Brownian Motion Effects Research Articles

Vieta–Lucas polynomials-based collocation simulation to analyze the solvent fraction factor in active and passive control flow induced by torsional motion

The present research explores the Boger fluid flow past a stretching cylinder with torsional motion in the presence of the magnetic field. It is assumed that the cylinder rotates continuously around its axis and that the starting point's position along the axis correlates with the cylinder wall's expansion rate. Additionally, the consequence of active and passive control of nanoparticles, activation energy, thermophoresis, and Brownian motion effects are considered. Similarity variables transform the governing partial differential equations into non-dimensional ordinary differential equations (ODEs). Furthermore, the Vieta–Lucas polynomials-based collocation method (V-LPBCM) is employed to solve the resulting ODEs. The V-LPBCM outcomes of Nusselt and Sherwood numbers are compared with Runge–Kutta Fehlberg's fourth-fifth-order scheme for validation purposes. The impact of various dimensionless parameters on the different profiles is depicted in the graphical representation. The increase in values of the magnetic parameter, the ratio of relaxation time, and the Reynolds number decline the velocity profile. The velocity profile increases as the values of the solvent fraction parameter rise. The thermal profile increases as the heat source/sink, and thermophoretic parameters rise. The increase in values of activation energy parameter increases the thermal profile.

On the onset of stationary convection on Jeffrey nanofluid layer saturated with a porous medium: Brinkman model

In this paper, we investigate the onset of convection in a Jeffrey nanofluid layer saturated with the porous medium using Darcy-Brinkmann model. Normal mode analysis and Galerkin type weighted residual method (GWRM) are used to analyse conservation equations. Effects of Brownian motion and thermophoresis are taken into account in the Jeffrey nanofluid model. The Buongiorno model deployed for nanoparticles incorporates the influences of thermophoresis and Brownian motion. Three cases of free-free, rigid-rigid and rigid-free boundaries are considered. For stationary convection, the effects of Darcy number, Jeffrey parameter, Lewis number, nanoparticle Rayleigh number, porosity and modified diffusivity ratio for all the above mentioned boundary conditions are investigated analytically and graphically. The numerical computed values of stationary thermal Rayleigh number are presented graphically for three distinct combinations of boundary conditions. The study is of great significance in many different areas such as automotive, pharmaceutical, geophysics, soil sciences, food processing, oceanography, limnology, etc., and excellent coincidence is found regarding the present paper and earlier published work.

A comparative analysis on the dynamics of solid-liquid interfacial layer and nanoparticle diameter of magnetohydrodynamic nanofluid flow containing spherical and cylindrical-shaped alumina nanoparticles over a stretching curved surface

In this work, a comparative analysis on magnetohydrodynamic nanofluid flow containing spherical and cylindrical-shaped alumina nanoparticles over a stretching curved surface is mainly focused. The effects of Brownian motion, Joule heating, thermophoresis, chemical reaction and activation energy are taken into consideration in this work. It is important to mention that this analysis considers a 4 % volume fraction of the alumina nanoparticles. A thermal convective and zero-mass flux conditions are imposed to scrutinize the heat transfer analysis. The leading equations are transformed into dimensionless form by using suitable similarity variables. A numerical solution is obtained using the shooting technique. The acquired outcomes depict that greater magnetic factor enhances the skin friction coefficient. The greater magnetic factor, thermal Biot number, Eckert number, and interfacial layer thickness augment the heat transfer rate, while a greater nanoparticle diameter diminishes the thermal transfer rate. A higher magnetic factor has an increasing impact on thermal distribution and a reducing impact on velocity distribution. A greater curvature factor enhances both the velocity and thermal distributions. The concentration distribution is enhanced by the higher interfacial layer thickness and activation energy factor, while it is reduced by a higher nanoparticle diameter, Brownian motion factor, and chemical reaction factor. From the comparative analysis, it is found that the velocity, thermal, and concentration distributions are higher for the cylindrical-shaped nanoparticles compared to spherical-shaped nanoparticles.

