, the present study theoretically investigates the flow of a Jeffrey fluid induced with gold nanoparticles over a rotating sheet. The homogenization of the gold nanoparticle with the base fluid is due to the Tiwari‐Das approach. To investigate the flow profiles and dynamics of the sheet, the spectral local linearization method (SLLM) is used to obtain approximate solutions to the resulting system of nonlinear differential equations. The results obtained using the SLLM are validated by taking the limiting case and comparing against published literature results. The obtained results suggest that the velocity of the nanofluid and the heat transfer rate on the stretching and shrinking sheets exhibit an opposing behaviour. A blood sample with gold nanoparticles is advised for a reduced skin friction effect in the stretching sheet but a more significant drag force in the shrinking sheet than in the base fluid. For a unit value of the rotating parameter, the skin drag force reduces by 36% for the primary skin drag force and 57% for the secondary skin drag force.

Radiative Jeffrey fluid transport over a stretching surface with anomalous heat and mass flux

As a means of influencing technological advancements in engineering applications and various fluid products, the generalized Fourier’s and Fick’s models have proven to be of great importance. Industries such as power station engineering, high thermal material processing, and bio-heat elements apply the concept of anomalous heat and mass transfer mechanism. The objective of this study is to stimulate the flow of a radiative magnetohydrodynamics Jeffery fluid over an expanding surface with anomalous heat and mass transfer dynamics subjected to nth order reaction and variable thermophysical properties. A set of similarity transformations is used to neutralize the governing equations into a nondimensionless form. To obtain the model parametric analysis, a numerical tool via the spectral local linearization method (SLLM) is deployed after transformation of the governing flow equation from a two-unknown partial differential equations to a one-variable ordinary differential equation. It is observed that the thermal boundary layer thickness is found to be enhanced with increasing parametric values of magnetic, Eckert and radiation parameters. For the radiation parameter [Formula: see text], the skin drag force, Nusselt and Sherwood number increase by [Formula: see text], [Formula: see text] and [Formula: see text], respectively. Additionally, a [Formula: see text] increment in the nth order parameter boosts the rate of heat transfer by [Formula: see text] while it downsizes the Sherwood number by [Formula: see text].

Numerical examination of concentration-dependent wastewater sludge ejected into a drinking water source

One of the significant water-related health challenges globally is due to pollutant fate. Contaminants endanger the lives of humans, animals, and even plants. The present mathematical analysis explains reactive wastewater sludge ejected into a drinking water source from wastewater treatment plants. The assumption that wastewater sludge follows a power-law constitutive relation leads to nonlinear momentum and concentration equations. The contaminants are assumed to follow a nonlinear irreversible first-order sorption model. The numerical solution of the coupled problem is solved using the Bivariate Spectral Local Linearization Method and validated with the spectral Chebyshev weighted residual method. Profiles are presented for dimensionless flow velocity and concentration. Comprehensive explanations for the obtained results are provided with relevant applications.

Numerical Investigation for Nonlinear Thermal Radiation in MHD Cu–Water Nanofluid Flow in a Channel with Convective Boundary Conditions

The implications of nonlinear thermal radiation on a Cu–water nanofluid flow with varying viscosity characteristics and convective boundary conditions are investigated numerically in this article. The nonlinear model takes the combined effects of Joule dissipation and Ohmic heating into consideration. The Spectral Local Linearization Method (SLLM) is used to address the nonlinear governing model. The numerical investigation’s findings were conducted and compared with the existing study. In Cu–water nanofluid flows with variable viscosity and convective boundary conditions, nonlinear thermal radiation plays an important role, as this work insightfully demonstrates. Pertinent results for velocity, temperature, skin friction, and heat transfer rate are displayed graphically and discussed quantitatively with respect to various parameters embedded in the model. The results revealed that the Cu–water thermal distribution lessens as the nanoparticle volume fraction upsurges. The outcomes of this study have potential applications in industrial systems such as power plants, cooling systems, and climate control systems.

