Assumption Of Long Wavelength Research Articles

Influence of Temperature on The Concentration and thus on the MHD Oscillatory Flow of a Tangent Hyperbolic Fluid Through a Regular Permeable Channel

The aim of this research is to study the effect of temperature and concentration on oscillatory flow under the influence of magneto hydrodynamic (MHD) of a non-Newtonian hyperbolic fluid in a horizontal permeable channel. The problem formulation is non-linear and non-homogeneous partial differential equations. Using the perturbation technique, we solve the momentum equation under the assumptions of long wavelength and very low Reynolds number. After obtaining the solution, we used the “Mathematica 13” program to analyze the results through graphs, and the oscillatory flow and magnetic field were studied on the movement of the fluid, its temperature, and concentration.

MHD Flow of Jeffery Nanofluid Through Symmetric Ciliated Channel with Porous Medium: Biological Application

This paper emphasizes on examining the impact of a magnetic field, and porous medium on the non-Newtonian Jeffery nanofluid flows due to metachronal waves induced by ciliated structures that covering the inner walls of the symmetric channel. The governing equations namely continuity, motion, energy and nanoparticles concentration are formulated with suitable boundary conditions and simplified depending on the assumption of long wavelength and low Reynolds number. The simplified equations are solved by using Mathematica program. Further, these analytical solutions for velocity profile, temperature, concentration profiles and streamlines are graphically elucidated and discussed in detail. we concluded that the Hartman number and permeability parameter have opposite effect on the flow characteristics. Moreover, the Jeffery parameter has an increasing impact on the velocity profile whereas the dimensionless eccentricity of ellipse parameter decreases the velocity profile of the fluid.

Heat transfer model analysis of fractional Jeffery-type hybrid nanofluid dripping through a poured microchannel

This study investigates the impact of coupled heat and mass transfer on the peristaltic migration of a magnetohydrodynamic (MHD) stress-strain Jeffery-type hybrid nanofluid flowing through an inclined asymmetric micro-channel with a porous medium. The fundamental two-dimensional momentum and energy transport equations are simplified under the assumptions of long wavelength and low Reynolds number. To solve the momentum and heat transfer problems, two advanced fractional derivative approaches are employed: the fractal integral and the Prabhakar fractional derivative. The pressure difference is determined using numerical integration techniques, such as the Stehfest and Tzou's algorithms. The results are presented through graphs and tables, which illustrate the effects of various parameters on the velocity, heat transfer, and trapping phenomena. As a result, we concluded that, pressure gradients grow with higher Reynolds numbers and channel-inclined angles. The heat transfer rate is observed to decrease as the Darcy number and the orientation of the electromagnetic field increase. When comparing the fractional derivative approaches, the fractal operator exhibits a more significant impact on the momentum profiles compared to the Prabhakar fractional operator. This difference is attributed to the distinct characteristics of the integral kernels associated with each fractional derivative definition. Furthermore, when comparing hybrid nanofluids, water-based (H2O + Ag + TiO2) hybrid fluids have a somewhat more significant effect than (C6H9NaO7 + Ag + TiO2) hybrid nanofluids.

The profound effect of heat transfer on magnetic peristaltic flow of a couple stress fluid in an inclined annular tube

In this study, we explore the analysis of peristaltic flow with heat transfer occurring within the gap between coaxial inclined tubes. The inner tube’s wall is rigid, while the outer tube’s wall features a sinusoidal wave propagating through it. The cylindrical system is employed to formulate the problem. The flow is characterized using continuity, momentum, and energy equations. We apply the assumption of long wavelength and the low Reynolds number approximation to simplify the nonlinear governing equation, subsequently solving it through perturbation techniques. We investigate the impact of crucial parameters, such as the magnetic field, porous media, slipping conditions, and others, on the peristaltic flow of a couple stress fluid. Our focus lies on assessing their influence on axial velocity, pressure gradient, and flow streamlines. The outcomes are visually presented through graphical representations. Notably, an increase in the slipping parameter results in a reduction of fluid velocity, attributed to the reverse slipping of the flow. The introduction of a magnetic field leads to an augmentation of the pressure gradient. Moreover, elevating the peristaltic amplitude and heat source induces the formation of a vortex within the flow. The presence of porous media leads to an increase in the pressure difference of the fluid flow. The primary objective of this research is to enhance our understanding of the peristaltic motion of non-Newtonian fluid dynamics, specifically incorporating a couple stress fluid. This contributes to a deeper understanding of crucial fluids, such as blood, within the human circulatory system. The implications extend to biological and industrial applications like magnetic resonance imaging (MRI) and radiosurgery, advancing our scholarly understanding of fluid behavior, especially in non-Newtonian scenarios.

