Fourth Method Research Articles

Heat and mass transport of hydromagnetic Williamson nanofluid passing through a permeable media across an extended sheet of varying thickness

The primary goal of this work is to determine heat and mass transfer through fluid-flows sheets dealing mathematical modelling for stagnant and varying thick?ness, considering magnetic fields, permeability, heat source/sink, radiation, Joule heating, chemical reactions, and buoyancy force. The Runge-Kutta fourth order Method (RK-4th order) is used to transform PDE into ODE utilizing similarity con?versions. To tabularize mathematical remarks of the local parameters, RK-4th has been developed in MATLAB. For diverse parameters under diverse constant and changing thickness circumstances of fluid characteristics, Nusselt and Sherwood parameters are examined and quantified. Temperature, velocity, and volume frac?tion graphical representations are used to describe the effects of various factors. When it comes to irregular fluid properties, the coefficient of skin friction has a bigger impact than when it comes to continuous fluid characteristics. However, in the situation of inconstant fluid properties, the local Nusselt number is smaller than in the case of constant fluid characteristics. The RK 4th technique produced high precision computational results, according to the findings.

Exploration of casson fluid-flow along exponential heat source in a thermally stratified porous media

Objective of the present investigation is intended to study the MHD Casson fluids flow through an exponentially stretching surface. This free convective flow is in?vestigated in thermally stratified porous medium. Also viscosity along with thermal conductivity is varying with temperature. With the exponential decay for the inter?nal heat generation in the region and buoyancy force, the natural-convection is induced. Then the transformed set of equations of the flow after applying suitable similarity solutions were encountered by Shooting Technique in conjunction with the fourth ordered Runge-Kutta method. Outputs illustrates that with increased viscosity parameter an increasing velocity profile is noticed but a decrement is observed for temperature field in entire domain and near the wall for temperature gradient profile. Also with increased Casson fluids parameter decreasing velocity profile is noticed but an increment is observed for temperature field in entire do?main and for temperature gradient profile near the wall.

Anatomy of the IV Ventricle Applied to the Auditory Brainstem Implant (ABI)

Introduction: Hearing loss in its different degrees is widely recognized as one of the most common disabilities of humanity, it affects approximately 100 million people around the world, only in the United States there are more than 28 million1 Americans who suffer from it and it is expected These figures will increase significantly in the coming decades. The first Auditory Brainstem Implant (ABI) was developed in 1979 at the House Ear Institute in the United States by Dr. William House and Dr. William Hitselberger. The intricate anatomy of the IV ventricle is of great importance in ABI surgery. The IV ventricle in an ependymal cavity of the rhombencephalon, limited anteriorly by the brainstem and posteriorly by the cerebellum, in terms of its structure it can be divided into a roof, floor and two lateral recesses, it continues towards the cephalad with the cerebral aqueduct and caudally with the central medullary canal. Objective: To value the complex anatomy of the fourth ventricle Materials And Methods: A descriptive observational study was carried out in the chair of Normal Anatomy and Imaging Dr. Luis Dellepiane, from the Universidad del Salvador, CABA. During the months of August and September 2022. 6 cerebellums with brain stem and 3 formolized heads were used. Results: The fourth ventricle is a cavity that lies dorsal to the brainstem, ventral to the cerebellum, and medial to the cerebral peduncles. A floor and a roof are described as limits, in addition to two extensions called lateral recesses. The arrangement of these can be seen when performing a sagittal cut where the fourth ventricle shows the shape of a tent, with the floor being the base with a vental orientation, and the walls the roof with a dorsal orientation. Conclusions: The anatomical knowledge of the complex structure of the fourth ventricle is of vital importance in ABI surgery, it is necessary that the neurosurgeon and the otolaryngologist know the above for a better understanding of its intricate anatomy.

Higher order approximation in exponential form based on half-step grid-points for 2D quasilinear elliptic BVPs on a variant domain

This paper reports a new fourth order Finite Difference Method (FDM) in exponential form for two-dimensional quasilinear boundary value problem of elliptic type (BVPE) with variant solution domain. Further, this discretization is extended to solve the system of quasilinear BVPEs. Following are the main highlights of the proposed FDM:• An unequal mesh 9-point compact stencil is used to approximate the solution. Half-step points are used to evaluate the known variables of this problem. The convergence theory is studied for unequal mesh to validate the fourth order convergence of the suggested FDM.• It is applicable to BVPE irrespective of coordinate systems. Various benchmark problems, for example, Poisson equation in cylindrical coordinates, Burgers’ equation, Navier-Stokes (NS) equations in cylindrical and rectangular coordinates, are solved to depict their fourth order convergence.• Numerical results confirm the accuracy, trustworthiness and acceptability of the suggested numerical algorithm. These results endorse the superiority of the proposed FDM over the previously existing techniques of Mohanty and Kumar (2014), Mohanty and Setia (2014), Priyadarshini and Mohanty (2021).

