Spectral Relaxation Research Articles

A novel tetra hybrid bio-nanofluid model with stenosed artery

Abstract For treating and diagnosing cardiovascular diseases, the field of biomedical engineering is significant because it develops new ways and techniques. Stenosis is the narrowing of an artery, and it leads reduction in the flow rate of blood. This study investigates the blood flow mechanism in an artery using a mathematical model of Carreau nanofluid with four distinct nanoparticles. Tetra nanofluid model produces significant advancement in the simulation of blood flow through the stenosed arteries. The model is capable of predicting the pressure drop and velocity distribution for diagnosing and treating stenosis. The spectral relaxation approach is used to present the model's efficiency and effectiveness, which makes it a suitable method for solving the governing equations of this study. The findings of this study have important implications for the development of new treatments and diagnostic techniques for stenosis and other cardiovascular diseases.

Novel spectral methods for shock capturing and the removal of tygers in computational fluid dynamics

Spectral methods yield numerical solutions of the Galerkin-truncated versions of nonlinear partial differential equations (PDEs) involved especially in fluid dynamics. In the presence of discontinuities, such as shocks, spectral approximations develop Gibbs oscillations near the discontinuity. This causes the numerical solution to deviate quickly from the true solution. For spectral approximations of the inviscid Burgers equation in one-dimension (1D), nonlinear wave resonances lead to the formation of localised oscillatory structures called tygers in well-resolved areas of the flow, far from the shock. Recently, the author of [1] has proposed novel spectral relaxation (SR) and spectral purging (SP) schemes for the removal of tygers and Gibbs oscillations in spectral approximations of nonlinear conservation laws. For the 1D inviscid Burgers equation, it is shown in [1] that the novel SR and SP approximations of the solution converge strongly in L2 norm to the entropic weak solution, under an appropriate choice of kernels and related parameters. In this work, we carry out a detailed numerical investigation of SR and SP schemes when applied to the 1D inviscid Burgers equation and report the efficiency of shock capture and the removal of tygers. We then extend our study to systems of nonlinear hyperbolic conservation laws, such as the 2×2 system of the shallow water equations and the standard 3×3 system of 1D compressible Euler equations. For the latter, we generalise the implementation of SR methods to non-periodic problems using Chebyshev polynomials. We then turn to singular flow in the 1D wall approximation of the 3D-axisymmetric wall-bounded incompressible Euler equation [2]. Here, in order to determine the blowup time of the solution, we compare the decay of the width of the analyticity strip, obtained from the pure pseudospectral method (PPS), with the improved estimate obtained using the novel spectral relaxation scheme.

Hydromagnetic Non-Newtonian Nanofluid Flow Past Linealy Stretching Convergent-Divergent Conduit with Chemical Reaction

This paper investigates hydromagnetic non-Newtonian nanofluid flow past linearly stretching convergent-divergent conduit with chemical reaction using spectral ralaxation method. The fluid considered here is electrically conducting and is subjected to a constant pressure gradient and variable magnetic field. The two non-parallel walls are assumed not to intersect and the angle between the inclined walls is <i>θ</i>. The governing equations are continuity equation, momentum equation, species concentration, induction equation and energy equation. On modelling, the resulting partial differential equations are non-linear and are first transformed into system of ordinary differential equations through similarity transformation. The resulting boundary value problem is solved numerically using Spectral Relaxation Method. The results obtained after varying Hartman number, Unsteadiness parameter, Reynolds number, Solutal and Thermal Grashof number on velocity, concentration, temperature and induction profiles are represented in form of graphs. Some of the application of this study are, when extracting the energy from earth crust that varies in length between five to ten kilometres and temperature in between 500° and 1000°, nano-fluids are employed to cool the machinery and equipment working under high friction and high temperature. This present study considers nanofluid acting as a coolant of such equipment as well as acting as a lubricant thus reducing the rate of wear and tear of the equipment. The copper-water increases the thermophysical properties thus increasing heat transfer coefficient and hence increasing cooling rate.