Influence of inclined magnetic field and heat transfer on the peristaltic flow of Rabinowitsch fluid model in an inclined channel

The recent study is focused on discussion of heat transfer and magnetic field results of peristaltic flow of Rabinowitsch fluid model in an Inclined Channel. In this piece of research, peristalsis’s fundamental problem with heat transfer in the presence of a magnetic field is checked. An incompressible Rabinowitsch fluid is present in an inclined channel, which is considered as the reference for this research. The solutions are devised with the assumptions of long wavelength and low Reynolds number approximations. The resulting equations are then solved exactly by implementing various command of MATHEMATICA subject to relevant boundary conditions. Results are discussed for various flow quantities like temperature, velocity, tangential stress, pressure gradient and rise, and friction force. Computational simulations are performed to determine the flow quantities. This investigation goes beyond mere calculations and examines particle motion to gain deeper insights into flow quantities. Furthermore, this investigates how magnetic field and heat transfer parameters influence these peristaltic flow phenomena. The outcomes of important parameters were plotted and scrutinized. There is amultitude of medical implementations derived from the current consideration, such as the depiction of the gastric juice motion in the small intestine when an endoscope is inserted through it.

Analysis of two layered peristaltic-ciliary transport of Jeffrey fluid and in vitro preimplantation embryo development

The analysis of peristaltic-ciliary transport in the human female fallopian tube, specifically in relation to the growing embryo, is a matter of considerable physiological importance. This paper proposes a biomechanical model that incorporates a finite permeable tube consisting of two layers, where the Jeffrey fluid model characterizes the viscoelastic properties of the growing embryo and continuously secreting fluid. Jeffrey fluid entering with some negative pressure gradient forms the core fluid layer while continuously secreting Jeffrey fluid forms the peripheral fluid layer. The resulting partial differential equations are solved for closed-form solutions after employing the assumption of long wavelength. The analysis delineated that increasing the constant secretion velocity, Darcy number, and Reynolds number leads to a decrease in the appropriate residue time of the core fluid layer and a reduction in the size of the secreting fluid bolus in the peripheral fluid layer. Eventually, the boluses completely disappear when the constant secretion velocity exceeds 3.0 Progesterone (P4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_4$$\\end{document}) and estradiol (E2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_2$$\\end{document}) directly regulate the transportation of the growing embryo, while luteinizing hormone (LH) and follicle-stimulating hormone (FSH), prolactin, anti-mullerian hormone (AMH), and thyroid-stimulating hormone (TSH) have an indirect effects. Based on the number and size of blastomeres, the percentage of fragmentation, and the presence of multinucleated blastomeres two groups were formed in an in vitro experiment. Out of 50 patients, 26 (76.5%) were pregnant in a group of the good quality embryos, and only 8 (23.5%) were in a group of the bad quality embryos. The transport of growing embryo in the human fallopian tube and preimplantation development of human embryos in in vitro are constraint by baseline hormones FSH, LH, prolactin, E2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_{2}$$\\end{document}, AMH, and TSH.

