Solitonic solutions and stability analysis of Benjamin Bona Mahony Burger equation using two versatile techniques.

This study aims to explore the precise resolution of the nonlinear Benjamin Bona Mahony Burgers (BBMB) equation, which finds application in a variety of nonlinear scientific disciplines including fluid dynamics, shock generation, wave transmission, and soliton theory. Within this paper, we employ two versatile methodologies, specifically the extended exp ( - Ψ ( χ ) ) expansion technique and the novel Kudryashov method, to identify the exact soliton solutions of the nonlinear BBMB equation. The solutions we discovered involve trigonometric functions, hyperbolic functions, and rational functions. The uniqueness of this research lies in uncovering the bright soliton, kink wave solution, and periodic wave solution, and conducting stability analysis. Furthermore, the solutions' graphical characteristics were explored through the utilization of the mathematical software Maple 2022 ( https://maplesoft.com/downloads/selectplatform.aspx?hash=61ab59890f2313b2241fde3423fd975e ). The system's physical interpretation is defined through various types of graphs, including contour graphs, 3D-surface graphs, and line graphs, which use appropriate parameter values. These recommended techniques hold significant importance and are applicable in diverse nonlinear evolutionary equations found in the field of nonlinear sciences for illustrating nonlinear physical models.

The corrosion behavior of low carbon steel (AISI 1010) influenced by grain size through microstructural mechanical.

Low-carbon steel (AISI 1010) is the predominant material used in industrial food processing equipment. Such equipment is vulnerable to the corrosive environment produced by various production stages. Different processes, such as sulphonation and carbonation, are used in the processing of sugar in the sugar industry, creating a corrosive atmosphere. The corrosion behavior of low carbon steel (AISI 1010) is strongly influenced by grain size variations, which in turn affect the microstructural mechanical properties of the material. The mechanical behavior and performance of metallic materials, including their corrosion resistance, is determined by grain size which is an important parameter for this phenomena. The impact of low-carbon steel (AISI 1010) microstructure on corrosion behavior is discussed in this work. Heat treatment produces two different types of microstructure from the same material, which are then analyzed. Scanning Electron Microscopy (SEM) and Energy Dispersive Spectroscopy (EDS) have both been used to study characteristics including morphology and content. By supplying an appropriate corrosive medium, the corrosion performance of several microstructures of low-carbon steel (AISI 1010) was assessed, and corrosion rates were calculated using weight-loss and electrochemical techniques. Results show that the creation of a protective coating with a higher charge transfer resistance is caused by the adsorption process. The variety in phases and grain sizes may contribute to the corrosion stability of different microstructures, and as a result, the corrosion rate lowers as average grain sizes are reduced. Employing the galvanic effect, pearlite increases the rate of ferrite corrosion. The study's findings support the notion that quenching low-carbon steel (AISI 1010) results in a finer grain structure and greater corrosion resistance.

The significance of chemical reaction, thermal buoyancy, and external heat source to optimization of heat transfer across the dynamics of Maxwell nanofluid via stretched surface.

Energy loss during the transportation of energy is the main concern of researchers and industrialists. The primary cause of heat exchange gadget inefficiency during transportation was applied to traditional fluids with weak heat transfer characteristics. Instead, thermal devices worked much better when the fluids were changed to nanofluids that had good thermal transfer properties. A diverse range of nanoparticles were implemented on account of their elevated thermal conductivity. This research addresses the significance of MHD Maxwell nanofluid for heat transfer flow. The flow model comprised continuity, momentum, energy transport, and concentration equations in the form of PDEs. The developed model was converted into ODEs by using workable similarities. Numerical simulations in the MATLAB environment were employed to find the outcomes of velocity, thermal transportation, and concentration profiles. The effects of many parameters, such as Hartman, Deborah, buoyancy, the intensity of an external heat source, chemical reactions, and many others, were also evaluated. The presence of nanoparticles enhances temperature conduction. Also, the findings are compared with previously published research. In addition, the Nusselt number and skin friction increase as the variables associated with the Hartman number and buoyancy parameter grow. The respective transfer rates of heat are 28.26 % and 38.19 % respectively. As a result, the rate of heat transmission increased by 14.23 % . The velocity profiles enhanced while temperature profiles declined for higher values of the Maxwell fluid parameter. As the external heat source increases, the temperature profile rises. Conversely, buoyancy parameters increase as it descends. This type of problem is applicable in many fields such as heat exchangers, cooling of electronic devices, and automotive cooling systems.