Numerical simulation of antibacterial and antiviral mechanisms using silver nanoparticles with the dynamics of Casson–Walters-B and variable thermophysical properties

Purpose The purpose of this study is to consider the dynamics of Casson–Walters-B alongside gyrotactic microorganisms through the investigation of antibacterial and antiviral mechanisms using silver nanoparticles (AgNPs). The Casson fluid and Walters-B flow from the penetrable plate to the boundary layer (BL) in this analysis. The antiviral and antibacterial mechanisms of AgNPs were separately examined in this study. Design/methodology/approach The physical phenomenon of this problem was analyzed with partial differential equations (PDEs). These PDEs were changed into ordinary differential equations (ODEs) to further explain the significance of pertinent control parameters. The set of equations is solved numerically by implementing the spectral relaxation method (SRM). SRM is a numerical technique that uses the basic techniques of Gauss-Seidel. The SRM first decouples and linearizes the coupled nonlinear set of ODEs. Findings In this finding, it is found that the thermal radiation parameter produces higher temperatures within the BL to cause blockage in viral replications. It is found in this study that the magnetic parameter assisted in disinfection by lowering the antiviral and antibacterial mechanisms within the momentum BL. This is evident from the reduction in the velocity and momentum BL as the Casson and Walters-B parameters increase. Originality/value This paper is unique because it examined the antiviral and antibacterial mechanisms by using AgNPs. Prior to the authors’ understanding, no study of this type was conducted in the past. To the best of the authors’ knowledge, no other study in the past has examined the mechanisms of antiviral and antibacterial separately within the BL. Also, the simultaneous flow of Casson (honey) and Walters-B fluids were considered flowing through the vertical porous plate to the BL.

A method for determining the spectral relaxation functions of polymers under single stretching of micro samples

The principles of designing products made of the latest complex-structured polymer composite materials necessitate the need to take into account the large-scale structural effects determined by processes at the supramolecular and molecular levels of the polymer: relaxation, kinetic (breaking and recombination of chemical bonds), recrystallization of supramolecular structures, etc. The development of these processes is described by relaxation functions, which, in turn, can be calculated using the functions of relaxation time spectra. The purpose of the work was to develop a specialized equipment for testing micro-samples with a variable working part for uniaxial stretching along with the experimental technique and computational algorithms for processing the obtained measurement data, and experimental approbation of the developed approach to determining spectral relaxation functions. A method is proposed for estimating relaxation functions not at fixed stress levels within linear elasticity, at secant points of deformation diagrams, at fixed values of the linear elasticity modulus, but within an extended range of the sample deformation up to pre-rupture states. A set of test equipment designed for tensile tests of micro-samples with a thickness of the working part of 0.2 – 1.2 mm has been developed. The tooling can be installed on modern high-precision breaking machines. Tensile tests of polyethylene terephthalate micro-samples with a thickness of 50 and 175 μm were carried out taking into account the scale factor. A tensile test of micro-samples that are technologically stabilized by paper frames of a special shape is described. Diagrams illustrating the kinetics of changes in the spectral relaxation functions of oriented polyethylene terephthalate (PET) are constructed proceeding from the data of testing micro-samples with a constant strain rate. A method for using these diagrams in calculations of empirical relaxation time spectra is described. The results of testing micro-samples of polyethylene terephthalate are presented. Illustrative deformation diagrams of the studied polymer samples and calculated diagrams of functions of relaxation time spectra calculated according to the described method are given.

Inclusion of Hall and Ion slip consequences on inclined magnetized cross hybrid nanofluid over a heated porous cone: Spectral relaxation scheme

The cone geometry has a great significant for heat transmission in many industrial processes due to its ability to induce turbulence, enable directional flow, promote uniform temperature distribution, and offer versatility in applications. The current study aims to investigate the heat transport process of an inclined magnetized cross hybrid nanofluid over a heated porous cone under the influence of Hall and Ion slip consequences. Additionally, porous medium the flow is past under the effect of inclined uniform magnetic field and porosity of the medium is used to enhance heat transfer. The framed set of governing equations took the form of dimension free structure through appropriate transformations and then finally solved by an effective spectral relaxation method. Thermal impacts and heat transport mechanism associated with the hybrid flow is seen through different values of emerging parameters. Heat transport is seen higher with higher radiation parameters, as radiation and rising temperature are similar. Augmented values of Fr causes pressure drop in fluids which reduces the fluid motion and brings depreciation in velocity field. Eckert number also boosts the temperature of the fluid stirring via a porous rotating cone.