Magneto-hydrodynamic peristaltic flow of a Jeffery fluid in the presence of heat transfer through a porous medium in an asymmetric channel

In the present paper, the effects of magnetic field and heat transfer on the peristaltic flow of a Jeffery fluid through a porous medium in an asymmetric channel have been studied. The governing non-linear partial differential equations representing the flow model are transmuted into linear ones by employing the appropriate non-dimensional parameters under the assumption of long wavelength and low Reynolds number. Exact solutions are presented for the stream function, pressure gradient, and temperature. The frictional force and pressure rise are both computed using numerical integration. Using MATLAB R2023a software, a parametric analysis is performed, and the resulting data is represented graphically. For all physical quantities considered, numerical calculations were made and represented graphically. Trapping phenomena are discussed graphically. The obtained results can be applied to enhance pumping systems in engineering and gastrointestinal functions. This analysis permits body fluids such as blood and lymph to easily move inside the arteries and veins, allowing oxygen supply, waste elimination, and other necessary elements.

Deep learning based solution of nonlinear partial differential equations arising in the process of arterial blood flow

The present work introduces a deep learning approach to describe the perturbations of the pressure and radius in arterial blood flow. A mathematical model for the simulation of viscoelastic arterial flow is developed based on the assumption of long wavelength and large Reynolds number. Then, the reductive perturbation method is used to derive nonlinear evolutionary equations describing the resistance of the medium, the elastic properties, and the viscous properties of the wall. Using automatic differentiation, the solutions of nonlinear evolutionary equations at different time scales are represented using state-of-the-art physics-informed deep neural networks that are trained on a limited number of data points. The optimal neural network architecture for solving the nonlinear partial differential equations is found by employing Bayesian Hyperparameter Optimization. The proposed technique provides an alternate approach to avoid time-consuming numerical discretization methods such as finite difference or finite element for solving higher order nonlinear partial differential equations. Additionally, the capability of the trained model is demonstrated through graphs, and the solutions are also validated numerically. The graphical illustrations of pulse wave propagation can provide the correct interpretation of cardiovascular parameters, leading to an accurate diagnosis and successful treatment. Thus, the findings of this study could pave the way for the rapid development of emerging medical machine learning applications.

Effect of heat and mass transfer on the nanofluid of peristaltic flow in a ciliated tube

The current work focuses attention on discussing the peristaltic flow of Rabinowitsch nanofluid through ciliated tube. This technical study analyzes heat and mass transfer effects on the flow of a peristaltic flow, incompressible, nanofluid via a ciliated tube. The governing non-linear partial differential equations representing the flow model are transmuted into linear ones by employing the appropriate non-dimensional parameters under the assumption of long wavelength and low Reynolds number. The flow is examined in wave frame of reference moving with the velocity c. The governing equations have been solved to determine velocity, temperature, concentration, the pressure gradient, pressure rise and the friction force. Using MATLAB R2023a software, a parametric analysis is performed, and the resulting data is represented graphically. The results indicate that the various emerging parameters of interest significantly affect the nanofluid properties within the tube. The present study enhances the comprehension of nanofluid dynamics in tube and offers valuable insights into the influence of heat and mass transfer in such setups. Convective heat transfer is found to be greater at the boundaries resulting in decreased temperature there.

Peristaltic motion of a Casson nanofluid in a vertical layer with suction and injection

Inquisitive researchers have studied the movement of peristaltic nanofluids due to the enlightening impact of nanoliquids in various technological and therapeutic fields, particularly in the fluids transport mechanisms known as peristalsis. The Casson fluid belongs to a group of non-Newtonian fluids that, according to a particular stress threshold, exhibit elastic solid behavior before changing to liquid behavior. These fluids are known as viscoelastic fluids and have several uses in engineering, food preparation, drilling and other fields. The Casson nanofluid model is used in this investigation. In order to better understand this, this study examines the peristaltic motion of a Casson nanofluid in a vertical layer with suction/injection. The resulting flow model is successfully simulated under the realistic assumptions of long wavelength and low Reynolds number after obtaining the governing conservation equations. By using workable transformations, the derived partial differential equations are mathematically converted into a dimensionless form. Analytical solutions have been found for the resulting flow problem’s temperature distribution, velocity, pressure rate per wavelength and concentration of nanoparticles. Using Wolfram Mathematica software, the impacts of all physical characteristics on temperature, velocity, concentration fields, pressure rate, frictional force and pressure gradient are graphically studied. The influences of thermophoresis parameter Nt raise the temperature and diminish fluid concentration. By raising the suction and injection parameter k values, the velocity in the directions of x and y is decreased. The pressure rate enhances by raising the Reynolds number and diminishes by enhancing the Grashof number.