Comparative study of some non-Newtonian nanofluid models across stretching sheet: a case of linear radiation and activation energy effects.

The use of renewable energy sources is leading the charge to solve the world's energy problems, and non-Newtonian nanofluid dynamics play a significant role in applications such as expanding solar sheets, which are examined in this paper, along with the impacts of activation energy and solar radiation. We solve physical flow issues using partial differential equations and models like Casson, Williamson, and Prandtl. To get numerical solutions, we first apply a transformation to make these equations ordinary differential equations, and then we use the MATLAB-integrated bvp4c methodology. Through the examination of dimensionless velocity, concentration, and temperature functions under varied parameters, our work explores the physical properties of nanofluids. In addition to numerical and tabular studies of the skin friction coefficient, Sherwood number, and local Nusselt number, important components of the flow field are graphically shown and analyzed. Consistent with previous research, this work adds important new information to the continuing conversation in this area. Through the examination of dimensionless velocity, concentration, and temperature functions under varied parameters, our work explores the physical properties of nanofluids. Comparing the Casson nanofluid to the Williamson and Prandtl nanofluids, it is found that the former has a lower velocity. Compared to Casson and Williamson nanofluid, Prandtl nanofluid advanced in heat flux more quickly. The transfer of heat rates are 25.87 % , 33.61 % and 40.52 % at R d = 0.5 , R d = 1.0 , and R d = 1.5 , respectively. The heat transfer rate is increased by 6.91 % as the value of Rd rises from 1.0 to 1.5. This study is further strengthened by a comparative analysis with previous research, which is complemented by an extensive table of comparisons for a full evaluation.

Qualitative analysis and chaotic behavior of respiratory syncytial virus infection in human with fractional operator.

Respiratory syncytial virus (RSV) is the cause of lung infection, nose, throat, and breathing issues in a population of constant humans with super-spreading infected dynamics transmission in society. This research emphasizes on examining a sustainable fractional derivative-based approach to the dynamics of this infectious disease. We proposed a fractional order to establish a set of fractional differential equations (FDEs) for the time-fractional order RSV model. The equilibrium analysis confirmed the existence and uniqueness of our proposed model solution. Both sensitivity and qualitative analysis were employed to study the fractional order. We explored the Ulam-Hyres stability of the model through functional analysis theory. To study the influence of the fractional operator and illustrate the societal implications of RSV, we employed a two-step Lagrange polynomial represented in the generalized form of the Power-Law kernel. Also, the fractional order RSV model is demonstrated with chaotic behaviors which shows the trajectory path in a stable region of the compartments. Such a study will aid in the understanding of RSV behavior and the development of prevention strategies for those who are affected. Our numerical simulations show that fractional order dynamic modeling is an excellent and suitable mathematical modeling technique for creating and researching infectious disease models.

Computational study of a co-infection model of HIV/AIDS and hepatitis C virus models.

Hepatitis C infection and HIV/AIDS contaminations are normal in certain areas of the world, and because of their geographic overlap, co-infection can't be precluded as the two illnesses have a similar transmission course. This current work presents a co-infection model of HIV/AIDS and Hepatitis C virus with fuzzy parameters. The application of fuzzy theory aids in tackling the issues associated with measuring uncertainty in the mathematical depiction of diseases. The fuzzy reproduction number and fuzzy equilibrium points have been determined in this context, focusing on a model applicable to a specific group defined by a triangular membership function. Furthermore, for the model, a fuzzy non-standard finite difference (NSFD) technique has been developed, and its convergence is examined within a fuzzy framework. The suggested model is numerically validated, confirming the dependability of the devised NSFD technique, which successfully retains all of the key properties of a continuous dynamical system.

Insight into the dynamics of heat and mass transfer in nanofluid flow with linear/nonlinear mixed convection, thermal radiation, and activation energy effects over the rotating disk.

