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The translocation of polymers through nanopores is a complex process influenced by various factors. In this study, the translocation behavior of a two-dimensional active polymer chain, comprised of a head active Brownian particle (ABP) and a tail passive polymer chain, through a nanopore is studied using Langevin dynamics simulations. Results show that the effect of the self-propulsion force of the ABP on the translocation differs significantly from the driving force inside the pore for traditional polymer translocations. Specifically, the translocation time τ initially increases with increasing the magnitude fs of the self-propulsion force and then decreases with a further increase in fs. A small fs lowers the potential barrier for the translocation and thus promotes slow translocations, whereas a large fs directly pulls the polymer chain through the nanopore following the scaling relation τ ∝ fs−1. Moreover, two asymptotic scaling relations between τ and polymer length N, τ ∝ Nα, are found, with the exponent α of about 2.5 for small fs or long N and the exponent α of about 1.4 for short active polymers with large fs. We discover that the slow rotation of the ABP accelerates the translocation process. [ABSTRACT FROM AUTHOR]

Biased and accelerated molecular simulations (BAMS) are widely used tools to observe relevant molecular phenomena occurring on time scales inaccessible to standard molecular dynamics, but evaluation of the physical time scales involved in the processes is not directly possible from them. For this reason, the problem of recovering dynamics from such kinds of simulations is the object of very active research due to the relevant theoretical and practical implications of dynamics on the properties of both natural and synthetic molecular systems. In a recent paper [A. Rapallo et al., J. Comput. Chem. 42, 586–599 (2021)], it has been shown how the coupling of BAMS (which destroys the dynamics but allows to calculate average properties) with Extended Diffusion Theory (EDT) (which requires input appropriate equilibrium averages calculated over the BAMS trajectories) allows to effectively use the Smoluchowski equation to calculate the orientational time correlation function of the head–tail unit vector defined over a peptide in water solution. Orientational relaxation of this vector is the result of the coupling of internal molecular motions with overall molecular rotation, and it was very well described by correlation functions expressed in terms of weighted sums of suitable time-exponentially decaying functions, in agreement with a Brownian diffusive regime. However, situations occur where exponentially decaying functions are no longer appropriate to capture the actual dynamical behavior, which exhibits persistent long time correlations, compatible with the so called subdiffusive regimes. In this paper, a generalization of EDT will be given, exploiting a fractional Smoluchowski equation (FEDT) to capture the non-exponential character observed in the relaxation of intramolecular distances and molecular radius of gyration, whose dynamics depend on internal molecular motions only. The calculation methods, proper to EDT, are adapted to implement the generalization of the theory, and the resulting algorithm confirms FEDT as a tool of practical value in recovering dynamics from BAMS, to be used in general situations, involving both regular and anomalous diffusion regimes. [ABSTRACT FROM AUTHOR]

We propose a Brownian ratchet for the unidirectional transport of stimuli-responsive molecules confined in a series of asymmetric geometries. It relies on repetitive cycles of aggregation and dispersion, which cause significant changes in molecular distribution within the confining geometry and enable the Brownian motion of the molecules to be ratcheted in a specific direction. To demonstrate the feasibility of the proposed Brownian ratchet, we conducted Brownian dynamics simulations where stimuli-responsive molecules were repeatedly aggregated and dispersed in a series of truncated conical tubes by altering intermolecular interactions. These simulations demonstrated the unidirectional transport of the molecules, indicating the efficacy of the proposed Brownian ratchet. Furthermore, we found that it becomes more effective with higher concentrations of molecules. This study suggests that, through the deliberate control of molecular assembly and disassembly by stimuli-responsive intermolecular interactions, it is possible to achieve directional and controlled molecular transport in various nanoscale applications. [ABSTRACT FROM AUTHOR]

As the physicochemical properties of ultrafine bubble systems are governed by their size, it is crucial to determine the size and distribution of such bubble systems. At present, the size or size distribution of nanometer-sized bubbles in suspension is often measured by either dynamic light scattering or the nanoparticle tracking analysis. Both techniques determine the bubble size via the Einstein–Stokes equation based on the theory of the Brownian motion. However, it is not yet clear to which extent the Einstein–Stokes equation is applicable for such ultrafine bubbles. In this work, using atomic molecular dynamics simulation, we evaluate the applicability of the Einstein–Stokes equation for gas nanobubbles with a diameter less than 10 nm, and for a comparative analysis, both vacuum nanobubbles and copper nanoparticles are also considered. The simulation results demonstrate that the diffusion coefficient for rigid nanoparticles in water is found to be highly consistent with the Einstein–Stokes equation, with slight deviation only found for nanoparticle with a radius less than 1 nm. For nanobubbles, including both methane and vacuum nanobubbles, however, large deviation from the Einstein–Stokes equation is found for the bubble radius larger than 3 nm. The deviation is attributed to the deformability of large nanobubbles that leads to a cushioning effect for collision-induced bubble diffusion. [ABSTRACT FROM AUTHOR]

Beyond well-documented confinement and surface effects arising from the large internal surface and severely confining porosity of nanoporous hosts, the transport of nanoconfined fluids remains puzzling in many aspects. With striking examples such as memory, i.e., non-viscous effects, intermittent dynamics, and surface barriers, the dynamics of fluids in nanoconfinement challenge classical formalisms (e.g., random walk, viscous/advective transport)—especially for molecular pore sizes. In this context, while molecular frameworks such as intermittent Brownian motion, free volume theory, and surface diffusion are available to describe the self-diffusion of a molecularly confined fluid, a microscopic theory for collective diffusion (i.e., permeability), which characterizes the flow induced by a thermodynamic gradient, is lacking. Here, to fill this knowledge gap, we invoke the concept of "De Gennes narrowing," which relates the wavevector-dependent collective diffusivity D0(q) to the fluid structure factor S(q). First, using molecular simulation for a simple yet representative fluid confined in a prototypical solid (zeolite), we unravel an essential coupling between the wavevector-dependent collective diffusivity and the structural ordering imposed on the fluid by the crystalline nanoporous host. Second, despite this complex interplay with marked Bragg peaks in the fluid structure, the fluid collective dynamics is shown to be accurately described through De Gennes narrowing. Moreover, in contrast to the bulk fluid, the departure from De Gennes narrowing for the confined fluid in the macroscopic limit remains small as the fluid/solid interactions in severe confinement screen collective effects and, hence, weaken the wavevector dependence of collective transport. [ABSTRACT FROM AUTHOR]