Mathematical Modelling for Peristaltic Flow of Sutterby Fluid Through Tube under the Effect of Endoscope

In this work, the mathematical modelling of peristaltic transport for incompressible Sutterby fluid through the cavity between coaxial tubes where the inner tube is fixed and the outer tube has sinusoidal rhythmic fluctuations along the channel’s walls is presented. Under the assumption of long wavelength and the low Reynolds number, the governing equations (motion, temperature, and concentration) are illustrated in cylindrical coordinates. The analytical solution for the temperature and concentration of the fluid flow is obtained using Mathematica 11.3, whereas the perturbation technique is employed to find the closed form of the velocity profile. The variation of the axial velocity, stream function, temperature, concentration, and heat transfer are graphically discussed under the impact of interesting involved parameters.

Inclined MHD Effects in Tapered Asymmetric Porous Channel with Peristalsis: Applications in Biomedicine

This paper emphasized an inclined magnetohydrodynamics (MHD) effects in tapered asymmetric porous channel with peristalsis in the presence of slip boundary conditions. Here we considered the two-dimensional channel with a porous medium. The fundamental assumptions of long wavelength and low Reynolds number are applied in the relevant nonlinear equations for momentum, heat, and mass transfer as part of mathematical modeling. The equations subjected to slip boundary conditions have been solved numerically by the Mathematica software. Various essential physical characteristics of velocity, temperature, concentration, and heat transfer rate are captured graphically in the end. The velocity profile is found parabolic for various involved parameters. It is observed that the embedded parameters behave in the exact opposite manner when compared with temperature and concentration distributions. The sinusoidal behavior of the heat transfer rate is also displayed. The unique aspect of this effort is specifically to relate the Joule heating, Darcy resistance, and inclined magnetic field effects in peristaltic flow for a non-Newtonian Jeffrey fluid in an asymmetric tapered channel under the influence of slip boundary conditions. Such preferences have a wide range of applications in engineering, biology, and industry. The outcomes of the presented work are also proficient in the medical field for the treatment of cancer using MHD. The MHD also aids in controlling blood pressure during systolic and diastolic pressure conditions by regulating the blood flow stream.

Biological flow of thermally intense cilia generated motion of non-Newtonian fluid in a curved channel

The energy loss during the beating cilia phenomenon in the human stomach causing acidity in the blood flow under certain conditions has been a serious topic in the modern medical field. Therefore, the current study intends to exhibit a theoretical analysis of mixed convective transport of non-Newtonian Casson fluid observed by ciliary motion walls in the curved channel. The flow of constitutive equations is used to modify in curvilinear coordinates into a wave frame for two-dimensional flow due to the complication of the flow regime. The attributes of biological ciliary approximation are revealed through the control of viscous and inertial impacts utilizing the long-wavelength assumption and obtained the analytical closed form solutions for the normalized equations. The impacts of physical parameters on the velocity profile and heat flow phenomena are discussed. It is observed that the flow velocity, the momentum bolus and the trapped bolus are reduced in the cilia transport channel by enhancing the channel curvature. A validity of admirable comparison is also noticed with previously results.

Progression of blood-borne viruses through bloodstream: A comparative mathematical study