A three-dimensional unsteady flow of Casson nanofluid with suspension of microorganisms with variable thermal conductivity: A modified Fourier theory approach

The study of nanofluids is important due to valuable applications in drug delivery systems, thermal processes, solar management systems, microfluidic devices, extrusion phenomenon, chemical processes etc. The objective of current analysis is to investigates the enhanced thermal performances of magnetized Casson nanofluid with suspension of microorganisms. An unsteady periodically oscillating flow due to bidirectional moving porous surface have been considered. The analysis is subject to assumptions of variable thermal conductivity. The modelled problem is based on implementation of modified Fourier theories. The Buongiorno nanofluid model is used to predicts the significance of Brownian motion and thermophoresis effects. Chemical reaction species are also attributed. For solution methodology, homotopy analysis scheme is implemented. The convergence region is specified. The physical impact of problem is visualized. The significant applications of parameters have been focused. The claimed results offer significance in cooling systems, chemical reactions, air conditioning, solar thermal systems, automotive radiators, heat exchangers in power plants etc.

Cascaded lattice Boltzmann simulation of Newtonian and non-Newtonian mixture nanofluids with variable thermophysical properties in a cavity with vertical heat radiator

The central moments-based cascaded lattice Boltzmann method (CLBM) for then Newtonian and non-Newtonian Buongiorno’s model mixture nanofluids (CuO, ZnO, Al2O3-water) has been implemented and applied in a square chamber with a vertical heat radiator using accelerated graphics processing unit (GPU) computing through compute unified device architecture (CUDA) C/C++ platform. Due to the higher numerical stability, the CLBM is a superior numerical tool to the raw moments-based MRT-LBM (multiple-relaxation-time lattice Boltzmann method). Three different models for the viscosity and thermal conductivity of the nanofluids: (i) the Binkmann model for the constant viscosity and the Maxwell model for the constant thermal conductivity (ii) Binkmann and Maxwell model with temperature dependent Brownian motion and (iii) Corcione model with non-Newtonian fluid where the temperature and strain rate determine the nanofluid effective thermal conductivity and viscosity, have been used. The enclosure’s upper and bottom walls are thermally adiabatic, but the left and right walls are uniformly cold. A vertical heater is immersed in the middle position of the cavity. The benchmark results for non-Newtonian, Newtonian, and nanofluids for the various computational domains are used to validate the current code adequately. The Bingham number (Bn), the Rayleigh number (Ra), and The volume fraction of the nanoparticles (ϕ) are the three key parameters that are varied in this investigation to demonstrate the effects of natural convection on the isotherms, streamlines, isolines of nanoparticle volume fractionation, yielded and unyeilded zone, and average Nusselt number (Nu¯). The Brownian motion effects of the nanoparticles augmented the average rate of heat transfer and the use of the Bingham nanofluids reduced the heat transfer enhancement. For the CuO-water nanofluid, the augmentation of the rate of heat transfer is 15.42% from ϕ=0 to 4% while Ra=106 and the corresponding heat transfer enhancement for the ZnO-water nanofluid is 11.11%. For the Bingham fluid, the rate of heat transfer increases 7% from Ra=105 to Ra=106 while ϕ=2% and Bn=0.3. The findings can be applied to optimize automotive radiator systems, which are crucial for maintaining engine temperature.