Numerical spectral approach for studying activation energy behavior in viscoelastic fluid flow through non-Darcian medium

The work examines the effects of MHD incompressible viscoelastic fluid under nonlinear thermal radiation while flowing in a non-Darcy porous medium. The utilization of the Darcy-Brinkmann-Forchheimer model has thus been implemented in the formulation of the momentum equation. The study posits the existence of a chemical phenomenon which involves elements A and B as two chemical species. The diffusion coefficient of chemical species exhibits inequality when considered for viscoelastic fluid. Numerical solutions are generated using SRM, spectral relaxation technique for governing flow problems. The current algorithm is formulated and implemented using the computational software MATLAB. The results exhibit a considerable degree of agreement with formerly established numerical outcomes within the framework of a specific scenario. The observations from this study provide evidence that chemical species B operates as a catalyst in a subsurface environment that is oriented horizontally. As a result, the connection between the homogeneous-heterogeneous scheme can be observed in the context of isothermal cubic autocatalytic occurrences and processes of the first order, subsequently. The utilization of the heterogeneous reaction parameter offers notable advantages in reducing the concentration of the bulk-fluid while simultaneously enhancing the concentration of the catalyst situated over the surface. The current findings contribute to the exploration of the computational study of diffusivities in MHD viscoelastic fluid flow. Specifically, this research inquires the effects of nonlinear thermal radiation and homogeneous-heterogeneous reactions.

Thermal diffusivity of inclined magnetized Cross fluid with temperature dependent thermal conductivity: Spectral Relaxation scheme

Understanding and controlling the thermal transport phenomena are crucial in numerous applications. The current research emphasizes thermal diffusivity of an inclined magnetized Cross fluid with temperature-dependent thermal conductivity with a computational iterative spectral relaxation scheme. Cross mathematical model is employed to characterizes non-Newtonian behavior and to uncover viscoelastic properties of fluid. Flow is incorporated under temperature thermal influence and external inclined magnetic strength is considered for thermal variations. Various prominent factors, including cross index, magnetic field, inclination angle, temperature-dependent thermal conductivity are analyzed on the fluid's thermal diffusivity. The flow governing PDEs are converted into system of ODEs by using suitable transformation. Spectral relaxation computation scheme is then used for controlling the new set equations. SRM algorithm controlling subsystems is built through MATLAB. Numerical results are illustrated by MATLAB graphs. Physical quantities such as Sherwood numbers, Nusselt and skin friction coefficient are visually taken place through statistical graphs with two cases of imposed magnetic field. The results of this investigation shed light on how non-Newtonian fluids behave when exposed to temperature changes and magnetic fields and useful in understanding and leverage these effects for specific applications.

Transporting Heat with Hybrid Carreau Nanofluid Over Rotating Cone with Slip and Hall Parameters

Background: Improvement in thermal system and its efficiency can be achieved by involving the hybrid nanoparticles due to its vital impact. This report analyzes Carreau Nanofluid with various nanoparticles for enhanced thermal efficiency. A rotating permeable cone with Hall and Ion slip forces is utilized in the setup. To evaluate momentum transportation, a cone is rotated and generalized Ohm’s law is applied, including an inclined magnetic force. Heat transfer analysis considers viscous dissipation, heat generation, and joule heating. Please shorten the given text for me to be able to assist you better. Novelty: This study innovatively uses spectral relaxation to solve characteristics of a magnetized, inclined Carreau Nanofluid. It investigates the effects of Hall and ion slip forces on a rotating, heated porous cone. No discussion yet on inclined magnetized environment for Carreau Yasuda NF movement over rotating cone with spectral relaxation. Formulation: PDEs governing Carreau fluid viscosity simulation transformed into ODEs with similarity transformation. The study includes graphs and tables displaying the impact of limitations on current and velocity fields. Findings: Higher energy and Eckert numbers increase heat transport, while Hall ion slip parameters enhance liquid waves. Hybrid nanoparticle speed slows due to ion slip and Hall parameters.