Background and ObjectivesBlood-borne pathogens are contagious microorganisms that can cause life-threatening illnesses, and are found in human blood. It is crucial to examine how these viruses spread through blood flow in the blood vessel. Keeping that in view, this study aims to determine how blood viscosity, and diameter of the viruses can affect the virus transmission through the blood flow in the blood vessel. A comparative study of bloodborne viruses (BBVs) such as HIV, Hepatitis B, and C, has been addressed in the present model. A couple stress fluid model is used to represent blood as a carrying medium for virus transmission. The Basset-Boussinesq-Oseen equation is taken into account for the simulation of virus transmission. MethodsAn analytical approach to derive the exact solutions under the assumption of long wavelength and low Reynolds number approximations is employed. For the computation of the results, a segment (wavelength) of blood vessels about 120 mm with wave velocities in the range of 49 − 190 mm/sec are considered, where the diameter of BBVs ranges from 40-120 nm. The viscosity of the blood varies from 3.5-5.5 × 10−3 Ns/m2 which affect the virion motion having a density range 1.03 − 1. 25 g/m3. ResultsIt shows that the Hepatitis B virus is more harmful than other blood-borne viruses considered in the analysis. Patients with high blood pressure are highly susceptible for transmission of BBVs. ConclusionsThe present fluid dynamics approach for virus spread through blood flow can be helpful in understanding the dynamics of virus propagation inside the human circulatory system.

Thermal performance of iron oxide and copper (Fe3O4, Cu) in hybrid nanofluid flow of Casson material with Hall current via complex wavy channel

The nanoparticles have substantial uses in the treatment of several diseases and in drug delivery systems and the nanoparticles are injected in the base fluid which is transported in the cardiovascular system on the mechanism of peristalsis. This study highlights the Casson hybrid nanofluid thermal inspection with blood base fluid. The copper and iron oxide nanoparticles are used to assess the hybrid nanofluid characteristics. The conduit for the present analysis is considered non-uniform complex wavy and curved. The base fluid is considered as a Casson fluid which reports the shear thinning and thickening consequences of blood base liquid. The fundamental conservation laws are utilized to model the flow problem and simplified under the assumption of long wavelength and creeping transport. The shooting method is used to compute the different flow and heat transfer characteristics The impact of various interesting parameters is examined graphically.

On solitary-wave solutions of fifth-order KdV type of model equations for water waves

<p style='text-indent:20px;'>The paper concerns capillary-gravity surface waves propagating on a two-dimensional incompressible and inviscid fluid with or without an obstacle placed at a flat horizontal bottom. Formally second-order correct model equations, analogous to the first-order correct KdV equation, are derived under the classical assumptions of long wavelength and small amplitude of the surface waves. The model equations are a fifth-order KdV type of equations where the obstacle at the bottom introduces forcing terms in the equations. If the forcing is zero, the equation can possess a special Hamiltonian structure after a BBM term is introduced. The existence and set stability of solitary-wave solutions for the fifth-order KdV-BBM type of equations without forcing are studied. If the forcing term is included, only a special case is considered, which is the forced fifth-order KdV type equation (also called forced Kawahara equation) and models the water waves when both the surface tension and wave speed are near their critical values. The existence of small or some large solitary-wave solutions is obtained and the Lyapunov stability of small solitary-wave solutions is proved. Other large amplitude solutions are studied numerically.</p>

Numerical Examination on Impact of Hall Current on Peristaltic Flow of Eyring-Powell Fluid under Ohmic-Thermal Effect with Slip Conditions

Aims:: This article is intended to investigate and determine the combined impact of Slip and Hall current on Peristaltic transmission of Magneto-hydrodynamic (MHD) Eyring- Powell fluid. Background: The hall term arises, taking strong force-field under consideration. Velocity, thermal, and concentration slip conditions are applied. The energy equation is modeled by considering the Joule-thermal effect. To observe the non-Newtonian behavior of the fluid, the constitutive equations of Eyring-Powell fluid are encountered. Objective: Flow is studied in a wave frame of reference traveling with the wave's velocity. The mathematical modeling is done by utilizing adequate assumptions of long wavelength and low Reynolds number. Method: The closed-form solution for momentum, temperature, and concentration distribution is computed analytically using the regular perturbation technique for the small fluid ter(A). Results: Graphical results are presented and discussed in detail to analyze the behavior of sundry parameters on flow quantities (i.e., velocity, temperature, and concentration profile). It is noticed that Powell-Eyring fluid parameters (A,B) have a significant role in the outcomes. Conclusion: The fluid parameter A magnifies the velocity profile, whereas the other fluid parameter B shows the opposite behavior.

