Nonlinear Ordinary Differential Equations Research Articles

Periodic and Axial Perturbations of Chaotic Solitons in the Realm of Complex Structured Quintic Swift-Hohenberg Equation

This research work employs a powerful analytical method known as the Riccati Modified Extended Simple Equation Method (RMESEM) to investigate and analyse chaotic soliton solutions of the (1 + 1)-dimensional Complex Quintic Swift–Hohenberg Equation (CQSHE). This model serves to describe complex dissipative systems that produce patterns. We have found that there exist numerous chaotic soliton solutions with periodic and axial perturbations to the intended CQSHE, provided that the coefficients are constrained by certain conditions. Furthermore, by applying a sophisticated transformation, the provided transformative approach RMESEM transforms CQSHE into a set of Nonlinear Ordinary Differential Equations (NODEs). The resulting set of NODEs is then transformed into an algebraic system of equations by incorporating the extended Riccati NODE to assume a series form solution. The soliton solutions to this system of equations can be found as periodic, hyperbolic, exponential, rational-hyperbolic, and rational families of functions. A variety of 3D and contour visuals are also provided to graphically illustrate the axially and periodically perturbed dynamics of these chaotic soliton solutions and the formation of fractals. Our findings are noteworthy because they shed light on the chaotic nature of the framework we are examining, enabling us to better understand the dynamics that underlie it.

Magnetohydrodynamic Stagnation Point Flow and Heat Transfer of Casson Fluids Over a Stretching Sheet

This research investigates the effects of heat transfer on the stagnation-point flow of a non-Newtonian Casson fluid in a two-dimensional magnetohydrodynamic (MHD) boundary layer over a stretched sheet, considering thermal radiation impacts. By employing similarity transformations, the governing partial differential equations are transformed into nonlinear ordinary differential equations. The obtained self-similar equations are numerically solved using the Optimal Homotopy Analysis Method (OHAM). The numerical results are graphically represented, showcasing the influence of various parameters on fluid flow and heat transfer characteristics. The study uncovers important dynamics in transport phenomena. Examining and illustrating the effects of dimensionless parameters on velocity, temperature, and concentration profiles reveal significant insights. Moreover, skin friction and Nusselt number results for Casson fluids are analyzed and presented. The findings indicate that the Casson parameter and Hartman number act in opposition to fluid momentum, while the thermal conductivity parameter enhances fluid temperature. Thus, this research provides valuable insights into MHD boundary layer flows of non-Newtonian Casson fluids with thermal radiation effects, and the OHAM solution method proves effective in predicting flow transport properties.

Mathematical analysis for flow of hybrid nanofluid over a vertical stretchable surface: Assisting and opposing flows

Research Problem: The importance of improving the temperature properties of commonly used fluids in industrial processes is being addressed in this research. Nanofluids, which are composed of extremely small particles dispersed in common liquids such as water or petrol, are the main subject of this area of study. Using a vertically stretchable surface subjected to thermal radiation, the study examines the heat transfer behavior and efficiency of nanofluids. Methodology: Nanofluids that convey heat are studied by applying the fundamental rules of fluid physics to the variables that control their motion. To measure the amount of energy transferred, a nanofluid model is used. Similarity transformations are used to convert the system’s differential equations into ordinary differential equations (ODEs). The subsequent set of nonlinear ODEs is solved using numerical methods. Utilizing graphical analysis, patterns of velocity and temperature may be seen, and their responses to changes in other parameters can be investigated. Implications: This research has important implications for our knowledge of how nanofluids act in heat transfer applications, especially when exposed to thermal radiation and working with vertically stretchy surfaces. The effects of flow direction and thermal conductivity on distributions of velocity and temperature were elucidated, among other important results. More effective heating and cooling systems may be possible as a result of these findings, which have consequences for improving heat transfer processes in industrial environments. Future Work: To better understand how nanofluids behave in heat transfer applications, future studies might investigate more complicated situations and boundary circumstances. It may be possible to optimize nanofluid formulations by studying the impact of various nanoparticle kinds and concentrations on heat transfer efficiency. Research could be more applicable to real-world industrial processes if the numerical results were experimentally validated.