In this paper, we study linear and nonlinear mixed convection, activation energy, and heat radiation effects caused by nanoparticles. This study aims to improve the understanding of how nanofluids behave in the presence of rotating disks and develop more efficient and effective cooling technologies. The flow problem consisted of partial differential equations (PDE). It is challenging to calculate these equations as a result of these nonlinear PDEs. Consequently, we use appropriate similarities to transform them into ordinary differential equations (ODEs). The bvp4c Matlab built-in technique is then used to resolve these ODEs. The velocities, temperature, and concentration outcomes with the various factors are examined graphically. Additionally, tables are employed to analyze the skin friction and Nusselt number values. It is analyzed that increasing the linear and linear mixed convection parameters enhances the velocity profiles of nanofluid. Enhancements in heat are analyzed by increasing nonlinear thermal radiation and enhancement in concentration is examined by increasing activation energy. Furthermore, as the variables for thermophoresis and Brownian motion are increased, the Nusselt number falls. The heat transfer rate is 27.16% for [Formula: see text] and 39.28% for [Formula: see text]. Thus, the heat transfer rate is enhanced 12.12%. This study's practical applications include improving the behavior of fluids and the transfer of heat in rotating frameworks, which may affect energy systems, heat exchangers, and cooling advances in technology.

An investigation into a semi-porous channel's forced convection of nano fluid in the presence of a magnetic field as a result of heat radiation.

This study investigates the impact of heat radiation on magnetically-induced forced convection of nanofluid in a semi-porous channel. The research employs Akbari-Ganji's and Homotopy perturbation methods to analyze the effects of multiple parameters, including Hartmann number, Reynolds number, Eckert number, radiation parameter, and suction parameter, on the flow and heat transfer characteristics. The results demonstrate that increasing Reynolds number, suction, and radiation parameters increases temperature gradient, providing valuable insights into improving heat transfer in semi-porous channels. The study validates the proposed methods by comparing the results with those obtained from other established methods in the literature. The main focus of this work is to understand the behavior of nanofluids in semi-porous channels under the influence of magnetic fields and heat radiation, which is essential for various industrial and engineering applications. The future direction of this research includes exploring the effects of different nanoparticle shapes and materials on heat transfer performance and investigating the influence of other parameters, such as buoyancy forces and variable properties, on the flow and heat transfer characteristics. The findings of this study are expected to contribute to the development of more efficient thermal management systems in the future.

The stability analysis of a nonlinear mathematical model for typhoid fever disease.

Typhoid fever is a contagious disease that is generally caused by bacteria known as Salmonella typhi. This disease spreads through manure contamination of food or water and infects unprotected people. In this work, our focus is to numerically examine the dynamical behavior of a typhoid fever nonlinear mathematical model. To achieve our objective, we utilize a conditionally stable Runge-Kutta scheme of order 4 (RK-4) and an unconditionally stable non-standard finite difference (NSFD) scheme to better understand the dynamical behavior of the continuous model. The primary advantage of using the NSFD scheme to solve differential equations is its capacity to discretize the continuous model while upholding crucial dynamical properties like the solutions convergence to equilibria and its positivity for all finite step sizes. Additionally, the NSFD scheme does not only address the deficiencies of the RK-4 scheme, but also provides results that are consistent with the continuous system's solutions. Our numerical results demonstrate that RK-4 scheme is dynamically reliable only for lower step size and, consequently cannot exactly retain the important features of the original continuous model. The NSFD scheme, on the other hand, is a strong and efficient method that presents an accurate portrayal of the original model. The purpose of developing the NSFD scheme for differential equations is to make sure that it is dynamically consistent, which means to discretize the continuous model while keeping significant dynamical properties including the convergence of equilibria and positivity of solutions for all step sizes. The numerical simulation also indicates that all the dynamical characteristics of the continuous model are conserved by discrete NSFD scheme. The theoretical and numerical results in the current work can be engaged as a useful tool for tracking the occurrence of typhoid fever disease.

Novel insights for a nonlinear deterministic-stochastic class of fractional-order Lassa fever model with varying kernels.