A Novel Two Point Optimal Derivative free Method for Numerical Solution of Nonlinear Algebraic, Transcendental Equations and Application Problems using Weight Function

It’s a big challenge for researchers to locate the root of nonlinear equations with minimum cost, lot of methods are already exist in literature to find root but their cost are very high In this regard we introduce a two-step fourth order method by using weight function. And proposed method is optimal and derivative free for solution of nonlinear algebraic and transcendental and application problems. MATLAB, Mathematica and Maple software are used to solve the convergence and numerical problems of proposed and their counterpart methods.

New Analytical Method For Solution of Second Order Ordinary Differential Equations With Variable Coefficients

In this study, we propose four methods for the analytical solution of second order ordinary non-homogeneous differential equations with variable coefficients. In the first case, the method directly gives the solution in explicit or integral form. In the second method, the solution of the problem reduces to the solutions of adjoined second order ordinary differential equation of homogeneous type. As long as the analytical solution of two adjoined equations can be solved, the analytical solution can always be found. In the third method, the differential equation is transformed into Riccati equation. Riccati equation is solved by means of a method recently developed. In order to solve non-homogeneous differential equation, the fourth method is developed. The strategy is different but the solution is again based on the solution of Riccati equation.

Consistency and Convergence Analysis of an 𝐹(𝑥,𝑦) Functionally Derived Explicit Fifth-Stage Fourth-Order Runge-Kutta Method

The purpose of this paper is to analyze the consistency and convergence of an explicit fifth-stage fourth-order Runge-Kutta method derived using 𝒇(𝒙,𝒚) functional derivatives. The analysis revealed that the method is consistent and convergent. The implementation of this method on initial-value problems was done in a previous paper, and it revealed that the method compared favorably well with the existing classical fourth stage fourth order explicit Runge Kutta method.

Industrial ion-exchange chromatography development using discontinuous Galerkin methods coupled with forward sensitivity analysis

In this work, a discontinuous Galerkin method coupled with forward sensitivity analysis (DG-FSA) is presented. The DG-FSA method is used to reduce computational cost required for model-based ion-exchange chromatography development using industrial load samples. As an example, the design of an anion-exchange chromatography step is considered. This step is used to purify an experimental peptide product called Protein G from Novo Nordisk A/S (Bagsværd, Denmark). The results demonstrate, that a fourth order DG-FSA method can reduce computational cost of inverse problems by a factor ×16 compared to a second (low) order DG-FSA method. Furthermore, the fourth-order DG-FSA method enable the computation of probability distributions of optimized processing conditions given uncertainty in model parameters or inputs. This analysis is not possible within a reasonable timeframe when applying the second (low) order DG-FSA method. The design procedure facilitates the optimization of the Protein G purification step. In an experimental validation run, the productivity is increased by 70% while sacrificing 4% yield at a similar purity constraint compared to an experiment with baseline performance.

Explicit K-symplectic methods for nonseparable non-canonical Hamiltonian systems

We propose efficient numerical methods for nonseparable non-canonical Hamiltonian systems which are explicit, K-symplectic in the extended phase space with long time energy conservation properties. They are based on extending the original phase space to several copies of the phase space and imposing a mechanical restraint on the copies of the phase space. Explicit K-symplectic methods are constructed for two non-canonical Hamiltonian systems. Numerical tests show that the proposed methods exhibit good numerical performance in preserving the phase orbit and the energy of the system over long time, whereas higher order Runge–Kutta methods do not preserve these properties. Numerical tests also show that the K-symplectic methods exhibit better efficiency than that of the same order implicit symplectic, explicit and implicit symplectic methods for the original nonseparable non-canonical systems. On the other hand, the fourth order K-symplectic method is more efficient than the fourth order Yoshida’s method, the optimized partitioned Runge–Kutta and Runge–Kutta–Nyström explicit K-symplectic methods for the extended phase space Hamiltonians, but less efficient than the the optimized partitioned Runge–Kutta and Runge–Kutta–Nyström extended phase space symplectic-like methods with the midpoint permutation.