Comparative analysis of non‐newtonian fluids over an exponentially stretching sheet with convective boundaries

AbstractThe primary objective of this research is to explore the behavior of several non‐Newtonian fluids, including Casson, Williamson, and Maxwell fluids, over an exponentially stretching sheet considering an inclined magnetic field into account. Non‐Newtonian fluids can be encountered in many industrial and biological applications. They differentiate themselves by their sophisticated viscosity and flow properties. For the purpose of optimizing applications like coating technologies, bioengineering, and polymer processing, it is essential to comprehend their flow dynamics. This work illuminates these fluids' behaviors under convective boundary conditions, which is important for numerous industrial processes. Due to the convective boundary conditions, heat transfer at the sheet is affected by the surrounding fluid. The dominating flow field's nonlinear partial differential equations (PDEs) are synthesized into a system of coupled nonlinear ordinary differential equations (ODEs) using appropriate similarity transformations, and the resulting equations are then numerically solved using the BVP4C solver in MATLAB software. To demonstrate the behaviors of velocity, temperature, and concentration, a parametric research has been attempted. Significant parameter's effect on velocity, temperature, concentration, skin friction coefficient, Nusselt number, and Sherwood number have been investigated, and numerical findings are shown graphically. The numerical data is validated to previously published results on a variety of particular instances and found to be in great agreement. For varying values of the porosity parameter, Darcy‐Forchheimer parameter, and magnetic field, the fluid velocity falls. It is claimed that as the Forchheimer number and the porosity parameter expands, the momentum boundary layer thickness and the velocity profile diminishes. Furthermore, at the maximum levels of Schmidt number, the temperature profile rises synchronously, although the concentration profile reflects the flip pattern.

Gelation in input-driven aggregation.

We investigate irreversible aggregation processes driven by a source of small mass clusters. In the spatially homogeneous situation, a well-mixed system consists of clusters of various masses whose concentrations evolve according to an infinite system of nonlinear ordinary differential equations. We focus on the cluster mass distribution in the long-time limit. An input-driven aggregation with rates proportional to the product of merging partners undergoes a percolation transition. We examine this process analytically and numerically. There are two theoretical schemes and two natural ways of numerical integration on the level of a truncated system with a finite number of equations. After the percolation transition, the behavior depends on the adopted approach: The giant component quickly engulfs the entire system (Flory approach), or a nontrivial stationary mass distribution emerges (Stockmayer approach). We also outline ageneralization to ternary aggregation.

GRNMOPT: Inference of gene regulatory networks based on a multi-objective optimization approach

Background and objectiveThe reconstruction of gene regulatory networks (GRNs) stands as a vital approach in deciphering complex biological processes. The application of nonlinear ordinary differential equations (ODEs) models has demonstrated considerable efficacy in predicting GRNs. Notably, the decay rate and time delay are pivotal in authentic gene regulation, yet their systematic determination in ODEs models remains underexplored. The development of a comprehensive optimization framework for the effective estimation of these key parameters is essential for accurate GRN inference. MethodThis study introduces GRNMOPT, an innovative methodology for inferring GRNs from time-series and steady-state data. GRNMOPT employs a combined use of decay rate and time delay in constructing ODEs models to authentically represent gene regulatory processes. It incorporates a multi-objective optimization approach, optimizing decay rate and time delay concurrently to derive Pareto optimal sets for these factors, thereby maximizing accuracy metrics such as AUROC (Area Under the Receiver Operating Characteristic curve) and AUPR (Area Under the Precision-Recall curve). Additionally, the use of XGBoost for calculating feature importance aids in identifying potential regulatory gene links. ResultsComprehensive experimental evaluations on two simulated datasets from DREAM4 and three real gene expression datasets (Yeast, In vivo Reverse-engineering and Modeling Assessment [IRMA], and Escherichia coli [E. coli]) reveal that GRNMOPT performs commendably across varying network scales. Furthermore, cross-validation experiments substantiate the robustness of GRNMOPT. ConclusionWe propose a novel approach called GRNMOPT to infer GRNs based on a multi-objective optimization framework, which effectively improves inference accuracy and provides a powerful tool for GRNs inference.