Entropy generation of thermophysical properties on heat and mass transfer pulsatile flow of non-Newtonian nanofluid

Purpose The purpose of this study is to investigate the effects of entropy generation of some embedded thermophysical properties on heat and mass transfer of pulsatile flow of non-Newtonian nanofluid flows between two porous parallel plates in the presence of Lorentz force are taken into account in this research. Design/methodology/approach The governing partial differential equations (PDEs) were nondimensionalized using suitable nondimensional quantities to transform the PDEs into a system of coupled nonlinear PDEs. The resulting equations are solved using the spectral relaxation method due to the effectiveness and accuracy of the method. The obtained velocity and temperature profiles are used to compute the entropy generation rate and Bejan number. The influence of various flow parameters on the velocity, temperature, entropy generation rate and Bejan number are discussed graphically. Findings The results indicate that the energy losses can be minimized in the system by choosing appropriate values for pertinent parameters; when thermal conductivity is increasing, this leads to the depreciation of entropy generation, and while this increment in thermal conductivity appreciates the Bejan number, the Eckert number on entropy generation and Bejan number, the graph shows that each time of increase in Eckert will lead to rising of entropy generation while this increase shows a reduction in Bejan number. To shed more light, these results were further demonstrated graphically. The current research was very well supported by prior literature works. Originality/value All results are presented graphically, and the results in this article are anticipated to be helpful in the area of engineering.

A computational investigation of diffusivities and heat transfer in the flow of viscoelastic fluid through Darcy–Brinkman–Forchheimer medium

The main objective of this work is to examine the effects of non-linear thermal radiation and induced magnetic fields on the behavior of viscoelastic fluid as it flows through a porous material that does not follow Darcy’s law. Hence, the Darcy–Brinkman–Forchheimer model has been employed when formulating the momentum equation. The research postulates the presence of a chemical process involving two chemical species, A and B. The research utilizes the spectral relaxation method (SRM) for the numerical solution of the altered governing equations. The present algorithm is formulated and executed on computational software MATLAB. The findings demonstrate a high level of concurrence with previously known numerical outcomes in the context of a specific scenario. The findings of this research demonstrate that chemical species B functions as a catalyst in a horizontally subsurface environment. Consequently, the relationship between the homogeneous-heterogeneous scheme may be seen in the context of isothermal cubic autocatalytic events and first-order processes, respectively. The use of the heterogeneous reaction parameter offers significant benefits in reducing the concentration of the bulk fluid while increasing the concentration of the catalyst located on the subsurface. Moreover, the results indicate that the impacts of induced magnetic and viscoelastic factors on velocity and induced magnetic fields are similar in their outcomes but differ in their fundamental nature.

Dynamics of Tangent Hyperbolic Fluid Past a Semi-infinite Plate with the Significance of Joule Heating, Thermal Radiation and Soret-Dufour Mechanisms

The present investigation concentrates on the unsteady flow of tangent hyperbolic liquid past a vertical plate under the influence of Lorentz force, Joule heating, and viscous dissipation. The mathematical modelling leads to nonlinear coupled partial differential equations (PDEs). Suitable non-dimensional quantities are applied to the governing PDEs to obtain dimensionless systems of equations. The transformed boundary layer PDEs are solved with the aid of the spectral relaxation method (SRM). The SRM employs the Gauss-Seidel techniques to linearize and decouple the system of nonlinear PDEs. The applied magnetic field acts as an opposition to the flow by producing the Lorentz force. The Weissenberg parameter, alongside the magnetic parameter, is observed to decline the velocity profile. An increment in thermal radiation parameter is observed to enhance the thickness of the hydrodynamic and thermal boundary layer. Therefore, the thermal condition and convective flow are improved with heat generation and thermal radiation in the flow phenomenon. This investigation is unique because it investigates the combined influence of Soret-Dufour and MHD, viscous dissipation, and Joule heating. This study plays a significant role in astrophysics, heat exchanger devices, MHD power generation, and geothermal energy extraction. When this study is compared to studies that have already been done, it agrees with those studies.