Lassa fever is a hemorrhagic virus infection that is usually spread by rodents. It is a fatal infection that is prevalent in certain West African countries. We created an analytical deterministic-stochastic framework for the epidemics of Lassa fever employing a collection of ordinary differential equations with nonlinear solutions to identify the influence of propagation processes on infected development in individuals and rodents, which include channels that are commonly overlooked, such as ecological emergent and aerosol pathways. The findings shed light on the role of both immediate and subsequent infectiousness via the power law, exponential decay and generalized Mittag-Leffler kernels. The scenario involves the presence of a steady state and an endemic equilibrium regardless of the fundamental reproduction number, [Formula: see text], making Lassa fever influence challenging and dependent on the severity of the initial sub-populations. Meanwhile, we demonstrate that the stochastic structure has an exclusive global positive solution via a positive starting point. The stochastic Lyapunov candidate approach is subsequently employed to determine sufficient requirements for the existence and uniqueness of an ergodic stationary distribution of non-negative stochastic simulation approaches. We acquire the particular configuration of the random perturbation associated with the model's equilibrium [Formula: see text] according to identical environments as the presence of a stationary distribution. Ultimately, modeling techniques are used to verify the mathematical conclusions. Our fractional and stochastic findings exhibit that when all modes of transmission are included, the impact of Lassa fever disease increases. The majority of single dissemination pathways are less detrimental with fractional findings; however, when combined with additional spread pathways, they boost the Lassa fever stress.

Significance of heat transfer rate in water-based nanoparticles with magnetic and shape factors effects: Tiwari and Das model.

Nanofluids are implementable in a variety of applications, such as heat exchangers, the healthcare sector, the cooling of various devices, hybrid-powered machines, microelectronics, power plants, chemical processes, astronomical technology, cancer treatment, etc. Nanofluids also have enhanced heat transmission and thermal efficiency. The heat radiation of nanoparticles and the natural-convective flow of electrically conducting nanofluids over the rotating disk using Darcy Forchheimer's porous media, thermal radiation is investigated in this paper. The nanoparticles titanium dioxide and single-walled carbon nanotubes are taken into account with base fluid water. The main goal of this investigation is to enhance heat transfer in nanofluids. The mathematical solution for the model has been obtained through the utilization of cylindrical coordinates. The flow model, which forms the basis of the investigation, is constructed around partial differential equations (PDEs). To address the inherent nonlinearity of these PDEs, physical similarities are employed to transform them into ordinary differential equations (ODEs). Subsequently, the fourth-order Runge-Kutta technique is employed via Matlab to solve these ODEs. The graphical examination of the velocities and temperature with various parameters is an exquisite display of scientific artistry. The magnetic field component is anticipated to exhibit an inverse correlation with velocities, while the temperature profile is expected to surge with the rise of the nonlinear mixed convection parameter. Additionally, the skin friction and Nusselt number are meticulously computed and presented in a tabular format, adding a touch of elegance to the already breathtaking analysis. By boosting the radiation parameter, the Nusselt value declined. Moreover, it is observed that the nanofluids having a laminar nanoparticle shape have a greater heat transfer rate.

Comparative study of ternary hybrid nanofluids with role of thermal radiation and Cattaneo-Christov heat flux between double rotating disks.

Heat and mass transfer are crucial to numerous technical and commercial operations, including air conditioning, machinery power collectors, crop damage, processing food, heat transfer mechanisms, and cooling, among numerous others. The fundamental purpose of this research is to use the Cattaneo-Christov heat flux model to disclose an MHD flow of ternary hybrid nanofluid through double discs. The results of a heat source and a magnetic field are therefore included in a system of PDEs that model the occurrences. These are transformed into an ODE system using similarity replacements. The first-order differential equations that emerge are then handled using the computational technique Bvp4c shooting scheme. The Bvp4c function in MATLAB is used to numerically solve the governing equations. The influence of the key important factors on velocity, temperature, nanoparticles concentration, and is illustrated visually. Furthermore, increasing the volume fraction of nanoparticles improves thermal conduction, increasing the heat transfer rate at the top disc. The graph indicates that a slight increase in melting parameter rapidly declines the velocity distribution profile of nanofluid. The temperature profile was boosted due to the growing outcomes of the Prandtl number. The increasing variations of the thermal relaxation parameter decline the thermal distribution profile. Furthermore, for some exceptional instances, the obtained numerical answers were compared to previously disclosed data, yielding a satisfactory compromise. We believe that this discovery will have far-reaching ramifications in engineering, medicine, and the field of biomedical technology. Additionally, this model can be used to examine biological mechanisms, surgical techniques, nano-pharmacological drug delivery systems, and the therapy of diseases like cholesterol using nanotechnology.