Impact of thermal conductivity of a Williamson’s nanofluid flow due to a stretching sheet

This paper intends to build a mathematical model of a two-dimensional Williamson nanofluid flow due to the stretching of a sheet linearly. The flow geometry is influenced by the magnetic field that is applied externally to the system. The induced magnetic field is infinitesimal and hence neglected. However, the flow structure is incorporated with the Brownian motion and thermophoresis effects as it alter the physics of the flow. The equations that model the flow comprise the highly nonlinear coupled simultaneous system. Thus, a numerical technique namely finite difference accompanied with the Thomas algorithm is adopted to approach the flow system. The motion, temperature, and concentration of the Williamson nanofluid flow are studied for the different flow controlling parameters. The co-efficient of skin-friction, heat, and mass transfer rates is also computed. The streamlines, isotherms, and iso-concentration are plotted to picturise the flow phenomena in the complete domain. The study reveals that the temperature of the flow raises with the Brownian motion of the nanoparticles and the trend is opposite with the concentration. The strength of the streamlines, isotherms, and the concentration contour is identified to be high for the least magnitude of Weissenberg number. The Brownian motion raises the heat transfer rate and slows down the mass transfer rate.

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.

Mathematical modelling for viscoinelastic nanofluid flow over a stretching sheet with machine learning: an application to tissue adhesive

ABSTRACT The medicated tissue adhesive on a stretching surface through Prandtl–Eyring nanofluid flow is emphasized in the current article to estimate the heat transfer rate and optimize the adhesion process. The effects of Brownian motion and thermophoresis on electrically conducting viscoinelastic nanofluid are taken into consideration with the sight of convective states. The modeled governing equations are nondimensionalized by operating similarity variables to stimulate the optimization process. The result of an executed model is solved scientifically by employing the NDSolve technique. The influence of various parameters on the fluid momentum, thermal, and concentration distributions is accentuated through graphs. Furthermore, the machine learning approach is enhanced to analyze the physical quantities of interest in the entire region. The outcomes are validated to those that have already been published in the pertinent area literature to determine the effectiveness of viscoinelastic nanofluid. The findings revealed that the Prandtl–Eyring fluid parameter enhances the momentum, while the Hartmann number indicates the reverse trend. In addition, it delivers that the proposed machine learning model is capable of forecasting the physical quantities with lower error ( 10 − 3 ) and is a powerful engineering tool that can be effectively employed in a viscoinelastic nanofluid.

Analysis of Brownian motion and thermophoresis effects with chemical reaction on Williamson nanofluid flow over permeable stretching sheet

This study warrants a broad analysis on the simultaneous effects of Brownian and thermophoresis on the chemically reacting Williamson nanofluid flow via a permeable expanding sheet. The analysis includes the properties of slip velocity and thermal radiation, providing a more representative picture of the physical phenomena. The differential equations governed by demonstrating the fluid flow phenomena are renewed to a set of nonlinear differential equations utilizing similarity rules. These transformed equations are subsequently handled numerically adopting the fourth-order Runge-Kutta method. The results reveal the significant control of Brownian motion together with thermophoresis and additionally, the inclusion of velocity slip and thermal radiation remarkably affect the velocity, temperature, and concentration distributions. Parametric studies show the validation of the present system to variations in the Williamson fluid parameter, slip parameter, radiative heat parameter, Brownian motion parameter, and thermophoresis parameter.

Impact of the Brownian motion and thermophoretic diffusion during the radiative MHD hybrid nanofluid flow past a stretching sheet

The article aims to analyze the effects of thermophoretic and Brownian motion on steady three-dimensional magnetohydrodynamics with fully developed natural convective hybrid nanofluid flow past a bidirectionally extending sheet. We assumed the water-based copper and aluminum nanoparticles suspension under the influence of the rotational effect, nonlinear chemical reaction, thermal radiations, viscous dissipation, and heat source. The flow field is modeled with the help of the basic equations. Furthermore, the problem is reduced to ordinary differential equations (ODEs) with the similarity variables. The reduced system of ODEs is solved with the semianalytical method (homotopy analysis method). The results for the state variables are displayed through graphs tables for various pertinent parameters. The thermal profile falls with the higher values of the Brownian and thermophoresis parameters, while the concentration profile shows an opposite trend with the increasing values of the Brownian parameter. Also, the slip parameter decreases both the thermal and concentration profiles as well as the surface drag. The velocity profiles along both directions fall with the higher magnetic strength and porosity parameters. The heat source and radiations parameter enhances the thermal profile with increasing values. The study also recommends the opposite trends for the axial and transverse velocities with increasing value of the stretching ratio factor. The proposed method convergence is present through [Formula: see text] curves for the regions [Formula: see text] [Formula: see text] [Formula: see text] and [Formula: see text] The skin friction and Nusselt number are displayed through tables numerically for various values of volume fraction and other important parameters.