Pengaruh Metode Sterilisasi Permukaan terhadap Kultur Biji Jeruk Japansche Citroen (JC) Citrus limonia Osbeck

Effect of Surface Sterilization Methods on Seed Culture of JC Citrus limonia Osbeck Japansche Citroen (JC) Citrus limonia Osbeck is one type of citrus that is commonly used as rootstock. JC seed propagation through in vitro culture will be more effective. The initiation stage is the first step of in vitro culture to obtain microbial-free explants and initiate the initial growth. At this stage the problem of contamination becomes the main limiting factor. This study aims to obtain the appropriate method of sterilizing of JC orange seed explants in in vitro culture propagation. A total of four sterilization methods have been tested at the Tissue Culture Laboratory, Department of Biology, Faculty of Mathematics and Natural Sciences, Hasanuddin University. The sterilization material used is tween 80, fungicide, 20-30% NaOCl and 90% alcohol. The variables observed in this study were the time of appearance of contamination, the percentage of types of contaminants (bacteria and fungi), the percentage of sterile explants and the percentage of live explants after 28 days of culture. The results showed that the fourth method was the optimal sterilization method with the lowest contamination level of 30% of the other three methods with the highest explant survival rate of 60% compared to the other three methods.

Flow and Heat Transfer Analysis MHD Nanofluid due to Convective Stretching Sheet

Objectives: The study of flow and heat transfer on a permeable stretching sheet of Magnetohydrodynamic nanofluid under the influence of convective boundary condition is presented in this article. Mathematical modeling for the law of conservation of mass, momentum, heat and concentration of nanoparticles is executed. Methods: Governing nonlinear partial differential equations are reduced into nonlinear ordinary differential equations and then shooting method with fourth order Adams-Moulton Method is employed for its solution. Findings: The effects of magnetic parameter (0  M  2), Thermophoresis parameter (0:1  Nt  0:7) Lewis number (1  Le  4), Suction parameter (0  fw  3), Biot number(0:1  Bi  0:7) and Viscous dissipation(0  Ec  4) on axial velocity, temperature and concentration profiles are shown graphically. Numerical results were compared with another numerical approach and an excellent agreement was observed. The solutions under the impacts of different physical governing parameters are illustrated by means of graphs and tables. Effects of viscous dissipation is also discussed. Novelty: Despite the enormous importance and repeated application of nanofluids in industry and science, no attempt has been made to investigate the viscous dissipation effect on heat transfer with a permeable linear stretch sheet. Keywords: MHD; Nanofluid; Stretching Sheet; Viscous dissipation; Shooting technique; Adams-Moulton Method

ANALYTICAL SOLUTION OF MODIFIED FORCED VAN DER POL VIBRATION EQUATION USING MODIFIED HARMONIC BALANCE METHOD

For obtaining analytical solutions to the modified forced Van der Pol equation, the modified harmonic balance method has been developed. In classical harmonic balance method, the numerical procedure is used for solving a set of nonlinear algebraic equations. But it requires laborious computational attempt and accurate primary guesses values which makes it very hard-working to calculate. According to our method, a set of nonlinear algebraic equations has been converted to a set of linear algebraic equations by using a nonlinear one instead of a set. As a result, it reduces the massive computational work. This method provides not only better results than the existing harmonic balance method but also provides very close solutions to the corresponding numerical results. It is noticeable that there is substantial similarity between the approximate and the numerical results attained by the fourth order Runge-Kutta method. Moreover, the method is facile and straightforward. This technique may play great role to handle strongly nonlinear damped systems with external forces.

Numerical Solution of Hirota-satsuma Coupled Kdv System by Rbf-ps Method

In this paper, the Hirota-Satsuma coupled Korteweg-de Vries system is solved numerically by using radialbasis function-Pseudospectral method. The radial basis functions are used to approximate the space derivatives in the system. Moreover, the system has become a system of ordinary differential equations with independent variable , and this system is solved by Runge-Kutta fourth order method, with the help of MATLAB R2020a. Also, a comparison has been made between approximate solutions obtained by the proposed method and exact solutions

Derivation of a fourth-order Co-simulation method for linear systems

In this article, we present a detailed derivation of a fourth order co-simulation method. This method is implicit and based on Hermite extrapolation with two support points and their derivatives. The convergence order of the local and global errors is analyzed and tested on two linear systems from the mechanical and the electrical fields. Both systems are decomposed into two subsystems to perform co-simulation. We compare the fourth-order method with lower-order methods, confirming the expected convergence of the local error and showing that the global error of the derived method corresponds to O(H4).