The dynamics of a soft particle suspended in a viscous fluid can be changed by the presence of an elastic boundary. Understanding the mechanisms and dynamics of soft–soft surface interactions can provide valuable insights into many important research fields, including biomedical engineering, soft robotics development, and materials science. This work investigates the anomalous transport properties of a soft nanoparticle near a visco-elastic interface, where the particle consists of a polymer assembly in the form of a micelle and the interface is represented by a lipid bilayer membrane. Mesoscopic simulations using a dissipative particle dynamics model are performed to examine the impact of micelle's proximity to the membrane on its Brownian motion. Two different sizes are considered, which correspond to ≈ 10 − 20 n m in physical units. The wavelengths typically seen by the largest micelle fall within the range of wavenumbers where the Helfrich model captures fairly well the bilayer mechanical properties. Several independent simulations allowed us to compute the micelle trajectories during an observation time smaller than the diffusive time scale (whose order of magnitude is similar to the membrane relaxation time of the largest wavelengths), this time scale being hardly accessible by experiments. From the probability density function of the micelle normal position with respect to the membrane, it is observed that the position remains close to the starting position during ≈ 0.05 τ d (where τd corresponds to the diffusion time), which allowed us to compare the negative excess of mean-square displacement (MSD) to existing theories. In that time range, the MSD exhibits different behaviors along parallel and perpendicular directions. When the micelle is sufficiently close to the bilayer (its initial distance from the bilayer equals approximately twice its gyration radius), the micelle motion becomes quickly subdiffusive in the normal direction. Moreover, the temporal evolution of the micelle MSD excess in the perpendicular direction follows that of a nanoparticle near an elastic membrane. However, in the parallel direction, the MSD excess is rather similar to that of a nanoparticle near a liquid interface. [ABSTRACT FROM AUTHOR]

Single-file transport occurs in various scientific fields, including diffusion through nanopores, nanofluidic devices, and cellular processes. We here investigate the impact of polydispersity on particle currents for single-file Brownian motion of hard spheres when they are driven through periodic potentials by a constant drag force. Through theoretical analysis and extensive Brownian dynamics simulations, we unveil the behavior of particle currents for random binary mixtures. The particle currents show a recurring pattern in dependence of the hard-sphere diameters and mixing ratio. We explain this recurrent behavior by showing that a basic unit cell exists in the space of the two hard-sphere diameters. Once the behavior of an observable inside the unit cell is determined, it can be inferred for any diameter. The overall variation of particle currents with the mixing ratio and hard-sphere diameters is reflected by their variation in the limit where the system is fully covered by hard spheres. In this limit, the currents can be predicted analytically. Our analysis explains the occurrence of pronounced maxima and minima of the currents by changes in the effective potential barrier for the center-of-mass motion. [ABSTRACT FROM AUTHOR]

We propose a generalization of the stochastic resetting mechanism for a Brownian particle diffusing in a one-dimensional periodic potential: randomly in time, the particle gets reset at the bottom of the potential well it was in. Numerical simulations show that in mirror asymmetric potentials, stochastic resetting rectifies the particle's dynamics, with a maximum drift speed for an optimal average resetting time. Accordingly, an unbiased Brownian tracer diffusing on an asymmetric substrate can rectify its motion by adopting an adaptive stop-and-go strategy. Our proposed ratchet mechanism can model the directed autonomous motion of molecular motors and micro-organisms. [ABSTRACT FROM AUTHOR]

We propose a stochastic Schrödinger equation in which the momentum is coupled to a white Gaussian noise. In the stochastic representation, the kinetic energy representing the self-interaction of momentum is reduced to a linear term of momentum. As such, the quantum evolution operator factorizes into two contributions due to the momentum and the potential, respectively. The exact quantum propagator thereby becomes an expectation of the stochastic one in which the amplitude results from the potential with a fluctuating position: The particle moves with a constant velocity, subjected to a complex Brownian motion. We demonstrate that the stochastic Schrödinger equation can be feasibly used to derive the quantum propagators for the linear potential and the harmonic oscillator system. Novel semiclassical and other approximations may be developed from the new representation of quantum mechanics. [ABSTRACT FROM AUTHOR]

Relativistic ratcheting of Dirac fermions on the surface of topological insulator Bi 2 Se 3 attached to a spiral multiferroic oxide is investigated. We find that the Dirac fermions on the surface of topological insulator Bi 2 Se 3 exhibit pronounced Brownian motion, tuned by the strength of exchange field established by the interaction of spin degrees of Dirac fermions and multiferroic oxide. The surface Dirac fermions show ratchet effect as a net current under the influence of orthogonal, commensurate ac drives in the presence of a symmetric periodic potential set by the exchange field. [ABSTRACT FROM AUTHOR]

A vast array of phenomena, ranging from chemical reactions to phase transformations, are analyzed in terms of a free energy surface defined with respect to a single or multiple order parameters. Enhanced sampling methods are typically used, especially in the presence of large free energy barriers, to estimate free energies using biasing protocols and sampling of transition paths. Kinetic reconstructions of free energy barriers of intermediate height have been performed, with respect to a single order parameter, employing the steady state properties of unconstrained simulation trajectories when barrier crossing is achievable with reasonable computational effort. Considering such cases, we describe a method to estimate free energy surfaces with respect to multiple order parameters from a steady state ensemble of trajectories. The approach applies to cases where the transition rates between pairs of order parameter values considered is not affected by the presence of an absorbing boundary, whereas the macroscopic fluxes and sampling probabilities are. We demonstrate the applicability of our prescription on different test cases of random walkers executing Brownian motion in order parameter space with an underlying (free) energy landscape and discuss strategies to improve numerical estimates of the fluxes and sampling. We next use this approach to reconstruct the free energy surface for supercooled liquid silicon with respect to the degree of crystallinity and density, from unconstrained molecular dynamics simulations, and obtain results quantitatively consistent with earlier results from umbrella sampling. [ABSTRACT FROM AUTHOR]