Effects of some embedded thermophysical properties on heat and mass transfer using erying powell model non-Newtonian nanofluid, between two poropus parallel plates

The effects of couple stress on the heat and mass transfer of pulsatile using Erying powel model non-Newtonian nanofluid flows between two porous parallel plates in the presence of Lorentz force are elucidated. The governing partial differential equations (PDEs) were non-dimensionalized using suitable non-dimensional quantities to transform the PDEs into a system of coupled non-linear partial differential equations (PDEs). The resulting equations are solved using the spectral relaxation method (SRM). The obtained results were plotted for concentration, temperature, and velocity and analyzed using some pertinent embedded parameters and physical quantities of scientific and engineering interest. In order to shed more light, these results were further demonstrated graphically. and in tabular forms.

Unsteady mhd flow of tangent hyperbolic liquid past a vertical porous plate plate

The analysis in this communication addresses the unsteady MHD flow of tangent hyperbolic liquid through a vertical plate. The model on mass and heat transport is set up with Joule heating, heat generation, viscous dissipation, thermal radiation, chemical reaction and Soret-Dufour in the form of partial differential equations (PDEs). The PDEs are simplified into a dimensionless PDEs by utilizing a suitable quantities. The simplified equations are solved by utilizing the spectral relaxation method (SRM). The outcomes shows that increase in the Weissenberg and the magnetic field degenerates the velocity profile. The thermal radiation is found to elevate the velocity and temperature profiles as its values increases. The impact of Soret and Dufour on the flow is found to alternate each other. The computational outcomes for concentration, temperature and velocity are illustrated graphically for all encountered flow parameters. The present outcomes are compared with previous outcomes and are found to correlate.

Spectral Relaxation Imaging Microscopy II: Complex Dynamics.

The dynamics of condensed matter can be measured by the time-dependent Stokes shift of a suitable fluorescent probe. The time-dependent spectral correlation function is typically described by one or more spectral relaxation correlation times, which, in liquid solvents, characterize the timescales of the dipolar relaxation processes around the excited-state probe. The phasor plot provides a powerful approach to represent and analyze time and frequency-domain data acquired as images, thus providing a spatial map of spectral dynamics in a complex structure such as a living cell. Measurements of the phase and modulation at two emission wavelength channels were shown to be sufficient to extract a single excited-state lifetime and a single spectral relaxation correlation time, supplying estimates of the mean rate of excited-state depopulation and the mean rate of spectral shift. In the present contribution, two more issues were addressed. First, the provision of analytic formulae allowing extraction of the initial generalized polarization and the relaxed generalized polarization, which characterize the fluorescence spectrum of the unrelaxed state and the fully relaxed state. Second, improved methods of model discrimination and model parameter extraction for more complex spectral relaxation phenomena. The analysis workflow was illustrated with examples from the literature.

Mathematical Modeling on Magnetohydrodynamics Upper Convected Maxwell Fluid Flow Past a Flat Plate Using Spectral Relaxation Approach

The focus of this treatise is on the scrutiny of MHD heat and mass transfer motion of upper convection Maxwell (UCM) fluid in a thermally radiated flat plate. The models of the flow equations were considered when there is a temperature difference: the Cattaneo-Christov model and the Soret-Dufour mechanisms. A magnetic field of firmness was inflicted in opposition to the flow. The flow inspection is controlled by partial differential equations (PDEs). Suitable similarity variables were utilised on the PDEs to obtain a set of nonlinear ordinary differential equations (ODEs). The simplified set of ODEs shall be answered by exploiting the spectral relaxation method (SRM). The SRM is a numerical technique that solves differential equations by utilising the repetition of a sequence of operations that is iterated iteratively by first decoupling the coupled systems of equations. The magnetism was found to decline the velocity and hydrodynamic boundary layer due to the Lorentz force. The Deborah number was found to enhance the velocity contour. The Eckert number was discovered to improve the temperature profile due to the production of heat energy within the boundary layer. An increase in Prandtl number was found to enhance the hydrodynamic and thermal boundary layer thickness. The local skin friction and Nusselt number were found to be elevated by the increase in the Dufour parameter.