Analysis of entropy generation and MHD thermo‐solutal convection flow of Ellis nanofluid through inclined microchannel

AbstractThis study investigates heat, mass transport, and entropy production in Ellis nanofluid flow through an inclined permeable microchannel, considering Navier's slip effects with convective boundary conditions. It incorporates nanoparticle's thermophoresis and Brownian motion effects under a transverse magnetic field, with fluid suction and injection at microchannel walls. Under appropriate physical assumptions, the problem is presented as nonlinear ordinary differential equations, which are later nondimensionalized. The MATLAB bvp4c solver is used for numerical solutions of the transformed equations. Graphical depictions in the study illustrate how various factors influence velocity, temperature, concentration, Bejan number, and entropy generation. Engineering parameters, affected by changes in critical factors, are presented in tabular format, including the skin friction coefficient, Nusselt number, and Sherwood number. Notably, the enhancement in Ellis fluid parameter has a dual effect, enhancing velocity and Bejan number in the microchannel's lower half, while reversing in the upper half. For the increment in Ellis parameter, the impact on Bejan number for 0.5 is significant and the effect on entropy production contrasts with that of Bejan number. This research offers practical insights for designing efficient microfluidic heat exchangers and developing advanced nanofluids for improved thermal performance while minimizing entropy generation. Additionally, it underscores the potential for innovation within the domain of microfluidics and nanomaterial‐driven heat transfer systems. Furthermore, it should be noted that the flow behavior of Ellis nanofluids within microchannels can closely replicate natural flow patterns found in biological systems, offering insights that could have numerous applications in biology and related fields.

Exploring the influence of morphology on magnetized Ree–Eyring tri‐hybrid nanofluid flow between orthogonally moving coaxial disks using artificial neural networks with Levenberg–Marquardt scheme

AbstractThe present study presents an analysis of Ree–Eyring tri‐hybrid nanofluid flow between two expanding/contracting disks with permeable walls by applying the computing power of Levenberg–Marquardt supervised neural networks (LM‐SNNs). The effects of thermal radiation, Brownian motion, and thermophoresis were also thoroughly examined. The results are presented for tri‐hybrid nanofluid with SWCNT and MWCNT and Fe2O3 and H2O base fluid. The coupled non‐linear PDE system is transformed into a system of ODE associated with convective boundary conditions by applying the appropriate transformations. This is then accomplished numerically by using the finite difference‐based BVP‐4c MATLAB code that implements the three‐stage Lobatto IIIA formula. The results are novel and have been validated with LM‐SNNs outcomes. It has been observed that both numerical outcomes and LM‐SNNs produce equivalent results, and both approaches exhibit a drop in the velocity profile for the magnetic field near the lower plate and a rise near the upper plate. The skin friction against the Prandtl number increases, whereas the Nusselt number decreases at the upper disc. Compared to BVP‐4c numerical approaches, the given LM‐SNNs model is more dependable, efficient, and time‐saving because it requires less work and produces results quickly.