Inspired by significant physiological applications of peristaltic transport, a mathematical model for the peristaltic pumping of a Jeffrey nanofluid containing gyrotactic microorganisms through a flexible and vertical symmetric channel is investigated, along with the effects of thermal radiation, heat source/sink, chemical reaction, porous medium and Hall current. Swimming microorganisms in a model of non-Newtonian fluid has several biological and ecological benefits, including in the pharmaceutical industry, biofertilizers, biofuel technology, biosensors, etc. With these presumptions in mind, a conducting Jeffery fluid flow containing microorganisms via a porous vertical conduit is proposed. The expressions for the flow quantities are established by solving the governing equations of this study analytically using the homotopy perturbation method (HPM). A detailed examination is performed using the tables and graphical representations to comprehend the impact of significant components on this analysis. In addition, the results for Newtonian nanofluid are obtained as a special case and discovered that its velocity is lower than the Jeffrey nanofluid. It is observed that the best velocity distribution can be seen at larger thermal Grashof number and Darcy number. The size of the trapped bolus enhances with the increase of the Hall parameter. Furthermore, the density of the motile microorganism distribution declines for higher bioconvection Peclet number and bioconvection constant. [ABSTRACT FROM AUTHOR]

Activation energy is the fundamental unit of energy required to initiate chemical reactions. Some instances of initiation energy use include liquid dispersions bite dust fashioning, polymer ejection, food handling, and paper manufacturing. In view of this, the present study investigates the impact of steady, incompressible magnetized Casson–Maxwell non-Newtonian nanofluid between two stationary porous disks. The fluid movement is created by uniform injection in the direction of the axial of stationary disks. It is noticed that the thermal conductivity of the fluid varies with varying temperature. By using Buongiorno nanofluid concept the Cattaneo–Christov thermal expression is implemented. Along with this, activation energy is considered. By introducing the suitable similarity variables, the fluid model is reduced in terms of ordinary differential equations and numerical solutions are generated by using inbuild bvp4c function in MATLAB. The various dimensionless parameters impact on velocity, temperature, and concentration are presented graphically. A numerical table is presented to show the variation of local-Nusselt and -Sherwood numbers on various values of different parameters. The study reveals that improvement in Casson parameter will incline the fluid velocity, but an opposite trend is seen in the case of a magnetic field. A rise in the Brownian motion and thermophoresis parameter will enhance both temperature profiles. Improved values of activation energy will increase the concentration. The rate of heat transfer is observed more in the case of the upper disk than the lower disk. [ABSTRACT FROM AUTHOR]

The novelty of this paper is examining the impacts of Hall currents on Sisko nanofluid slip flow generated by an exponentially stretching sheet in the existence of entropy generation. Entropy generation assessment, Brownian, thermophoresis and Bejan numbers during convection flow are explored in the presence of the Hall effect. The pertinent parameters are Hall parameter m, a magnetic field parameter M, Brownian motion parameter N b , thermophoresis parameter N t , generalized thermal Biot number γ 1 , generalized velocity slip parameter λ and material parameter of Sisko fluid A. The changes in pertinent parameters on principal and secondary velocities, entropy generation and temperature are discussed. The coefficients of local skin friction, Brownian, thermophoresis and Nusselt/Sherwood numbers are expressed in a tabular structure. Two different kinds of power-law nanofluid, Pseudoplastic (n = 0. 7) and dilatant fluid (n = 1. 5) are considered. The current results exposed that growth in magnetic field parameter diminishes the nanofluid axial velocity and boosts the profiles of temperature, secondary nanofluid velocity and nanoparticle volume fraction. The coefficients of local skin friction are enhanced according to a growth in the magnetic field factor. The Pseudoplastic fluid supports the velocity, temperature and nanoparticle volume fraction profiles compared to the dilatant fluid. The local entropy generation number, Bejan number, local skin friction coefficients and local Nusselt/Sherwood numbers are influenced by the pertinent parameters. [ABSTRACT FROM AUTHOR]

Due to innumerable applications of nanofluid in heat transfer phenomena as well as engineering processes, the research on this innovative fluid over conventional fluid got popularity among researchers. Here, we have considered a non-Darcy porous surface medium for generalized Eyring–Powell fluid model under thermophoretic as well as Brownian movements. No mass flux phenomena along with heat sink-source and activation energy aspects are scrutinized; characteristics of random motion of fluid and thermophoresis diffusion characteristics for generalized Eyring–Powell fluid are examined briefly. The system of nonlinear PDEs is reduced to nonlinear ODEs by using the similarity variable technique; the numerical scheme bvp4c is used along with shooting technique. The physical aspects like flow of fluid, temperature profile, concentration for variation of concerned parameters have been computed and demonstrated pictorially with the help of graphs. It is observed that the velocity of nanofluid declines by increasing values of the power law index (q) and Eyring–Powell liquid parameters. Augmented values of Brownian moment, thermophoresis parameter as well as heat source rise with increase in temperature of nanofluid. The concentration profile of generalized Eyring–Powell nanofluid deteriorates for higher values of Schmidt number. Moreover, the transportation rate of heat declines against Pr, while it rises by increasing values of N t . [ABSTRACT FROM AUTHOR]

Presently, due to its extraordinary mechanical, thermal, electrical and biomedical facets nanofluids deliver several prospects to exaggerate the propensity of isothermal systems by augmenting the conductivity features of the host fluids. In various areas of the energy partition, nanoparticles show a remarkable measure in energy storage, energy variation, and energy convertible, i.e. thermoelectric plans, petroleum cells, supercapacitors, stellar cells, rechargeable batteries, light-radiating diode and carbon-based light-radiating diode, smart coatings. In this current conversation, we anticipated an unsteady 3D flow of the Sutterby nanofluid consequence of a bidirectional extended surface. To envision the thermophoresis and Brownian motion properties in Sutterby's nanofluid, the Buongiorno association is utilized in an additional refined technique. Variable thermal conductivity with heat source/sink property occurred deliberated considering heat transmission techniques. The appropriate transformation is applied for transposing the PDEs into nonlinear ODEs. For numerical results, the bvp4c programmed is prerequisite for elucidating the subsequent Ordinary differential equations. The distinct performance of the Sutterby nanofluid temperature and the concentration field are designated and discussed in the physical parameter's aspect. It is clear that the temperature of the Sutterby fluid decreases with respect to the ratio of stretching rates parameter and similar developments are observed for the thermophoresis and Brownian motion parameters. Furthermore, the concentration profile declines for sophisticated estimates of the Lewis number and thermophoresis parameters. [ABSTRACT FROM AUTHOR]