A mathematical treatment of the impact of p53 signalling on the expression of the transcription factor E2F in the CycE/Cdk2 subsystem in cancerous cells

Complex networks of proteins and genes control cell growth until mitosis. These components play crucial roles in determining the characteristics and timing of each reaction in the cell. A family of cyclins and cyclin-dependent kinases regulates the progression of the cell from one stage to the next, while certain inhibitors regulate cell proliferation, significantly impacting this process. We examine the impact of p53 protein production in the cyclin E/cyclin-dependent kinase 2 (CycE/CDK2) subsystem. Although the precise functioning of the p53 protein is not fully understood, it is known to exhibit pulsatile behaviour, triggered in response to DNA damage. Consequently, the expression of the p53 protein within the cell system increases with the severity of DNA damage. Similarly, levels of CycE/CDK2 are substantially elevated in instances of DNA damage.To investigate this subsystem, we have developed a mathematical model of the CycE/CDK2 subsystem, presented as non-linear ordinary differential equations. Our primary aim is to determine the conditions that could theoretically result in tumorigenesis. We conduct a dynamical systems analysis to investigate the presence of stable limit cycles, which indicate the standard operational states of cells. Our investigation reveals the levels of p53 protein at which the cell can correct defects, undergo apoptosis, or enter quiescence, and where the system exhibits a Hopf-bifurcation (limit cycles). This is the novelty of our study, as previous research has primarily focused on numerical simulations.Using MATLAB simulations, we produced various results in response to different expressions and concentrations of the p53 protein, allowing us to assess its influence on malignant cells. By altering the concentration of protein p53, we ascertain the specific cellular circumstances that facilitate its natural growth, self-correction in the presence of defective activity, and entry into a state of quiescence.This investigation is motivated by the significant role of oscillations in driving, controlling, and managing the cellular oversight machinery. These aspects are incorporated into developing a mathematical model that emulates cellular operations. From this research, we establish that E2F is a critical target to mitigate oncogenic activity, achievable by managing the pulsatile behaviour of the inhibitor p53 or inhibiting its production process within the cell machinery.

Mathematical Modelling Approach for Administration of Palatable Diet to Quantify Blood Glucose Level – A Reference to Systolic Blood Pressure

The study concerns the Mathematical analysis of some variations that arise in systolic blood pressure (SBP) for different human age groups due to endocrine disorders (diabetes). An attempt has been made to improve the blood glucose levels (both pre-prandial and post prandial) associated with SBP by the suitable administration of palatable diet. Red portions (Protein and Fat) and Black Portions (Carbohydrates containing sugar and starch) have been considered with the assumption of “weight” of an individual as constant. A Mathematical model has been developed by using coupled nonlinear ordinary differential equations to study the behaviour of blood glucose levels. These equations involve the terms as, the change in glucose and the change in insulin with respect to time, the food intake sensitivity constants and the step function which can provide the quantification of normal blood glucose levels. The effectiveness in the variation of systolic blood pressure is analysed for various age groups. The response of men and women aged 25 years and above and the case of juvenile is studied using multiple linear regression model. The assumption that the weight of an individual as constant is confirmed by ANOVA for the determination of blood-Glucose levels. The palatable diet composed of Protein (P), Fat (F) and Carbohydrate (C) as PFC model is simulated with Joselin’s Principle.