Computational framework of cobalt ferrite and silver-based hybrid nanofluid over a rotating disk and cone: a comparative study.

The dominant characteristics of hybrid nanofluids, including rapid heat transfer rates, superior electrical and thermal conductivity, and low cost, have effectively piqued the interest of global researchers. The current study will look at the impacts of a silver and cobalt ferrite-based hybrid nanofluid with MHD between a revolving disk and cone. The collection of partial differentiable equations is converted into a set of ODEs via similarity transformations. We used the Homotopy analysis approach from the BVPh 2.0 package to solve the ordinary differential equations. The volume proportion of nanoparticles increases and the temperature distribution profile also increased. It is more efficient for metallurgical, medicinal, and electrical applications. Furthermore, the antibacterial capabilities of silver nanoparticles might be used to restrict the growth of bacteria. A circulating disc with a stationary cone has been identified to provide the optimal cooling of the cone disc device while maintaining the outer edge temperature constant. This study's findings might be useful in materials science and engineering. The usage of hybrid nanofluid in heat transfer and heat pumps, coolants in manufacturing and production, producing cooling, refrigerators, solar thermal collectors, and heating, air conditioning, and climate control applications are only a few examples.

Simulation of the water-based hybrid nanofluids flow through a porous cavity for the applications of the heat transfer.

This study looks at the natural convections of Cu + Al2O3/H2O nanofluid into a permeable chamber. The magnetic field is also executed on the flow field and the analysis has been approached numerically by the control volume method. The study of hybrid nanofluid heat in terms of the transfer flux was supplemented with a wide range of parameters of hybrid nanofluid fractions, Rayleigh numbers Hartmann numbers and porosity factor. It's also determined that the flow and thermal distribution are heavily affected by the concentration of the nanoparticles. The concentration of nanoparticles increases the transport of convective energy inside the enclosure. The primary findings demonstrate that a rise in both the Rayleigh number and Darcy number leads to an improvement in convective heat transfer within the enclosure. However, the porosity has a negligible effect. Additionally, the rotation in a clockwise direction has a beneficial impact on the dispersion of heat transfer throughout the cavity. Furthermore, it is concluded that hybrid nanofluids are more reliable than conventional fluids in improving thermal properties.

A computational fluid dynamics analysis on Fe3O4-H2O based nanofluid axisymmetric flow over a rotating disk with heat transfer enhancement.

In present times modern electronic devices often come across thermal difficulties as an outcome of excessive heat production or reduction in surface area for heat exclusion. The current study is aimed to inspect the role of iron (III) oxide in heat transfer enhancement over the rotating disk in an axisymmetric flow. Water is utilized as base fluid conveying nano-particle over the revolving axisymmetric flow mechanism. Additionally, the computational fluid dynamics (CFD) approach is taken into consideration to design and compute the present problem. For our convenience, two-dimensional axisymmetric flow configurations are considered to illustrate the different flow profiles. For radial, axial, and tangential velocity profiles, the magnitude of the velocity, streamlines, and surface graphs are evaluated with the similarity solution in the computational fluid dynamics module. The solution of dimensionless equations and the outcomes of direct simulations in the CFD module show a comparable solution of the velocity profile. It is observed that with an increment in nanoparticle volumetric concentration the radial velocity decline where a tangential motion of flow enhances. Streamlines stretch around the circular surface with the passage of time. The high magnetization force [Formula: see text] resist the free motion of the nanofluid around the rotating disk. Such research has never been done, to the best of the researchers' knowledge. The outcomes of this numerical analysis could be used for the design, control, and optimization of numerous thermal engineering systems, as described above, due to the intricate physics of nanofluid under the influences of magnetic field and the inclusion of complex geometry. Ferrofluids are metallic nanoparticle colloidal solutions. These kinds of fluids do not exist in nature. Depending on their purpose, ferrofluids are produced using a variety of processes. One of the most essential characteristics of ferrofluids is that they operate in a zero-gravity environment. Ferrofluids have a wide range of uses in engineering and medicine. Ferrofluids have several uses, including heat control loudspeakers and frictionless sealing. In the sphere of medicine, however, ferrofluid is employed in the treatment of cancer via magneto hyperthermia.