The aim of this study is to investigate the effects of thermal radiation and chemical reactions on magnetohydrodynamic hyperbolic tangent liquid, which includes nanoparticles on a stretched surface while taking into account Brownian motion and thermophoresis. The nonlinear partial differential equations governing the system are converted into nonlinear ordinary differential equations through suitable similarity transformations. The focus of the study is to elucidate important engineering concepts such as skin friction, Sherwood number, and heat transfer, as well as to understand the effects of various expressions on the different profiles. The Keller-box approach, a sophisticated numerical tool, is used to get the numerical answers to the current enquiry. The generated findings are extensively tested for correctness and dependability. The findings of this study might have far-reaching ramifications for a variety of technical applications, including heat exchangers, chemical reactors, and thermal management systems.The results show that the rate of mass transfer rises with the increment in the factors of chemical reaction, thermal radiation, nanoparticles volume, and Brownian motion. [ABSTRACT FROM AUTHOR]

The main purpose of this work is to investigate the innovation of flow of two-dimensional (2D) ferrofluid flow passing upon stretched surface having the effect of a magnetic dipole. The said problem is selected since its use is very common in biomedical as well as engineering applications together with systems of drug targeting under magnetic effects. The impacts of magnetic dipole along with radiation parameter in flow of ferromagnetic cross fluid for a stretched region are investigated in detail by use of suitable similarity variables the nonlinear, ODEs are obtained. The desired ODEs are resolved numerically by using RK fifth-order method parallel to shooting scheme. Impacts of ferromagnetic interaction, viscous dissipation, Curie temperature, and Buongiorno parameters with convective boundary conditions are perceived for velocity, temperature and concentration fields. Furthermore, the terms like velocity, mass transfer and thermal gradients are under consideration and pictorial scrutinizing is done. Moreover, temperature of ferromagnetic fluid upsurges for enlargement in the values of ferrohydrodynamics interaction and Curie temperature parameters. Concentration of ferrofluid reveals a contrary tendency against the parameters of thermophoresis and Brownian motion. Owing to extensive application prospects of magnetized nanofluids, this area has received interest from engineers and researchers; nanofluids have a noteworthy preference over ordinary fluids. [ABSTRACT FROM AUTHOR]

This work investigates the stochastic nonlinear Schrödinger equation in a more extended form, influenced by multiplicative noise which represents the temporal change of fluctuations. To obtain novel optical soliton solutions, the nonlinear partial differential equation is transformed into a nonlinear ordinary differential equation via symmetry reduction (non-classical symmetry). This stochastic nonlinear problem is proposed to be solved by using the modified generalized Riccati equation mapping method. The resulting stochastic solitons show how waves dispersion throughout transmissions via optical fibers. With the use of this method, we can investigate an expansive range of solutions from important physical standpoints, such as dark, bright, singular, and periodic solitons, as well as their noise term effects related to Brownian motion based on the Itô sense. Both 2D and 3D graphs are used to display the impact of the noise term on the solitons. The comes about and calculations show the importance, exactness, and effectiveness of the strategy. The model under consideration is also examined through the concept of modulation instability analysis. Different stable and unstable nonlinear stochastic differential equations that are found in mathematics, physics, and other connected ranges can be solved by utilizing this technique. Furthermore, the bifurcation of phase portraits are studied. [ABSTRACT FROM AUTHOR]

In this study, we present an exact derivation of a meso-scale mathematical model for analyzing heat transfer in nanofluids through variational convergence, targeting the reduction of discrepancies between theoretical predictions and experimental data. The model derives distinct sets of partial differential equations for microscale, mesoscale, and macroscale simulations, taking into account several influencing factors across different scales. By employing the weak convergence of distributions and the theory of distributions, we establish variational convergence between the PDEs at different scales. Significantly, the mesoscale model leads to a derivation of the quadratic dependence of thermal conductivity on the particle volume fraction. Our numerical evaluations reveal a marked improvement in prediction accuracy, with the proposed model reducing prediction error in some cases by as much as 92% compared to some existing linear models. Additionally, when tested against available experimental data, the model shows a closer alignment reinforcing its potential for enhancing the prediction and understanding of nanofluid heat transfer. Hence, this paper represents a valuable contribution to nanofluid heat transfer research, providing a promising direction for future advancements in the field. [ABSTRACT FROM AUTHOR]

In this article, an accurate computational approaches based on Lagrange basis and Jacobi-Gauss collocation method is suggested to solve a class of nonlinear stochastic Itô-Volterra integral equations (SIVIEs). Since the exact solutions of this kind of equations are not still available, so finding an accurate approximate solutions has attracted the interest of many scholars. In the proposed methods, using Lagrange polynomials and zeros of Jacobi polynomials, the considered system of linear and nonlinear stochastic Volterra integral equations is reduced to linear and nonlinear systems of algebraic equations. Solving the resulting algebraic systems by Newton's methods, approximate solutions of the stochastic Volterra integral equations are constructed. Theoretical study is given to validate the error and convergence analysis of these methods; the spectral rate of convergence for the proposed method is established in the L ∞ -norm. Several related numerical examples with different simulations of Brownian motion are given to prove the suitability and accuracy of our methods. The numerical experiments of the proposed methods are compared with the results of other numerical techniques. [ABSTRACT FROM AUTHOR]

The Brownian bridge or Lévy–Ciesielski construction of Brownian paths almost surely converges uniformly to the true Brownian path. We focus on the uniform error. In particular, we show constructively that at level N , at which there are $d=2^N$ points evaluated on the Brownian path, the uniform error and its square, and the uniform error of geometric Brownian motion, have upper bounds of order $\mathcal {O}(\sqrt {\ln d/d})$ , matching the known orders. We apply the results to an option pricing example. [ABSTRACT FROM AUTHOR]

This article is concerned with the practical stability performance of nonlinear impulsive stochastic functional differential systems driven by G-Brownian motion (G-ISFDSs). Comparing with traditional Lyapunov stability theory, practical stability can portray qualitative behaviour and quantitative properties of suggested systems. By employing G-Itô formula, Lyapunov–Razumikhin approach and stochastic analysis theory, some novel conditions for pth moment practical exponential stability and quasi-sure global practical uniform exponential stability of G-ISFDSs are established. The obtained results show that impulses may influence dynamic behaviour of the addressed system. Two numerical examples are given to verify the validity of our developed results. [ABSTRACT FROM AUTHOR]