A mathematical insight to control the disease psoriasis using mesenchymal stem cell transplantation with a biologic inhibitor

Psoriasis is a chronic, non-contagious, immune-mediated skin disorder. Inflammation of the skin’s surface is characterised by scaly white, red, or silvery spots that occur due to the hyper-proliferation of keratinocytes in the epidermal layer. Primarily, pharmaceutical drugs or immune therapy are used to treat psoriasis. We are all aware that, certain therapeutic strategies can have some adverse effects, and over time, that hidden inflammation may manifest. This article introduces a mathematical model for psoriasis, formulated by employing a set of nonlinear ordinary differential equations (ODEs) that describe the densities of T-cells, dendritic cells (DCs), keratinocytes, and mesenchymal stromal cells (MSCs) as basic cell populations. A tumor necrosis factor-α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document} (TNF-α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$TNF-\\alpha$$\\end{document}) inhibitor has been imposed from the initial stage of the treatment regime, using the optimal control theoretic approach, and the numerical results have been observed. After 80 days of monitoring using only biologic TNF-α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$TNF-\\alpha$$\\end{document} inhibitors, if this approach did not provide the intended outcomes (when severity arises), stem cells are administered a few times in a pulsed manner as a cell replacement technique in addition to this anti TNF-α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$TNF-\\alpha$$\\end{document} medicine. We have observed the combined therapeutic benefit of stem cell replacement with a TNF-α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$TNF-\\alpha$$\\end{document} inhibitor from a mathematical point of view. The theoretical analysis and the numerical results revealed that stem cell transplantation, along with a TNF-α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$TNF-\\alpha$$\\end{document} inhibitor, is a promising psoriasis treatment option moving forward.

Numerical study of unsteady flow behavior of Cu-ethylene glycol nanoparticle on radially stretching sheet with Joule Heating effect

This article proposes a mathematical investigation of unsteady flow and heat transfer in the presence of Joule Heating over a radially stretching sheet using a nanofluid of Cu-Ethylene glycol. With an extensive numerical study, we reveal the novel interaction between the shape factors of nanoparticles and surface deformations brought about by stretching. As opposed to earlier studies that have mostly concentrated on traditional nanoparticle forms, our investigation methodically looks at the unique behaviors of Cu-EG nanoparticles on stretching surfaces. The research findings offer great potential for numerous practical applications, in addition to providing insight into basic concepts related to fluid dynamics and heat transfer. The solution to this issue is significant for enhancing thermal management in manufacturing environments, such as cooling systems used in aerospace and electronics. Therefore, our work establishes a foundation for novel methods of creating materials with customized qualities, opening the door for the creation of next-generation technologies that are more sustainable and functional. A numerical solution of the highly non-linear ordinary differential equation is attained with suitable boundary conditions by applying BVP4C in MATLAB. Impact of pertinent parameters on Cu-Ethylene glycol nanofluid Joule Heating concentration, as well as Eckert, Prandtl, and Biot-number on flow and heat transport, are studied. Important results show that the Joule Heating effect raises the total heat transfer rate by roughly 15 %, and the addition of Cu nanoparticles improves thermal conductivity by around 22 %. The findings show that the combined influences of Joule Heating and nanoparticle concentration greatly increase the heat transfer efficiency, offering important new information for the optimization of cooling systems in a range of industrial applications. Finding of the current study is that the shape factor of platelets effectively transfers heat and flow, with sphere forms convey the least amount of heat.

Thermohaline convection in MHD Casson fluid over an exponentially stretching sheet

Abstract This study investigates the thermohaline convection in MHD Casson fluid over an exponentially stretching sheet. This study has practical significance in industrial processes, materials processing, energy systems, and environmental applications. The governing equations describing the conservation for an electrically conducting fluid flow, thermal and concentration transports are considered based on the principles of mass, momentum, energy and concentration equations. Our first step involves transforming the governing nonlinear partial differential equations into a coupled nonlinear ordinary differential equations with the help of suitable similarity transformations. Second step, infinite domain [0, ∞) of the problem to a finite domain [0, 1] through a coordinate transformations. This specific choice is motivated by the wavelet's significance in the finite domain of [0, 1]. Third step, we effectively solve the resulting coupled nonlinear ordinary differential equations using the numerical Hermite wavelet method (HWM). This approach proves to be a valuable technique for obtaining significant results and insights in our study. Finally, the effect of known physical parameters on velocity, temperature and concentration are analysed through tables and graphs.