Eminence of ferrite particle shapes in stratified nanofluids concerning the melting phenomenon: Lie group and spectral analysis

The current study is being done to determine how the shape factors of NiZnFe2O4 (nickel zinc ferrite) nanosolid particles affect the free convective flow of engine oil (C8H18) based stratified nanofluid over a melting stretchable surface, which play a part in establishing flow patterns and thermal features. NiZn ferrite nanoparticles of needle, platelet, and brick shapes are used to assess the impact of shape factors in the presence of melting phenomena, heat generation/absorption, and viscous dissipation. Optimal solutions are obtained by the spectral local linearization method via Lie group analysis, with an emphasis on residual errors. According to the evaluation, this type of nanofluid is found to have a lower friction factor, entropy, and Bejan number when compared to conventional fluids. In the presence of viscous dissipation, brick-shaped particles are found to have a higher heat transport rate, whereas needle-shaped particles minimize entropy by 58.66%. Suspended ferrite nanoparticles with a melting effect reduce the entropy up to 62.4% and stratified nanofluid with a brick shape has a higher heat transfer rate as compared to ordinary nanofluid. It is also observed that heat absorption produces less heat transport compared to heat generation. This research is found to be useful in many sectors, such as tumor treatments, electromagnetic interfaces (EMI), microwave applications, bone plate surgeries, and aerodynamic extrusion processes.

Double diffusion and Hall effects on MHD sinusoidal natural convection flow of silver water-based nanofluid from a porous vertical plate

This paper scrutinizes Hall current, Soret and Dufour impacts on natural convective flow of nanofluid attributable to variation in sinusoidal surface temperature over a vertical plate through a porous medium with strong transverse magnetic field applied normally to the flow. In this regard, the silver metal is considered as nanoparticles with water as base fluid. The overlapping multi-domain bivariate spectral local linearization method (OMD-BSLLM) has been utilized to solve the dimensionless governing equations which are attained by means of appropriate transformations. The obtained results are portrayed via graphical and tabular formations to inspect flow fields, shear stresses, heat and mass transmission characteristics for varying thermo-physical parameters. We found that there is an enhancement in the flow fields, shear stresses and heat transportation with the use of silver nanoparticles. Thermal and concentration boundary layer thickness enhance by using porous material, whereas diminish with improvement in Hall effect and ratio of buoyancy forces. The flow characteristics decline with the inclusion of porous medium while elevates with increment in Hall parameter. Moreover, an upgrade in thermal-diffusion correspond to a substantial growth in concentration field along with mass transfer rate. Current analysis can be useful in MHD energy generators, and industrial applications such as heating and cooling procedures owing to the involvement of nanoparticles having superior thermal conductivity features.

A Novel Multivariate Spectral Local Quasilinearization Method (MV-SLQLM) for Modelling Flow, Moisture, Heat, and Solute Transport in Soil

Conventionally, the problem of studying the transport of water, heat, and solute in soil or groundwater systems has been numerically solved using finite difference (FD) or finite element (FE) methods. FE methods are attractive over FD methods because they are geometrically flexible. However, recent studies demonstrate that spectral collocation (SC) methods converge exponentially faster than FD or FE methods using a few grid points or on coarse grids. This work proposes and applies a multivariate spectral local quasilinearization method (MV-SLQLM) to model the transportation and interaction of soil moisture, heat, and solute concentration in a nonbare soil ridge. The MV-SLQLM uses a quasilinearization method (QLM) to linearize any nonlinear equations and then employs a local linearization method (LLM) to decouple the linearized system of PDEs to form a sequence of equations that are solved in a computationally efficient manner. The MV-SLQLM is thus an extension of the bivariate spectral local linearization method (BI-SLLM) that fails to deal with a 2D problem and is a modification of the MV-SQLM whose efficiency is compromised when operating on high dense solution matrices. We use the residual error norms of the difference between successive iterations to affirm convergence to the expected solution. To illustrate the application and check the solution accuracy, we conduct systematic analyses of the effect of model parameters on distribution profiles. Findings are in good agreement with theory and literature, thereby revealing suitability of the MV-SLQLM to solve coupled nonlinear PDEs with environmental fluid dynamics applications.

Study of nonlinear quadratic convection on magnetized viscous fluid flow over a non-Darcian circular elastic surface via spectral approach

The present work investigates quadratic convection on magnetized viscous fluid flow on a circular elastic surface susceptible to Rosseland nonlinear thermal radiation and the nonlinear Boussinesq approximation. The flow is traversing through a Darcy-Brinkman-Forchheimer porous material. The energy equation investigates the implications of heat source/sink, Joule heating, and viscous dissipation. Utilizing suitable similarity variables, the hypothesized mathematical modelling is converted into nonlinear systems. Numerical solutions of nonlinear differential equations are computed using the spectral technique, often recognized as the spectral local linearization method (SLLM). The proposed approach SLLM is based on decoupling and linearizing systems of linear equations using a basic linearization process combined with spectral collocation linearization. The computational findings for nondimensional parameters are reported for the velocity and temperature profiles. As a particular case of our investigation, we also perform a comparison with published results.