Mixed convective magneto flow of nanofluid for the Sutterby fluid containing micro-sized selfpropelled microorganisms with chemical reaction: Keller box analysis

The current work aims to scrutinize the bioconvection Sutterby nanofluid flow of the Cattaneo-Christov heat and mass flux over a rotating disk. The effects of thermophoresis and Brownian motion receive considerable consideration. The process of analyzing heat and mass transfer phenomena involves taking into account the impacts of thermal radiation and chemical reactions that are susceptible to convective boundary conditions. Firstly, we reduce the PDEs of the physical model to ODEs through alter transformation and then numerically solved the transformed ODEs using Keller Box technique. An analysis of numerical data follows to ascertain the role of numerous flow variables on the flow profiles. Based on the findings, it is evident that an increase in the fluid variable Δ and the porous variable K leads a decrease in the, radial F'(ζ), axial F'(ζ) and tangential G(ζ) velocities. Furthermore, we find that the growing values of the thermal radiation Rd variable and the thermal Biot number B T greatly aid in raising the fluid’s temperature. Concentration profile shows decreasing behavior for rising values of Schmidt number Sc but upsurge for solutal Biot number B C . The microorganism is decayed with greater Lewis number Lb and Peclet number Pe.

Activation energy and angular momentum in electromagnetic radiation micropolar nanofluids: Focus on microbial eukaryotic species

Microbial eukaryotic species play a crucial role in biomedical research, aiding in the study of bacterial impurities, microorganism pathogenesis, and development of tactics to combat antimicrobial struggle. These species represent a complex and diverse aspect of bacteriological life, influencing ecosystems, human health, and technological progress. This study aims to create a comprehensive computational model to analyze the magnetohydrodynamics of a non-Newtonian micropolar nanofluid over an exponentially stretchable surface. It incorporates the Buongiorno model, which considers thermophoretic diffusion and Brownian motion effects to study the thermal behavior of micropolar nanofluids. It is also investigated how thermal radiation affects the current model. The classical Navier's stokes equations of motions of the current model are transform into a system of ordinary differential equation by employing similarity approach. The classical Navier-Stokes equations of motion are transformed into ordinary differential equations using similarity transformations, and MATLAB is used to solve them numerically. Here we considered three different cases, (i)-injection fw>0, (ii)-impermeable wall fw=0, (iii)-suction fw<0 which are illustrated visually. The consequence of various flow parameters effects on velocity, temperature, concentration, motile microorganism, and angular profiles are illustrated graphically. The high concordance between the model's results and the available data validates its originality. Present results indicate that while a larger porosity and Hartman number decrease velocity, increasing the mass and thermal convective factors raises the velocity profile. Raising the thermophoretic and magnetic parameters causes the temperature profile to climb; however, raising the temperature exponent and Prandtl number causes it to fall. The behavior of micropolar nanofluids is better understood thanks to this research, which could have applications in a variety of industries including manufacturing, energy, electronics, and healthcare. The novelty of the current model is verified using data that has already been published, and a great agreement is observed. When the values of the parameter K lies between the ranges 0.2<K< 0.3, and 0.3<K< 0.4, percentage increment noted in heat transfer enhancement is about 2.3 % and 6.3 % Until now, no such investigation has been performed to examine the implications of three-dimensional bio-convection micropolar based Casson fluid flow under the activation energy and suction/injection. From the outcomes, it was established that nanofluids are more fruitful for heat transfer enhancement.

Influence of activation energy and variable thermal conductivity on magneto-convective nonlinear thermo-radiative Casson nanofluid containing motile microorganisms over a sinusoidal surface