Electro-magnetohydrodynamic (EMHD) Darcy–Forchheimer flow of Sutterby nanofluid with variable thermal conductivity over a stretching sheet: Finite difference approach

This paper examines the enactment of a two-dimensional, steady, non-Newtonian nanofluid flow over a stretching sheet. The utilization of magnetic influences acting in the direction normal to the Darcy–Forchheimer boundary layer flow of the Sutterby nanofluid with variable thermal conductivity is taken into consideration. This study takes into account the effects of thermophoresis and Brownian motion. The study found that a 15% increase in magnetic field strength resulted in a 10% increase in heat transfer rate. Similarly, a 20% increase in nanoparticle volume percentage causes a 12% increase in the convective heat transfer coefficient. The problem’s model is formulated in the form of partial differential equations (PDEs), transformed via similarity transformation into nonlinear ordinary differential equations (ODEs). Applying the finite difference method yields the solution to reduced equations. EMHD Darcy–Forchheimer flow and nanofluid dynamics are combined in cutting-edge technology. This is important for many industrial and technical applications. Moreover, providing a strong computational framework provides a precise simulation of the flow behavior. By providing insights into the intricate interactions between electromagnetic forces, porous medium effects, and variable thermal conductivity in nanofluids flow across a stretched sheet, this study makes an essential contribution to the science of fluid dynamics. This research is very significant and enlightening for researchers and professionals who are interested in the design and optimization of heat transfer systems. The fluid flow is examined thoroughly and graphically, and the relationship between the profiles of velocity, temperature, and concentration and other important physical limitations is investigated. The effect of various physical parameters on concentration, velocity, temperature, skin friction, Nusselt number and heat flow coefficient is verified and examined using graphs and tables.

Stability analysis of dual solutions for nonlinear radiative magnetohydrodynamic flow of [formula omitted] hybrid nanofluid over a nonlinearly shrinking surface

The present work explores the existence and temporal stability of dual solutions with the consequence of nonlinear thermal radiation on hybrid nanofluid flow (including Silver and Titanium dioxide nanoparticles in water) past a permeable shrinking sheet. The analysis also considers the united outcomes of suction/injection, Joule heating, viscous dissipation, and magnetohydrodynamics. Employing realistic assumptions and suitable similarity transformations, the governing nonlinear partial differential equations are formulated and altered into a nonlinear ordinary differential equations system. These equations are then solved numerically using the Lobatto IIIA technique. It is observed that dual solutions can occur within a precise range of the shrinking surface parameter. Analyzing the temporal stability of these dual solutions under small disturbances shows that the upper solution branch is stable and represents a physically realistic solution to the problem. In contrast, the lower solution branch is unstable and not physically realizable. No solution exists beyond the critical λc=−1.3915 for the shrinking parameter. The critical values of shrinking parameter λc=−1.2565,−1.3188, and −1.4161 correspond to volume fractions of hybrid nanofluid with φAg−TiO2 of 2%,4%, and 8%, respectively. No solution exists beyond this critical point. The graphical representation and quantitative explanation demonstrate how various emergent characteristics affect momentum and thermal boundary layer profiles, Nusselt number, and skin friction. The velocity and temperature profile of hybrid nanofluid can be improved by adding a small volume of nanoparticle volume fraction. Thermal boundary layer thickness is amplified by an accumulation in the shrinking parameter, power index of velocity component, thermal radiation parameter, and temperature difference ratio. Sheering stress and heat transfer coefficient improve with adding more nanoparticles in the base fluid for the first solution braches, but opposite effects are found in the second solutions. The contributions of this research are significant both theoretically, in terms of advancing the mathematical modeling of hybrid nanofluid flow with heat transfer in engineering systems, and practically, in terms of applications to engineering cooling systems.