The squeezing flow bears a major importance in everyday phenomena and has vast industrial and biomedical applications. The current study looks at the nanofluid flow among two infinite "parallel plates" that are squeezed. The velocity slip and first‐order compound response have been considered in this problem for a clear understanding of their consequences in the flow of nanofluid and heat transport mechanism. This fluid replica thinks about "Brownian motion" and the influences of "thermophoresis" of nanofluid. The novelty of this work lies in exploring the combined effects of first‐order chemical reaction and the velocity slip on unsteady squeezing flow of nanofluid between two parallel plates as one has not yet reported such effects. The prevailing equations are altered into simplified forms by deploying suitable similarity transformations. Then "numerical solutions" of these equations are obtained by applying the fourth‐order "Runge–Kutta method" with the help of the shooting technique. The accuracy is verified by using two different methods and also comparing our data with the available existing literature. The main goal is to study heat and mass transfer through unsteady squeezing plates by the influence of velocity slip and chemical reaction. The consequences of diverse pertinent parameters on fluid flow, thermal, and concentration fields have been explored in this study. With the rise in "velocity slip parameter" from 0 to 1, 81.37% decrease in skin friction coefficient, 15.81% increase in Nusselt number, and 29.13% increase in Sherwood number are observed. Rising values of the chemical reaction parameter from 0.3 to 0.5, the mass transfer coefficient increases by 66.94%. [ABSTRACT FROM AUTHOR]

The 3-D Casson nanofluid flow over a nonlinear permeable stretching surface is examined in the present work. The generalized form of Fourier's heat flux and Fick's mass flux are incorporated with the additional impacts of the magnetic field, chemical reaction, thermal radiation, and convective conditions for heat transfer. Buongiorno's model is used for the analysis of Brownian motion and molecular diffusion. The flow mechanism has been formulated in the form of a nonlinear system of partial differential equations, which are converted to the nondimensional form of the system of ordinary differential equations, using the similarity substitution. The homotopy analysis method has been applied for the solution of a derived nondimensional set of differential equations. The consequences of flow constraints on the energy, mass, and velocity fields are presented. It has been noted that the mass and energy curves are the increasing functions of the Forchheimer number, porosity factor, Hartman number, and thermophoresis parameters. Furthermore, it is found that compared to passive control, active control of nanoparticles gives a higher rate of energy transmission. [ABSTRACT FROM AUTHOR]

In this paper, we look at higher-order nonlinear Schrö dinger equation (HONLSE) through stochastic sense. This equation is examined in the presence of Brownian motion and noise term. Using the robust solver, we generate several new crucial stochastic solutions for the HONLSE. During fibre transmissions, the HONLSE coefficients, such as nonlinearity, dispersion and noise term, influenced the solitonic picture. The solitary properties of communication fibers were altered by higher-order features. To illustrate how these optical solutions behave physically, certain representations of the acquired solutions as super and shock-like shapes are introduced. The presented research can be extended to other nonlinear equations with comparable properties. [ABSTRACT FROM AUTHOR]

We propose a condition which is valid for a class of continuous Gaussian processes that may fail to be self-similar or have stationary increments. Some examples include the sub-fractional Brownian motion and the bi-fractional Brownian motion and the sub-bifractional Brownian motion. Under this assumption, we show an upper bound for the difference between the inner product associated with a class of Gaussian process and that associated with the fractional Brownian motion. This inequality relates a class of Gaussian processes to the well studied fractional Brownian motion, which characterizes their relationship quantitatively. As an application, we obtain the optimal Berry-Esséen bounds for the quadratic variation when H ∈ (0 , 2 3 ] and the upper Berry-Esséen bounds when H ∈ (2 3 , 3 4 ]. As a by-product, we also show the almost sure central limit theorem (ASCLT) for the quadratic variation when H ∈ (0 , 3 4 ]. The results in the present paper extend and improve those in the literature. [ABSTRACT FROM AUTHOR]

Fractional Brownian motion (fBm) is an experimentally-relevant, non-Markovian Gaussian stochastic process with long-ranged correlations between the increments, parametrised by the so-called Hurst exponent H ; depending on its value the process can be sub-diffusive (0 < H < 1 / 2) , diffusive (H = 1 / 2) or super-diffusive (1 / 2 < H < 1) . There exist three alternative equally often used definitions of fBm—due to Lévy and due to Mandelbrot and van Ness (MvN), which differ by the interval on which the time variable is formally defined. Respectively, the covariance functions of these fBms have different functional forms. Moreover, the MvN fBms have stationary increments, while for the Lévy fBm this is not the case. One may therefore be tempted to conclude that these are, in fact, different processes which only accidentally bear the same name. Recently determined explicit path integral representations also appear to have very different functional forms, which only reinforces the latter conclusion. Here we develop a unifying equivalent path integral representation of all three fBms in terms of Riemann–Liouville fractional integrals, which links the fBms and proves that they indeed belong to the same family. We show that the action in such a representation involves the fractional integral of the same form and order (dependent on whether H < 1 / 2 or H > 1 / 2 ) for all three cases, and differs only by the integration limits. [ABSTRACT FROM AUTHOR]

This paper is concerned with quantum stochastic differential equations driven by the fermion field in noncommutative space Lp(풞) for 2≤p<∞$$ 2\le p<\infty $$. First, we investigate the existence and uniqueness of Lp$$ {L}&#x0005E;p $$‐solutions of quantum stochastic differential equations in an infinite time horizon by using the noncommutative Burkholder–Gundy inequality given by Pisier and Xu and the noncommutative generalized Minkowski inequality. Then, we investigate the stability, self‐adjointness, and Markov properties of Lp$$ {L}&#x0005E;p $$‐solutions and analyze the error of numerical schemes of quantum stochastic differential equations. The results of this paper can be utilized for investigating the optimal control of quantum stochastic systems with infinite dimensions. [ABSTRACT FROM AUTHOR]

This study aims to obtain the optical soliton solutions of the stochastic perturbed Radhakrishnan–Kundu–Lakshmanan equation which models the optical solitons in optical waveguides such as silica fibers with Kerr law in the presence of chromatic and third-order dispersions by multiplicative white noise in Itô calculus. The study constitutes one of the works aimed at adapting the model in accordance with the importance of the noise effect in nonlinear optics. In the first step, the nonlinear ordinary differential form of the investigated problem has been obtained by using an appropriate complex wave transformation. The enhanced Kudryashov technique, which is the combination of Kudryashov and the new Kudryashov methods, is applied to the nonlinear ordinary differential form. As the result, bright, dark and singular stochastic soliton solutions of the analyzed problem have been carried out by assigning appropriate parameter values and the impact of noise effect on the soliton behavior has been investigated. Lastly, the graphical representations and required comments have been presented in the related sections. [ABSTRACT FROM AUTHOR]