Spectral characteristics analysis of rocks and ores based on the generalized effective medium theory of induced polarization

To study the electrical characteristics of rocks and ores, two- and three-phase medium models with different mineral contents, attenuation coefficients, relaxation times, and ellipticities were established based on the generalized effective medium theory of induced polarization (GEMTIP) model and the Debye decomposition method. Furthermore, the corresponding program was written for numerical simulation, and the complex resistivity (CR) spectral characteristics and relaxation time distribution (RTD) characteristics were analyzed. At the same time, seven representative ore samples from different mining areas were selected, their structural compositions were observed, and their complex resistivity was measured to obtain the variation characteristics and Nyquist curves of ore phase spectra. The differential evolution (DE) algorithm was employed to write a curve parameter fitting program based on which parameter fitting was performed for the theoretical model and the measured curves of ore samples. The physical and electrical parameters of the curves were obtained, and the variation characteristics of each parameter were analyzed. The generalized effective medium theory of induced polarization model could be adopted to further study the induced polarization (IP) anomaly from the structural and electrical properties of rocks and ores, which has important guiding significance for energy resource exploration, deep prospecting beyond 500 m, and environmental investigation by electrical (magnetic) methods.

A Model on Free Convective Casson Fluid Flow Past a Permeable Vertical Plate with Gyrotactic Microorganisms

This study focused on free convective MHD Casson fluid flow past a permeable vertical plate with microorganisms and Soret-Dufour mechanisms. The physical model is governed by system of partial differential equations (PDEs). The set of PDEs were overhaul into a nonlinear ordinary differential equation by considering acceptable similarity variable. The spectral relaxation method (SRM) was utilized to obtain solution to the overhaul nonlinear ordinary differential equations. This study examined critically the significant of the Gyrotactic microorganisms on Casson fluid locomotion Also, the significance of parameters such as thermal radiation, Soret-Dufour mechanisms, Brownian motion, Joule heating and so on are examined on velocity, concentration, motile microorganism and temperature profiles. The Casson parameter was found to intensify the velocity contour and the hydrodynamic boundary layer thickness. A higher magnetic parameter gives rise to Lorentz force which declines the motion of the fluid. There is higher temperature within the boundary layer because of the presence of thermal radiation.

A unified feature-spatial cycle consistency fusion framework for robust image matching

Robust image matching is a fundamental and long-standing open problem in computer vision. Conventional wisdom has exploited redundancy to improve the robustness of image matching (e.g., from pairwise to multi-image correspondence), which works well in the spatial domain. Inspired by the success of global optimization-based approaches, we propose a novel extension of cycle consistency from multi-image to multi-descriptor matching in this paper, which integrates useful information from the feature domain. More specifically, we build upon previous work of permutation synchronization and construct a novel cycle consistency model for multi-descriptor matching. The construction of cycle consistency model is based on the analogy between multi-image matching and multi-descriptor matching in a virtual universe. It allows us to formulate multi-image and multi-descriptor matching as a constrained global optimization problem. We have developed a spectral relaxation algorithm to solve this optimization problem, admitting an efficient implementation via fast singular value decomposition (SVD). To demonstrate the robustness of the proposed method named Cycle Consistency Fusion (C2F), we have evaluated it in terms of both raw matching accuracy (pairwise or multi-image) and several higher level downstream tasks such as homography and camera pose estimation. Extensive experimental results have shown that our C2F outperforms state-of-the-art methods consistently across different datasets and vision tasks.

Numerical Simulation for COVID-19 Model Using a Multidomain Spectral Relaxation Technique

The major objective of this work is to evaluate and study the model of coronavirus illness by providing an efficient numerical solution for this important model. The model under investigation is composed of five differential equations. In this study, the multidomain spectral relaxation method (MSRM) is used to numerically solve the suggested model. The proposed approach is based on the hypothesis that the domain of the problem can be split into a finite number of subintervals, each of which can have a solution. The procedure also converts the proposed model into a system of algebraic equations. Some theoretical studies are provided to discuss the convergence analysis of the suggested scheme and deduce an upper bound of the error. A numerical simulation is used to evaluate the approach’s accuracy and utility, and it is presented in symmetric forms.