The role of TiO2 NPs catalyst and packing material in removal of phenol from wastewater using an ozonized bubble column reactor

Phenol is present as a highly toxic pollutant in wastewater, and it has a dangerous impact on the environment. In the present research, the phenol removal from wastewater has been achieved using four treatment methods in a bubble column reactor (treatment by ozone only, using packed bubble column reactor with ozone, utilizing ozone with TiO2 NPs catalyst in the reactor without packing, and employing ozone with TiO2 NPs in the presence of packing). The effects of phenol concentration, ozone dosage, TiO2 NPs additions, and contact time on the phenol removal efficiency were determined. It was found that at a contact time of 30 min, the phenol removal was 60.4, 74.9, 86.0, and 100% for the first, second, third, and fourth methods, respectively. The results indicated that the phenol degradation method using catalytic ozonation in a packed bubble column with TiO2 NPs is the best treatment method. This study demonstrated the advantages of using packing materials in a bubble column reactor to enhance the mass transfer process in an ozonation reaction and then increase the phenol removal efficiency. Also, the presence of TiO2 NPs as a catalyst improves the ozonation process via the production of hydroxyl routs. Additionally, the reaction kinetics of ozonation reaction manifested that the first order model is more applicable for the reaction. Eventually, the packed bubble column reactor in the presence of TiO2 NPs catalyst provided a highperformance removal of phenol with a high economic feasibility.

Investigation of facile spectroscopic approaches for rapid calycosin determination in invitro biological samples and pharmaceuticals; application to the content uniformity of capsules

Calycosin, the major bioactive isoflavonoid inAstragali Radix and an important anti-viral drug with a variety of pharmacological actions, is being determined by five different spectroscopic methods. Two spectrophotometric methods have been investigated including measuring the absorption spectra at λmax = 270 nm and the first derivative spectra at λ = 288 nm for methods I and II, respectively. For the first time; the native fluorescence of calycosin is measured without adding any reagents. The fluorescence intensity was measured at 340 nm after excitation at 282 nm in method III. The fourth method involves the direct measuring of a first derivative spectrofluorimetric emission peak at 292 nm. In method V synchronous fluorescence spectra were recorded in methanol at Δλ = 70 nm. The linear range for the fluorescence-based methods was 0.05–1.0 µg/mL and for the UV-based methods was 0.5–10.0 µg/mL. The methods were validated per International Council of Harmonization (ICHQ2R1) guidelines. The limits of detection were found to be down to 0.11 and 0.12 µg/mL for the spectrophotometric methods, and 15.0, 18.0,16.0 ng/ mL, for the spectrofluorimetric approaches respectively, representing the high sensitivity. Accordingly, this permitted the quantitation of calycosin in spiked human plasma samples with satisfactory percentage recoveries (94.50.–102.50 %). The methods were utilized for calycosin analysis in different matrices including plasma and capsules with high precision and accuracy.

Impact of exponential form of internal heat generation on water-based ternary hybrid nanofluid flow by capitalizing non-Fourier heat flux model

The flow of fluids containing nanoparticles is important in industrial applications, particularly in nuclear reactors and nuclear system cooling to enhance energy efficiency. In connection to this, the convective boundary layer flow of ternary hybrid nanofluid (water-based graphene-CNT-Silver) flow over a curved stretching sheet with activation energy is investigated in this article. In addition, the non-Fourier heat flux model is taken into account. The use of similarity variables transforms the existing partial differential equations into an ordinary differential equation, which is then numerically solved using the Runge-Kutta-Fehlberg fourth and fifth order (RKF-45) method combined with a shooting approach. The set of graphical results for the significant parameters on thermal, concentration, and velocity profiles is explored. Results reveal that the heat transport in ternary hybrid nanoliquid rises as the thermophoresis and Brownian motion parameters rise. The Biot number influences the thermal profile positively, whereas the increasing Schmidt number and Stefan blowing parameter values reduce mass transport. The curvature parameter has positive impact on skin friction and mass transport rate but negative impact on heat transport rate. The concentration profile rises with increased activation energy parameter, but declines with increased chemical reaction rate parameter.