Analysis of Magnetohydrodynamic Micropolar Nanofluid Flow due to Radially Stretchable Rotating Disk Employing Spectral Method

The present analysis is aimed at examining MHD micropolar nanofluid flow past a radially stretchable rotating disk with the Cattaneo-Christov non-Fourier heat and non-Fick mass flux model. To begin with, the model is developed in the form of nonlinear partial differential equations (PDEs) for momentum, microrotation, thermal, and concentration with their boundary conditions. Employing suitable similarity transformation, the boundary layer micropolar nanofluid flows governing these PDEs are transformed into large systems of dimensionless coupled nonlinear ordinary differential equations (ODEs). These dimensionless ODEs are solved numerically by means of the spectral local linearization method (SLLM). The consequences of more noticeable involved parameters on different flow fields and engineering quantities of interest are thoroughly inspected, and the results are presented via graph plots and tables. The obtained results confirm that SLLM is a stable, accurate, convergent, and computationally very efficient method to solve a large coupled system of equations. The radial velocity grows while the tangential velocity, temperature, and concentration distributions turn down as the value of the radial stretching parameter improves, and hence, in practical applications, radial stretching of the disk is helpful to advance the cooling process of the rotating disk. The occurrence of microrotation viscosity in microrotation parameters ( A 1 − A 6 ) declines the radial velocity profile, and the kinetic energy of the fluid is reduced to some extent far away from the surface of the disk. The novelty of the study is the consideration of microscopic effects occurring from the micropolar fluid elements such as micromotion and couple stress, the effects of non-Fourier’s heat and non-Fick’s mass flux, and the effect of radial stretching disk on micropolar nanofluid flow, heat, and mass transfer.

Entropy Generation Effects on Hydromagnetic Williamson Nanofluid Flow through a Porous Media

Background: Two-dimensional Williamson nanofluid flow with magnetic effects occurs through an extending surface immersed in a porous media. This includes the impact of the applied magnetic field, chemical reactions, variable thermal conductivity, and heat generation. Based on the above assumption, this study investigates a hydromagnetic Williamson nanofluid passed through a stretching surface embedded in a porous media that is being analysed by assuming the impact of thermal radiation and magnetic field on the flow properties. Methods: After using an appropriate similarity transformation, the governing equations with boundary conditions were converted into a dimensionless form. These derived ordinary differential equations are highly nonlinear partial differential equations that are solved numerically using the spectral local linearisation method. Results: An analysis and comparison of results with existing literature are reported here. Excellent agreement has been found between our results and those previously published. The impact of the magnetic field parameters, heat generation, variable thermal conductivity, and chemical reaction parameters on the velocity, thermal, and concentration profiles are inspected in graphical and tabular forms Conclusion: The outcomes indicate that the velocity reduces with the increase in Williamson, porosity, and magnetic field parameters, whereas the concentration profile improves with these parameters. Entropy generation rate is also enhanced when the concentration difference parameter, Reynolds number, and Brinkman number are increased. Our results are extremely relevant and prove the same. A rise in the porosity parameter drops the velocity profiles but increases the temperature and concentration profiles. The entropy generation number is enhanced when the concentration difference parameter, Reynolds, and Brinkman numbers are increased.

Irreversibility scrutinization on EMHD Darcy–Forchheimer slip flow of Carreau hybrid nanofluid through a stretchable surface in porous medium with temperature‐variant properties

AbstractThe significance of hybrid nanofluids in controlling heat transmission cannot be overemphasized. Therefore, this article scrutinizes the electromagnetized flow of Carreau hybrid nanofluid towards a stretching surface in a Darcy–Forchheimer porous medium with the occurrence of slip conditions. To form the hybrid nanofluid, the amalgamation of silver and alumina nanoparticles (NPs) embedded in water as conventional fluid is assumed. For accurate interception of the rate of heat and mass transport, thermal conductivity and mass diffusion conductance are presumed to be temperature variants. The modeling system of partial differential equations has been translated into a nondimensional form by means of suitable similarity conversions. Then, the subsequent system of ordinary differential equations is handled using overlapping domain decomposition spectral local linearization method to acquire numerical solutions. The choice of the method has been justified through the provision of errors, condition numbers, and computation time. The behavior of distinct fluid parameters on the flow features, quantities of engineering curiosity, and entropy is analyzed. Findings of paramount importance constitute that the superior thermal conductivity, heat transfer efficiency, and low production cost can be achieved through the hybridization of silver and alumina NPs. The role of thermal radiation and temperature‐variant thermal conductivity is to enhance the thermal transport performance of Carreau hybrid nanofluids. The velocity, energy, and mass profiles grow with the utilization of injection effects. The principal aspiration of the second law of thermodynamics (minimizing the rate of entropy generation) can be achieved by considering shear‐thinning Carreau fluid while reducing the porosity parameter and Brinkman number in the existence of velocity slip conditions in the flow system. Outcomes of the current flow model can play a significant role in biomedical, technological, and various manufacturing processes. The approximation of entropy contributes towards power engineering and aeronautical propulsion to anticipate the smartness of the overall system.