Weak solvability of elliptic variational inequalities coupled with a nonlinear differential equation

In this paper we establish existence, uniqueness, and boundedness results for an elliptic variational inequality coupled with a nonlinear ordinary differential equation. Under the general framework, we present a new application modeling the antiplane shear deformation of a static frictional adhesive contact problem. The adhesion process has been extensively studied, but it is usual to assume a priori that the intensity of adhesion is bounded by introducing truncation operators. The aim of this article is to remove this restriction.The proof is based on an iterative approximation scheme showing that the problem has a unique solution. A key ingredient is finding uniform a priori bounds for each iterate. These are obtained by adapting versions of the Moser iteration to our system of equations.

Signature of conservation laws and solitary wave solution with different dynamics in Thomas–Fermi plasma: Lie theory

We propose a Lie group method to discuss the modified KP equation appearing in Thomas–Fermi (TM) plasma, characterised by cold and hot electrons. The Lie method facilitates the identification of similarity reductions, infinitesimal symmetries, group-invariant solutions, and novel analytical solutions for nonlinear models. The similarity reduction method is carried out to transform the nonlinear partial differential equations (NLPDE) into the nonlinear ordinary differential equations (NLODE). This study focuses on solitary wave profiles due to their usefulness in various engineering applications, including monitoring public transportation systems, managing coastlines, and mitigating disaster risks. It also addresses the conservation laws associated with the modified KP equation. The generalised auxiliary equation (GAEM) scheme is used to compute the new solitary wave patterns of the modified KP equation, which explains the dynamics of nonlinear waves in Thomas–Fermi plasma. The idea of nonlinear self-adjointness is used to compute the conservation laws of the examined model. The graphical behaviour of some solutions is represented by adjusting the suitable value of the parameters involved.

On differential equations with exponential nonlinearities

Two-point boundary value problems for the second order nonlinear ordinary differential equations, arising in the heat conductivity theory, are considered. Multiplicity and existence results are established. The properties of solutions are studied. Estimates of the number of solutions are obtained. A bifurcation analysis was made and the bifurcation curves were presented. The analytical technique together with the phase plane analysis is used to obtain the results.

Mathematical Model for the Dynamics of Lassa Fever Incorporating Treatment and Isolation

Lassa Fever (Hemorrhagic Fever) is a widespread disease cause by Mastomys rodent and cause serious health problem leading to loss of lives. This research aims to analyze some existing with the intention of modifying or developing new one Mathematical Model for the Dynamics of Lassa Fever Incorporating Treatment and Isolation. We establish the positivity, boundedness, diseases free and endemic equilibria, basic reproduction number, local and global stability and carried out numerical simulation of the modified model. We formulate and analyze deterministic mathematical model of nine compartments for the transmission dynamics of Lassa Fever infection using a non-linear ordinary differential equation. We investigated a dynamic behavior of the modified model and performed the qualitative analysis of the model. The system has two equilibrium points, namely the disease-free equilibrium and the endemic equilibrium points. The basic reproduction number was calculated using the next-generation matrix and the stability of the model equations were carried out using MATLAB R2021a. the finding of this study shows that Lassa Fever can be significantly curtailed having the basic reproduction number less than unity and that if the implementation of Lassa Fever treatment, isolation is very effective this can reduced or eliminate the number of infected individuals.

Thermosolutal Marangoni convective flow of MHD tangent hyperbolic hybrid nanofluids with elastic deformation and heat source

Abstract In this work, the Marangoni convective flow of magnetohydrodynamic tangent hyperbolic ( F e 3 O 4 − Cu / {{\rm{F}}{{\rm{e}}}_{3}{\rm{O}}}_{4}-{\rm{Cu}}/ ethylene glycol) hybrid nanofluids over a plate dipped in a permeable material with heat absorption/generation, heat radiation, elastic deformation and viscous dissipation is discussed. The impact of activation energy is also examined. Hybrid nanofluids are regarded as advanced nanofluids due to the thermal characteristics and emerging advantages that support the desire to augment the rate of heat transmission. The generalized Cattaneo–Christov theory, which takes into account the significance of relaxation times, is modified for the phenomena of mass and heat transfer. The fundamental governing partial differential equations are converted to ordinary differential equations (ODEs) by adopting similarity variables. The Runge–Kutta–Fehlberg-45 technique is utilized to solve nonlinear ODEs. Regarding the non-dimensional embedded parameters, a graphic investigation of the thermal field, concentration distribution, and velocity profile is performed. The results show that the increasing Marangoni ratio parameter enhances velocity and concentration distributions while decreases the temperature distribution. The velocity profile is decreased and the efficiency of heat transfer is improved as the porosity parameter is increased. Nusselt number is diminished with the rising values of the porosity variable.