Atangana–Baleanu derivative-based fractional model of COVID-19 dynamics in Ethiopia

ABSTRACT The paper's main aim is to investigate the 2019 coronavirus disease in Ethiopia using a fractional-order mathematical model. It would also focus on the importance of fractional-order derivatives that may help us in modelling the system and understanding the effect of model parameters and fractional derivative orders on the approximate solutions of our model. A SELAIQHCR model is constructed using nonlinear differential equations in the Atangana–Baleanu non-integer operator in the Caputo sense. After that, the Chebyshev fourth kind spectral collocation method is used to change a fractional system to an algebraic system. Newton iterative technique is used to solve the converted system. The next-generation matrix technique is used to obtain the effective reproduction number. The COVID-19-free equilibrium point and endemic equilibrium point, solution positivity and boundedness, and their stability are all carefully done. The sensitivity of the effective reproduction value with respect to the key model parameters is discussed. The beginning values provided for our system were obtained using reports from the Ethiopian Public Health Institute from 29 February 2021 to 7 June 2021. The fundamental reproduction number is obtained with . The model's numerical solutions are represented graphically.

Thermal and entropy generation analysis of hybrid nanofluid flow through stretchable rotating system with heat source/sink

ABSTRACT This study presents the thermal-fluid transport and entropy generation of a hybrid nanofluid consisting of titanium oxide(TiO2) and gallic oxide(GO), flowing past a stretchable rotating system with a heat source/sink subjected to nonlinear radiation. The nanofluid transport past the rotating disk embedded in a porous medium is described utilizing a higher-order partial nonlinear coupled differential model simplified into an ordinary nonlinear model utilizing Karman’s transformation. This is analyzed utilizing the fourth fifth-order Runge Kutta Fehlberg method (RKF-45) and validated against other literatures for a simple condition that proves satisfactory. The analysis illustrates the impact of nanoparticle volume concentration on entropy generation. This shows that the increasing volume of nanoparticles concentration increases entropy, with the entropy of the hybrid nanofluid lower in relation to the nanofluid. At volume concentration of nanoparticles reveals an entropy magnitude of 7J/K at the lower disk, as the fluid approaches mid plate entropy steadily drops to 3J/K. Thereafter, the magnitude of entropy – as the nano mixture approaches the upper disk – steadily rises to 8J/K. The effect of nanoparticle volume concentration further depicts an increase in Bejan’s number. The study provides good insight into useful and practical applications, including turbines, power generating systems, and blood centrifuges, among others.

Distribution of non-uniform particles in an open channel flow from the concept of mixing length

This study deals with unsteady transport of suspended sediment in a fluid flow through an open channel that carries non-uniform particles coming from erodible sediment beds in which the flow is considered to be uniform and time-independent. To that purpose, the advection-diffusion equation is modified for the i-th grain-size class. The hiding and hindering effects caused by the interactions between non-uniform sediment particles have been taken into account through the modified expression of settling velocity. Additionally, the study utilizes the concentration-dependent expression of mixing length, which has been used previously for the transport of uniform sediment particles. The reference level for each non-uniform grain-size class has been calculated by determining the average saltation height of that class of grain. The effects of incipient motion probability, non-ceasing possibility and particle pick-up probability are taken into account while computing the reference concentration for each grain-size class. The governing equation has been solved numerically by the fourth order Runge-Kutta method. The temporal evolution of the grain-size distribution over a sediment bed has been shown at different heights. The findings indicate that starting from a unimodal bed distribution, a bimodal distribution of grain-size with one strong peak and one weak peak evolves to a bimodal distribution with two strong peaks as the vertical height increases. The effects of mixing length and modified settling velocity on the concentration profiles of non-uniform sediment particles have been shown. Both the effects result in a decrease in the magnitude of the concentration profile. Due to lack of data for unsteady transport, the obtained solution has been compared with the experimental data for steady transport of non-uniform grain-size particles at a sufficiently large time. Because the model reaches steady state after a sufficiently long time, has been shown through the analysis of relative change in concentration over time. Close agreement has been observed in all the cases. Also, the efficacy of the considered effects has been shown through the error analysis. The main advantage of the study is that, unlike most of the previous studies, the present model is able to predict the grain-size distribution in suspension without having any fitting parameters.