Nanofluids are a relatively new class of materials that have gained attention in recent years due to their unique physical and thermal properties. They are used as contrast agents in biomedicine, including for magnetic resonance imaging (MRI) and computed tomography (CT). Keeping the above applications in mind, this theoretical study intended to explore the consequence of transient magnetized Casson nanoliquid driven by a permeable bi-direction time-dependent stretching platform positioned inclined subject to nonlinear heat source/sink. The Brownian movement, thermophoretic force, chemical reaction, and variable internal heating impacts are incorporated into the proposed flow problem. The leading constitutive PDEs are diminished into coupled nonlinear self-similar dimensionless ODEs through pertinent non-dimensional quantities. The resulting problems are addressed utilizing "Particle Swarm Optimization (PSO)" and a hybrid shooting methodology inspired by the Runge–Kutta four (RK4) method. The novelty of this work is the investigation of the numerical solution of magnetized Casson nanoliquid enclosing thermal radiation and chemical reaction via PSO along with hybrid shooting technique over time-dependent stretching sheet, which has not been elaborated on to date. The physical appearance of relevant physical factors on different flow phenomena are evaluated via graphs. For the stability purpose of the numerical method Average Square Residue Error (ASRE) and Total Average Square Residue Error (TASRE) are computed. For the validation purpose the present work is associated with the available work and great correlation is found. [ABSTRACT FROM AUTHOR]

Modeling of physical systems must be based on their suitability to unavoidable physical laws. In this work, in the context of classical, isothermal, finite-time, and weak drivings, I demonstrate that physical systems, driven simultaneously at the same rate in two or more external parameters, must have the Fourier transform of their relaxation functions composing a positive-definite matrix to satisfy the Second Law of Thermodynamics. By evaluating them in the limit of near-to-equilibrium processes, I identify that such coefficients are the Casimir–Onsager ones. The result is verified in paradigmatic models of the overdamped and underdamped white noise Brownian motions. Finally, an extension to thermally isolated systems is made by using the time-averaged Casimir–Onsager matrix, in which the example of the harmonic oscillator is presented. [ABSTRACT FROM AUTHOR]

AbstractIn this study, we delve into the magnetohydrodynamic heat and mass transfer flow of a Casson nanofluid over specifically chosen linear and nonlinear stretching surfaces embedded in a porous medium to understand their distinct effects on fluid behavior. By focusing on the influences of Brownian motion, thermophoresis, thermal radiation, and chemical reactions, we transformed nonlinear partial differential equations into ordinary differential equations, leveraging the Runge-Kutta method and Shooting Techniques for numerical solutions of momentum, temperature, and concentration profiles under predetermined boundary conditions. Our results, depicted in both graphical and tabular forms, shed light on how various parameters, including the Casson fluid characteristics, magnetic fields, buoyancy ratio, and mixed convection effects, influence fluid dynamics. A notable finding is that an increase in the Brownian motion parameter intensifies the fluid velocity and temperature profiles, but reduces its concentration profile, unveiling complex interactions within the nanofluid dynamics. This investigation underscores the importance of linear and nonlinear stretching surfaces in mimicking practical industrial scenarios, thereby providing insights that are crucial for optimizing processes such as coating, cooling of electronic devices, and in the manufacturing of thin plastic films, where precise control over heat and mass transfer is essential. [ABSTRACT FROM AUTHOR]

Abstract\nHIGHLIGHTSA Newtonian nanofluid containing suspended nanoparticles can substantially improve heat transfer due to enhanced energy transport mechanisms. This theoretical study investigates heat and mass transfer in biological tissues using such a nanofluid under a magnetic field. These properties have promising medical and engineering applications. The nonlinear governing equations were transformed into ordinary differential equations using similarity variables and numerically solved with MATLAB boundary value problem solver bvp4c, subject to appropriate boundary conditions. Results demonstrated increasing the heat source parameter dramatically raised tumor interstitial temperature. This heating, along with improved nanoparticle accumulation within the tumor due to the thermal effects, are together essential for effective hyperthermia treatment. The model provides new insights into tuning heat and mass transport mechanisms in biological tissues via nanofluids for therapeutic applications. Therefore, the findings of this study may improve the efficacy of thermal therapy in treating cancer.This work examined magnetic field effects on heat transfer and nanoparticle (NP) transport in a Newtonian nanofluid within tissue surrounding a blood vessel.Elevating the external heat source power distributes NPs and increases tumor temperature.Boosting the thermophoresis coefficient enhances NP dispersion into tissue.Tuning heat and mass transport mechanisms via nanofluids shows promise for advancing hyperthermia cancer treatment.This work examined magnetic field effects on heat transfer and nanoparticle (NP) transport in a Newtonian nanofluid within tissue surrounding a blood vessel.Elevating the external heat source power distributes NPs and increases tumor temperature.Boosting the thermophoresis coefficient enhances NP dispersion into tissue.Tuning heat and mass transport mechanisms via nanofluids shows promise for advancing hyperthermia cancer treatment. [ABSTRACT FROM AUTHOR]

A p -adic Brownian motion is a continuous time stochastic process in a p -adic state space that has a Vladimirov operator as its infinitesimal generator. The current work shows that any such process is the scaling limit of a discrete time random walk on a discrete group. Earlier work required the exponent of the Vladimirov operator to be in (1 , ∞) , and the convergence was the weak convergence of probability measures on the Skorohod space of paths on a compact time interval. The current approach simplifies the earlier approach, allows for any positive exponent, eliminates the restriction to compact time intervals, and establishes some moment estimates for the discrete time processes that are of independent interest. [ABSTRACT FROM AUTHOR]