High-dimensional nonlinear flutter suppression of variable thickness porous sandwich conical shells based on nonlinear energy sink

Nonlinear energy sink (NES) is widely applied in engineering field due to the advantages of light weight, high robustness, unidirectional energy transfer, rapid and broadband vibration isolation. In this paper, nonlinear energy sink is utilized to suppress vibration of the variable thickness porous sandwich conical shells for the first time, and the high-dimensional nonlinear flutter suppression characteristics of the system of simply supported variable stiffness truncated porous sandwich conical shell coupled NES under aerodynamic force and thermal stress are investigated. By applying the first-order shear deformation theory (FSDT), Hamilton's principle and Galerkin technique, the high-dimensional nonlinear ordinary differential flutter suppression equations of the system appended with NES are established. The accuracy of the theoretical approach is ensured by the comparison of frequency results, while the NES dissipated kinetic energy ratio and the comparison of NES performance with other suppression systems are presented to prove the effectiveness of NES on nonlinear flutter suppression. The time history diagrams and limit cycle oscillation (LCO) amplitude curves, which reflect the high-dimensional nonlinear flutter suppression effect of NES, are obtained by employing the Runge-Kutta method. The effects of aerodynamic pressure, the parameters and positions of single NES, and the positions of parallel NES and series NES on the high-dimensional nonlinear flutter suppression characteristics of the system attached with NES are discussed in depth. Finally, the optimal high-dimensional nonlinear flutter suppression scheme is arrived.

Modeling heat‐mass transport for MHD bio‐convection Carreau nanofluid with Joule heating containing both gyrotactic microbes and nanoparticles diffusion

AbstractThe study of a bio‐convection is a natural progression that happens as microbes transport unsystematically in single‐celled or colony‐like environments; as they live ubiquitously, individuals, as in rodents, and plant forms. They're so much denser than liquid, owing to which, microbes develop a basis of bio‐convection. Gyrotactic microbes are individuals that dip up‐stream in contradiction of gravity in motionless liquid, producing the higher portion of the deferment to be thicker than the lesser part. Bioconvection's significance can be realized in a diversity of bio‐microsystems, for instance, bio‐tech allied to mass transport, biofuels, enzyme biosensors and fraternization. Together with nanofluids, a mixture of bioconvective is working to progress the structure's thermal enactment which has uses in diverse scientific structures. Recent study has related the progress of extrusion features, radiative heat progression and biofuel fabrication to the use of nanoparticles. The essential plans of the modern scrutinization are to examine the magneto bioconvection flow of nonlinear radiative Carreau fluid persuades by the nanofluid and Joule heating. Additionally, Convective conditions of heat, mass and motile microorganism with heat sink/source and chemical reaction have been explored. By means of similarity alteration to alter the nonlinear partial differential equations into nonlinear Ordinary differential equations (ODE). The solutions of subjected equations have been attained by exploiting the bvp4c algorithm. Homotopic algorithm has been also executed for comparison of bvp4c results and former studies. The impacts of relatable factors on diverse fields are sketched in graphic form. The study explores temperature field enhancement for thermo Biot and Brownian motion factors. Furthermore, the fluid concentration exaggerates for mass Biot and chemical reaction factor; however, declines for Brownian motion factor. The motile density field decays with the rising values for Peclet number and intensifies for motile density Biot factor. The comparison tables of current work and previous work also have been presented for the authentication of work with two different techniques.