Mixed Convection Flow over an Elastic, Porous Surface with Viscous Dissipation: A Robust Spectral Computational Approach

A novel computational approach is developed to investigate the mixed convection, boundary layer flow over a nonlinear elastic (stretching or shrinking) surface. The viscous fluid is electrically conducting, incompressible, and propagating through a porous medium. The consequences of viscous dissipation, Joule heating, and heat sink/source of the volumetric rate of heat generation are also included in the energy balance equation. In order to formulate the mathematical modeling, a similarity analysis is performed. The numerical solution of nonlinear differential equations is accomplished through the use of a robust computational approach, which is identified as the Spectral Local Linearization Method (SLLM). The computational findings reported in this study show that, in addition to being simple to establish and numerically implement, the proposed method is very reliable in that it converges rapidly to achieve a specified goal and is more effective in resolving very complex models of nonlinear boundary value problems. In order to ensure the convergence of the proposed SLLM method, the Gauss–Seidel approach is used. The SLLM’s reliability and numerical stability can be optimized even more using Gauss–Seidel approach. The computational results for different emerging parameters are computed to show the behavior of velocity profile, skin friction coefficient, temperature profile, and Nusselt number. To evaluate the accuracy and the convergence of the obtained results, a comparison between the proposed approach and the bvp4c (built-in command in Matlab) method is presented. The Matlab software, which is used to generate machine time for executing the SLLM code, is also displayed in a table.

Effects of yield stress and chemical reaction on magnetic two-phase nanofluid flow in a porous regime with thermal ray

This study investigates consequences of the steady flow of nanofluid via contracting cylinder utilizing the mathematical Buongiorno's model of nanofluid. Herein, the influence of magnetic field and porous materials are discussed in this paper. The parameters of heat sink/source and radiation are taken into respect. Furthermore, the react of chemical and the yield stress within the nanoingredients too, take up a new niche in this research. The transformations of similarity facilitate the paradigm of partial differential equations into ordinary differential equations. To hit the solutions of the nonlinear equations, the spectral local linearization method has been utilized. Consequences are discussed with diagrams and discussions. The physical consignments as a local Sherwood number, local Nusselt number and drag force are displayed. Excellent advancement in transmit of mass and heat is spotted, which can be conceived through graphs. Results elucidate that the transport of heat increased by increasing the porous medium permeability, thermal radiation, chemical reaction and magnetic field, but raising the heat sink/source and yield stress reduce the heat transfer, whereas the adverse behavior is noticed with the transmit of mass for these parameters.

Hall Effect on MHD Flow and Heat Transfer Over an Unsteady Stretching Permeable Surface In the Presence of Thermal Radiation and a Heat Source/sink

This paper employs the computational iterative approach known as Spectral Local Linearization Method (SLLM) to analyze Hall effect on MHD flow and heat transfer over an unsteady stretching permeable surface in the presence of thermal radiation and heat source/sink. To demonstrate the reliability of our proposed method, we made comparison with Matlab bvp4c routine technique and excellent agreement was observed. The governing partial equations are transformed into a system of ordinary differential equations by using suitable similarity transformations. The results are obtained for velocity, temperature, skin friction and Nusselt number.

Rheological Analysis of Suspended Single-Walled Carbon Nanotubes in a Walters' B fluid

Objective: In this paper, we present a rheological analysis of suspended single-walled Carbon nanotubes in a Walters' B fluid. Methods: We assume that the viscosity varies exponentially as a function of the temperature use the Reynolds model of viscosity for the study. A variable thermal conductivity is also assumed along with buoyancy, magnetic field, viscous dissipation and a convective boundary condition. The system of nonlinear coupled equations is solved using the spectral local linearization method. Results: Our solutions are validated using through comparison with previously published results for a given set of conditions. Conclusion: The study finds that good agreement is achieved.

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.