The activation energy of convective-radiative nanoliquids with sinusoidal walls has garnered significant academic interest in recent years. This focus arises due to the pivotal applications of nanoparticles in thermal engineering, industrial processes, and medical sciences. This article investigates the magnetohydrodynamic heat transfer characteristics of Casson nanofluids containing microorganisms influenced by an oscillatory surface. The study incorporates temperature-dependent viscosity and utilizes Buongiorno’s mathematical model to account for nonlinear thermal radiation, Brownian motion, and thermophoretic effects from using nanomaterials in Casson fluids. These effects enhance thermal conductivity, improving the heat transportation phenomenon while considering gyrotactic microorganism density distributions. The boundary layer flow problem is formulated using partial differential equations and associated boundary conditions, subsequently numerically simulated using the bvp4c function. The investigation explores the thermal behavior of nanoparticles in the presence of bioconvection phenomena, Lorentz force, chemical reactions, and activation energy. As a result, this model addresses variable thermal conductivity and bioconvection aspects in Casson nanofluids over a sinusoidal surface. Numerically computed results for the Nusselt number, motile density, and Sherwood number provide insights into several essential features. The findings reveal that an increase in the Casson fluid parameter correlates with a decreased velocity profile. The assumptions of variable thermal conductivity and temperature-dependent viscosity prove more effective in raising the temperature of nanoparticles. The nanoparticle concentration profile rises noticeably for smaller Schmidt number Sc values when the activation energy parameter is higher than larger Sc values. Additionally, the presence of microorganisms in Casson nanofluids leads to increased temperatures due to an elevation in the bioconvection Rayleigh number. Moreover, heightened oscillating frequency parameters decrease nanoparticle concentration and microorganism density. Including activation energy and oscillating frequency parameters further enhances the understanding of nanoparticle concentration and microorganism density dynamics, offering valuable contributions to theoretical research and practical applications across multiple interdisciplinary fields.

Numerical study on nanofluidic transport mechanism in Ellis flow within curved channel comprising compliant walls subjected to peristaltic activity

Peristaltic movement of fluid flows has significant applications in biomedical engineering, medicine, human physiology, etc. Specifically, it is very useful to understand and cure the very common intestinal diseases in human beings. A number of theoretical and empirical models are used to analyze peristaltic movement. In this work, the peristaltic movement of nanofluid is modeled with a non-Newtonian Ellis fluid model in a curved channel with compliant wall properties. The effects of Brownian motion, thermophoresis, and nonlinear radiations are considered in the heat transfer for better thermal analysis. The mathematical modeling of the physical problem yields the nonlinear partial differential equations with boundary conditions. First, the governing partial differential equations are non-dimensionalized, and then the resultant system is simplified by using the assumptions of a small Reynolds number and long wavelength. Then the obtained boundary value problem of differential equations is solved with the built-in Mathematica command NDSolve. The accuracy and reliability of the adopted procedure are verified by comparing the computed results with the reported literature. The impacts of the pertinent parameters (Brownian motion, thermal radiation, mixed convection, and thermophoresis phenomenon) on thermal energy, velocity, concentration, heat transfer rate, and stress at the lower wall are analyzed both in qualitative and quantitative manners. This study revealed some interesting facts, such as the peristaltic-driven motion of nanoliquid is strongly influenced by wall properties (i.e., wall elasticity, mass density, and wall damping). In addition, the flow experienced more resistance in the case of larger wall damping, but larger wall elasticity and mass density provide favorable movement for fluid motion. In addition, mixed convection plays a vital role in heat transfer and nanoparticle concentration in the curved domain. In addition, the curved channel walls have a higher stress factor than straight-plane channels. The results of the current study are very useful to understand many biological phenomena, such as the peristaltic movement of liquid during dialysis, food movement through the intestine, etc.

Numerical investigation of heat and mass transfer study on MHD rotatory hybrid nanofluid flow over a stretching sheet with gyrotactic microorganisms

This study signifies the advancing reader’s understanding of complex fluid dynamics, offering insights crucial for optimizing heat transfer processes, environmental engineering applications, and biomedical technologies. The focus of this work is to examine the heat and mass transference properties of electrically conductive hybrid nanofluid flow on a bi-directional stretching surface with gyrotactic microorganisms. The effects of thermophoresis, thermal radiation, Brownian motion, heat source, and chemical reaction are incorporated into the problem. The sheet is rotated about the z-axis with ω as its velocity. The modeled equations are changed to dimensionless form with the use of similarity variables and are then solved by employing the homotopy analysis method (HAM). It is concluded that the larger rotation factor boosts the velocity plot. Similarly, the thermal radiation and thermophoretic factor heighten the thermal gradient of the hybrid nanofluid. From the computed data, it is revealed that the microorganism plot shows a declining behavior against the Peclet and Lewis numbers. The findings of this work help in the optimization of cooling systems in electronics, power plants, and automotive engines by enhancing heat transfer efficiency. Moreover, in biomedical engineering, understanding microorganism behavior in fluid flow is critical for developing advanced drug delivery systems and biomedical diagnostics.