EFFECT OF A VARIABLE MAGNETIC FIELD ON PERISTALTIC SLIP FLOW OF BLOOD-BASED HYBRID NANOFLUID THROUGH A NONUNIFORM ANNULAR CHANNEL

This paper analyzes the impact of hybrid nanoparticles (Cu–TiO2) on a two-dimensional peristaltic blood flow pattern in a nonuniform cylindrical annulus in the presence of an external induced magnetic field with wall slip. Further, this study focuses on the flow dynamics of single and hybrid nanofluids through endoscopic or catheterized effects. The mathematical model consisting of continuity, linear momentum, thermal energy, and Maxwell’s equations is simplified under the assumptions of long wavelength and negligible Reynolds number. The Homotopy perturbation method (HPM) is employed to get an approximate analytical solution of nonlinear dimensionless momentum equations. Based on the mathematical relationships and graphic visualization, the influence of the pertinent parameters described the velocity profile, temperature distribution, induced magnetic field, current density distribution, wall shear stress, and heat transfer coefficient. With the help of contours, the trapping phenomenon is also presented. The results reveal that the Lorentz force significantly reduces the Cu–TiO2/blood nanofluid velocity, whereas the elevating Grashof number does the opposite. Compared with copper nanoparticles, hybrid nanoparticles have a higher wall shear stress. The increasing values of Reynolds numbers amplify the induced magnetic field on annular surfaces. In the axial direction, Lorentz force significantly decreases the current density distribution for hybrid nanofluid. Moreover, hybrid nanoparticles (Cu–TiO2) exhibit superior heat transfer than Copper (Cu) nanoparticles in the blood-based fluid. According to the graphical outcomes, hybrid nanoparticles are comparatively more effective than unitary nanoparticles in the blood.

Peristaltic analysis of Williamson blood flow model with solar biomimetic pump

Mathematical model of peristaltic motion for Williamson blood flow through esophagus is addressed with the coordination of biomimetic solar based pump. The transfer of heat and mass is examined under the assumption of diversified viscosity, diffusivity and conductivity. The novelty of the present manuscript is the consolidation of vertical peristaltic system, blood flow over an esophagus, biomimetic solar pump, variable thermo-physical properties, involvement of activation energy for chemical reaction. For the implementation of solar mimetic system, the equations are modeled under the presence of Rosseland's approximation and taking the assumption of long wavelength and small Reynolds number. The application of activation energy is seems through the chemical reaction which is taken near the walls of esophagus. We concluded that the velocity profile reveals the parabolic behavior and Williamson as well as viscosity parameter reduces the velocity fields. The pumping augmented pumping and free pumping areas are addressed. The temperature distributions are exhibits in the form of straight lines and we concluded that thermal conductivity and radiation parameters boost the temperature profile. The activation energy and diffusivity parameter decreases the concentration distribution. Streamlines for peculiar quantities of Weissenberg number and volumetric flow rates are derived and isothermal contour is also examined.

Propagation of H1N1 virus through saliva movement in oesophagus: a mathematical model.

H1N1 (Swine flu) is caused by the influenza A virus which belongs to the Orthomyxoviridae family. Influenza A is very harmful to the elderly, and people with chronic respiratory disease and cardiovascular disease. Therefore, it is essential to analyse the behaviour of virus transmission through the saliva movement in oesophagus. A mathematical paradigm is developed to study the saliva movement under the applications of transverse magnetic field. Jeffrey fluid model is considered for saliva to show the viscoelastic nature. The flow nature is considered creeping and assumptions of long wavelength and low Reynolds number are adopted for analytical solutions. The Basset–Boussinesq–Oseen equation is employed to understand the propagation of H1N1 virus through saliva under the effect of applicable forces such as gravity, virtual mass, basset force, and drag forces. The suitable data for saliva, oesophagus and H1N1 virus are taken from the existing literature for simulation of the results using MATLAB software. From the graphical results, it is observed that the susceptibility to viral infections is less because the magnetic field reduces the motion of the virus particle. Further, the chances of infections in males are more as compared to females and children due to variation in viscosity of saliva. Such findings provide an understanding of the mechanics of the virus floating through the saliva (viscoelastic fluids) in the oesophagus.