This paper aims to provide a consistent, finite-valued, and mathematically well-defined reformulation of Feynman’s path-integral measure for quantum fields obtained by studying the Wiener stochastic process in the infinite-dimensional Hilbert space of quantum states. This reformulation will undoubtedly have a crucial role in formulating quantum gravity within a mathematically well-defined framework. In fact, this study is fundamentally different from any previous research on the relationship between Feynman’s path-integral and the Wiener stochastic process. In this research, we focus on the fact that the classic Wiener measure is no longer applicable in infinite-dimensional Hilbert spaces due to fundamental differences between displacements in low and extremely high dimensions. Thus, an analytic norm motivated by the role of the fractal functions in the Wilsonian renormalization approach is worked out to properly characterize Brownian motion in the Hilbert space of quantum states on a compact flat manifold. This norm, the so-called fractal norm, pushes the rougher functions (physically the quantum states with higher energies) to the farther points of the Hilbert space until the fractal functions as the roughest ones are moved to infinity. Implementing the Wiener stochastic process with the fractal norm, results in a modified form of the Wiener measure called the Wiener fractal measure, which is a well-defined measure for Feynman’s path-integral formulation of quantum fields. Wiener fractal measure has a complicated formula of non-local terms but produces the Klein–Gordon action at the first order of approximation. Using complex integrals to compensate for the removal of non-local terms appearing in higher orders of approximation, the Wiener fractal measure turns into a complex measure and generates Feynman’s path-integral formulation of scalar quantum fields. This brings us to the main objective of this study. Finally, some various significant aspects of quantum field theory (such as renormalizability, RG flow, Wick rotation, regularization, etc.) are revisited by means of the analytical aspects of the Wiener fractal measure. [ABSTRACT FROM AUTHOR]

The role of variable viscosity and variable thermal conductivity in nanofluid flows is significant, as they can strongly influence the flow behavior and heat transfer performance of nanofluids. Keeping in mind the importance of these effects of variable characteristics, our motivation in this study is to investigate the role of nonlinear radiative heat flux on unsteady Casson nanofluid flow across two concentric stretched cylinders in the presence of temperature-dependent viscosity and thermal conductivity. A convective condition on the inner cylinder wall is also considered. In addition, the nanofluid is immersed with microorganisms that can swim and move independently. The addition of microorganisms has a significant role in the stability of the nanofluid flow. The influence of thermophoresis and Brownian motion on the flow, heat, mass, and microorganisms are scrutinized by employing the Buongiorno model. The governing flow equations are converted into a system of differential equations engaging similarity transformations, and the bvp4c method is employed to solve it numerically. Engineering parameters are computed and tabulated numerically. The findings demonstrate that as the unsteadiness parameter upsurges, the radial profile intensifies while the axial profile diminishes near the outer cylinder surface. It is also comprehended that both Lewis and bioconvective Lewis numbers reduce the motile density profiles. The accuracy of the presented model is also given in a graphical illustration by comparing it with a published result in a limiting case. [ABSTRACT FROM AUTHOR]

AbstractA hyperbolic tangent fluid model characterized by shear rate dependent viscosity together with the effects of hybrid nanoparticles, Brownian motion, thermo-diffusion, and Nield’s conditions, is utilized for thermal enhancement purpose. Five percent copper nanoparticles and twenty percent alumina nanoparticles are submerged into ethylene glycol with the parametric influence of tangent hyperbolic fluid to obtain the tangent hyperbolic hybrid nano suspension. Numerical solutions of the nondimensionalized conservation laws are found by the Keller-box method. The influence of various parametric factors on velocity, temperature, concentration, Nusselt number, and Sherwood number has been discussed. A constant Nusselt number is noted with the influence of Nield’s constraints. A 90% increase in thermal conductivity is achieved by dispersing 5% copper and 20% alumina nanoparticles into the ethylene glycol with the influence of hyperbolic tangent fluid. The error and convergence analysis of the numerical solution have been discussed, along with the validation of the obtained numerical results. [ABSTRACT FROM AUTHOR]

In this paper, we study asymptotic model change detection in multivariate linear regression by using the Kolmogorov–Smirnov function of the partial sum process of recursive residuals. We approximate the rejection region and also the power function of the test by establishing a functional central limit theorem for the sequence of the partial sum processes of the recursive residuals of the observations. When the assumed model is true, the limit process is given by the standard multivariate Brownian motion which does not depend on the regression functions. However, when the assumed model is not true (some models change), the limit process is represented by a vector of deterministic trend plus the standard multivariate Brownian motion. The finite sample size rejection region and the power of the test are investigated by means of Monte Carlo simulation. The simulation study shows evidence that the proposed test is consistent in the sense that it attains the power larger than the size of the test when the hypothesis is not true. We also demonstrate the application of the proposed test method to Indonesian economic growth data in which we test the adequacy of three-variate low-order polynomial model. The test result shows that the growth of the Indonesian economy is neither simultaneously constant nor linear. The test has successfully detect the appearance of a change in the model which is mainly caused by the COVID-19 pandemic in 2020. [ABSTRACT FROM AUTHOR]

This paper gives its contributions in four stages. First, we propose the analytical expressions of power spectrum density (PSD) responses and cross-PSD responses to seven classes of fractional vibrators driven by fractional Gaussian noise (fGn). Second, we put forward the analytical expressions of PSD and cross-PSD responses to seven classes of fractional vibrators excited by fractional Brownian motion (fBm). Third, we present the analytical expressions of PSD and cross-PSD responses to seven classes of fractional vibrators driven by the fractional Ornstein–Uhlenbeck (OU) process. Fourth, we bring forward the analytical expressions of PSD and cross-PSD responses to seven classes of fractional vibrators excited by the von Kármán process. We show that the statistical dependences of the responses to seven classes of fractional vibrators follow those of the excitation of fGn, fBm, the OU process, or the von Kármán process. We also demonstrate the obvious effects of fractional orders on the responses to seven classes of fractional vibrations. In addition, we newly introduce class VII fractional vibrators, their frequency transfer function, and their impulse response in this research. [ABSTRACT FROM AUTHOR]

In the last decades, the production of fuel ethanol from corn has spread as a valid renewable alternative to pursue sustainability goals. However the uncertain nature of both input (corn) and output (gasoline) prices, together with price dependent operational decisions, combine to make this difficult plant valuation require a real options approach. Moreover, this project is characterized by various sequential stages that contribute to increase its valuation difficulties. The purpose of this paper is to provide a reliable valuation methodology of a corn ethanol plant project able to consider the characteristics of the project. We apply the compound Real Options Approach to price a corn ethanol plant project considering that the corn and gasoline prices both follow a skew-geometric Brownian motion. We also propose a case study to show a real implementation of our theoretical model. The results show that the corn ethanol plant is financially attractive as renewable investment since the uncertainties inherent in the project add value, via managerial flexibility, to the real option valuation. [ABSTRACT FROM AUTHOR]