Effects of Brownian motion on solitary wave structures for 1D stochastic Poisson–Nernst–Planck system in electrobiochemical

This study deals with the time fractional 1D stochastic Poisson–Nernst–Planck (TFSPNP) system under the effect of multiplicative time noise. The M-truncated derivative (MTD) takes into consideration the fractional order time derivative. This is a steady-state Poisson–Nernst–Planck (PNP) equations that have applications in bioelectric dressings and bandages. To obtain the soliton solutions of TFSPNP, we use the generalized exponential rational functional method. These findings are presented in the form of trigonometric, exponential, and hyperbolic functions. Moreover, to show the effect of multiplicative time noise and MTD, we construct the plot of some solutions in the form of three-dimensional, two-dimensional, and their corresponding contours. These plots clearly show the effect of randomness in the wave structures for the exact solitary wave solutions that are attained. In general, the solutions become more stable when a noise term disrupts their symmetry.

A case study on effect of variable viscosity on non-newtonian nanofluid over an extendable cylindrical surface by utilizing Reynold’s model

Current artifact aims to investigate attributes of nanofluidic transport mechanism developed for dynamics of Williamson liquid over an extendable cylinder with novel physical aspects of magnetic field. Additionally, Newtonian heating is accounted at cylinder surface and Reynold viscosity model is implemented to delineate the aspects of temperature dependent viscosity. Thermophoresis, Brownian motion, and variable viscosity effects have been studied for heat and mass transfer analysis. Formulation of problems characterized by governing physical laws is conceded in the form of dimensional partial differential setup by executing boundary layer approach. Conversion of attained differential system into ODE’s is engrossed by capitalizing similarity transformations. Numerical procedures (Runge-Kutta and shooting) are implemented to resolve the problem and to attain solution. Effectiveness of sundry variables on associated distributions is revealed through graphical and tabular manner. Quantities of interest are also manipulated against the involved variables. Comparison of results to certify the numerical code is checked by making assessment with existing studies and found remarkable agreement.

Effect of Orally Ingested Water Containing H2-Filled Ultrafine Bubbles (UFBs) on Ethanol-Induced Oxidative Stress in Rats.

Ultrafine bubbles (UFBs), which are bubbles with diameters of less than 1 µm, are widely recognized for their ability to exist stably in liquid as a result of the effects of Brownian motion. In this study, we focused on hydrogen, known for its antioxidant potential, and explored the function of H2-filled UFBs, which encapsulate hydrogen, to determine their potential use as oral carriers for the delivery bioactive gases to living organisms. To this end, rats were orally administered ethanol to induce hepatic oxidative stress, and the effects of drinking H2-filled UFBs (H2 NanoGAS®) water for two weeks were evaluated to assess the reduction of oxidative stress. Continuous alcohol consumption was found to significantly increase the blood lipid peroxidation levels in the control group, confirming the induction of oxidative stress. An increase in blood lipid peroxidation was significantly inhibited by the consumption of concentrated H2 NanoGAS® (C-HN) water. Furthermore, the measurement of mitochondrial activity in the liver revealed that drinking H2 NanoGAS® water helped to maintain at a normal level and/or boosted the functional activity of the electron transport system in mitochondria affected by ethanol intake. To our knowledge, this study is the first to provide evidence for the use of orally ingested UFBs as carriers for the delivery gases to tissues, thereby exerting their physiological activity in the body. Our findings highlight the potential for the application of UFBs to various physiologically active gases and their utilization in the medical field in the future.