The use of renewable energy sources to achieve carbon neutrality is increasing. However, the uncertainty and volatility of renewable resources are causing problems in power systems. Flexible and low-carbon resources such as Energy Storage Systems (ESSs) are essential for solving the problems of power systems and achieving greenhouse gas reduction goals. However, ESSs are not being installed because of Korea's fuel-based electricity market. To address this issue, this paper presents a method for determining the optimal investment timing of Battery Energy Storage Systems (BESSs) using the Least Squares Monte Carlo (LSMC) method. A case study is conducted considering the System Marginal Price (SMP) and Capacity Payment (CP), which are electricity rates in Korea. Revenue is calculated through the arbitrage of a 10 MW/40 MWh lithium-ion BESS, and linear programming optimization is performed for ESS scheduling to maximize revenue. The ESS revenue with uncertainty is modeled as a stochastic process using Geometric Brownian Motion (GBM), and the optimal time to invest in an ESS is determined using an LSMC simulation considering investment costs. The proposed method can be used as a decision-making tool for ESS investors to provide information on facility investments in arbitrage situations. [ABSTRACT FROM AUTHOR]

Based on the Girsanov theorem for a kind of Volterra-Gaussian process, which are the generalization of fractional Brownian motion, Liouville fractional Brownian motion, and fractional Ornstein-Uhlenbeck process, we establish the Harnack inequalities for a class of stochastic functional differential equations driven by a kind of Volterra-Gaussian processes with a subordinator by an approximation technique. Some known results have been generalized and improved. [ABSTRACT FROM AUTHOR]

The greater the persistence in a financial time series, the more predictable it becomes, allowing for the development of more effective investment strategies. Desirable attributes for financial portfolios include persistence, smoothness, long memory, and higher auto-correlation. We argue that these properties can be achieved by adjusting the composition weights of the portfolio. Considering the fractal nature of typical financial time series, the fractal dimension emerges as a natural metric to gauge the smoothness of the portfolio trajectory. Specifically, the Hurst exponent is designed for measuring the persistence of time series. In this paper, we introduce an optimization method inspired by the Hurst exponent and signal processing to mitigate the irregularities in the portfolio trajectory. We illustrate the effectiveness of this approach using real data from an S &P100 dataset. [ABSTRACT FROM AUTHOR]

The theory of nanoliquids has revealed several fundamental properties, including a significant increase in thermal conductivity over the base fluid. In this study, we analyzed the nanoliquids two-dimensional laminar boundary layer flow over an exponentially stretching surface. Suitable variables are applied to simplify the nonlinear partial differential equations (𝑷𝑫𝑬𝒔) into ordinary differential equations (𝑶𝑫𝑬𝒔). The resulting equations are analytically solved by using the variational homotopy perturbation method (𝑽𝑷𝑯𝑴), and the graphical representation obtained with the help of the expressions for momentum, temperature, and concentration are evaluated for specific estimates of the dimensionless parameters, specifically the Lewis number(𝑳𝒆), Brownian motion parameter (𝑵𝒃), thermophoresis parameter (𝑵𝒕), Prandtl number (𝑷𝒓), of suction and injection parameters. [ABSTRACT FROM AUTHOR]

AbstractThe unsteady simulation of hydromagnetic radiative polar fluid, including thermophoresis, Brownian motion, and higher-order chemical reactions across a perpendicular permeable plate with heat radiation, is performed numerically. The nonlinear PDEs are solved by the explicit finite difference technique and studio developer FORTRAN. The stability and convergence of the present model and a comparison are done to obtain accuracy. The effects of various parameters such as Brownian motion, thermophoresis, radiative heat transfer, and higher-order chemical reactions on the velocity, temperature, and concentration fields are investigated. It is found that the parameters have a significant influence on velocity and temperature profiles, angular velocity, concentration, shear stress, angular momentum density, and Nusselt and Sherwood numbers. In addition, the local share stress rises with the chemical reaction, Eckert number, and thermophoresis, whereas it decreases with the magnetic field and porous medium. In addition, the Nu (local) intensifies with higher order chemical reactions and porous mediums, whereas it falls with Eckert number, Brownian effects, micro-rotation, and thermophoresis. The concentration profile decreases with higher radiation, and the Lewis number whereas it augments with higher radiation. With an Eckert number and thermophoresis, the temperature and velocity increase. Additionally, the higher order of chemical reaction and Brownian motion augment the Sherwood number, whereas the chemical reaction, magnetic field, and porous medium reduce it. Moreover, the study may help to understand the dynamics of flow and heat transfer for the design and optimization of various engineering applications such as heat exchangers, pollutant dispersion models, energy systems, biomedical, and so on. [ABSTRACT FROM AUTHOR]

We study Brownian motion on the space of distinct landmarks in Rd$\mathbb {R}^d$, considered as a homogeneous space with a Riemannian metric inherited from a right‐invariant metric on the diffeomorphism group. As of yet, there is no proof of long‐time existence of this process, despite its fundamental importance in statistical shape analysis, where it is used to model stochastic shape evolutions. We make some first progress in this direction by providing a full classification of long‐time existence for configurations of exactly two landmarks, governed by a radial kernel. For low‐order Sobolev kernels, we show that the landmarks collide with positive probability in finite time, whilst for higher‐order Sobolev and Gaussian kernels, the landmark Brownian motion exists for all times. We illustrate our theoretical results by numerical simulations. [ABSTRACT FROM AUTHOR]

In recent scenario world is facing the problem of energy consumption. Researchers are keen on developing less energy consuming devices; in this regard, heat transfer using nanofluid has got the attention of current researchers for application in heat exchangers. In present study, an experiment was performed on double pipe heat exchanger using CuO-water nanofluids and sodium lauryl sulphate as the surfactant to examine the thermal performance factor (TPF) and pressure drop. The studies were conducted for a single phase fully developed flow with volume fractions of 0.005%, 0.02%, 0.04%, and 0.07% in the turbulent range between Reynolds numbers 5500 and 15,000. Along with thermal conductivity, Brownian motion and thickness of interfacial layer are also responsible for heat transfer enhancement in heat exchangers. For a volume fraction of 0.07% at Reynolds number 5500, the maximum enhancement in Nusselt number was observed 67.9% with the penalty of 189.47% increase in friction factor. The highest TPF recorded during the experiment is 1.18 for a volume fraction of 0.07% at 5500 Reynolds number. In present study a novel correlation was also developed for Nusselt number and friction factor. For better understanding the characterization of CuO nanoparticle, XRD, FeSEM, and EDS testing were conducted in the laboratory. [ABSTRACT FROM AUTHOR]