Narrow Results

Bioheat transfer analysis in tissue has attracted the attention of numerous researchers due to its widespread potential applications in the medical field, mainly in thermotherapy and the human thermoregulation system. Also, temperature regulation of the human body primarily occurs through bioheat transfer. Due to the widespread biomedical applications of bio-heat transfer, we aim to investigate the movement of biofluid and bioheat in human organs with the influences of thermal radiation and ciliary waves. The mathematical model for Ellis fluid flow through a tube includes the metachronal wave of cilia motion and convective conditions. The governing equations are created based on mass, momentum conservation, and energy. The current problem is displayed and exact solutions are managed under long wavelength $(\delta \ll 1)$ and low Reynolds number $(R_e\ll 1)$ approximations. An analytical approach is employed to derive expressions for longitudinal velocity, temperature, pressure gradient, and stream function as a function of the parameters of the problem. The physical behavior of the peristaltic motion of the Ellis fluid is explained in detail and illustrated graphically for various parameter values. The results of the current study provide potential information for advancement in the biomedical industry, particularly in the development of biomedical devices and processes.

This investigation articulately addresses the role of gold nanoparticles in medical sciences from a different perspective. Aiming to highlight the significant usage of nanoparticles, four different types such as spherical, platelets, cylindrical and brick-like nanoparticles are brought into consideration with the main focus to achieve maximum heat enhancement. This motivation leads to mathematically formulating an electroosmosis blood flow. Casson fluid is treated as physiological fluid through an asymmetric microchannel. The nonlinear term of radiative heat flux is added on the right-hand side of the heat equation to report the impact of radiation which is beneficial in skin diseases. A closed-form solution is achieved with the help of physical approximation. Moreover, analytical expressions for velocity distribution, temperature field, shear stress, heat transfer rate and pressure gradient have been provided. The expression of stream function is also presented and the trapping phenomena are discussed. Besides studying the tremendous capacity of gold particles to enhance the heat transfer rate for targeting the maligned tissues as a prime objective, the current survey will also assist readers to explore the other similar metallic particles which can effectively be used as an alternative.

This paper deals with a study on flow of fluid which exhibits the characteristics of both ideal fluids and elastic solid and shows partial elastic recovery. For these types of fluids, Jeffrey six-constant model will be used that illustrates the most striking feature connected with the deformation of a viscoelastic substance and simultaneously displays the fluid-like and solid-like characteristics. The flow of the proposed fluid model will be generated in an inclined tube by sinusoidal wave trains propagation with constant speed along the walls of the tube. The governing equations of the fluid along with energy equation are modeled and simplified by using low Reynolds number and long wavelength assumptions. These equations will be solved by utilizing the homotopy perturbation technique and results of flow will be displayed in graphical form under the effects of Jeffrey model’s parameters.

A mathematical model is developed to investigate the entropy generation on peristaltic transport of the Ellis fluid through a uniform two-dimensional symmetric channel with elastic nature of the walls. An analysis of heat and mass transfer is also made to examine the effects of viscous dissipation. To simplify the governing equations, nondimensional analysis with low Reynolds number and large wavelength is done. Solutions of the problems are presented via a NDSolve Mathematica numerical technique. The effects of various parameters on flow characteristics, thermal characteristics and species characteristics have been computed and physically interpreted. The numerically acquired solutions are studied graphically for the effective analysis of the flow. The velocity and temperature profiles are parabolic in nature. Higher values of elastic parameters and chemical reaction parameters rapidly increase concentration profile for Newtonian case as compared to non-Newtonian case. The outcomes of this model can be applicable in various fields of biomedical engineering where smart peristaltic pumps can be engineered to transport the biological fluids without any contamination, i.e., electromagnetic peristaltic micro pumps.

In this research, we examine the mixed convection effects for peristaltic motion of tangent hyperbolic nanoliquid. On flexible channel walls, partial slip characteristics are applied. Influences of Ohmic heating and viscous dissipation are analyzed in the modeling. We evaluated the transportation of heat under nonlinear thermal radiation. The governing problem is first reduced into dimensionless form by using suitable transformations and then numerical technique is employed for the solution after utilizing small Reynolds number and large wavelength assumption. The problem is simulated employing the so-called Buongiorno’s formulation which includes the features of thermophoresis and random motion. In addition, a mass transport scheme is developed with first-order chemical reactions. The roles of sundry variables on velocity, coefficient of heat transfer, temperature and concentration are examined graphically. Velocity and temperature show similar behavior against thermal Grashof parameter. Concentration decreases for larger thermophoresis parameter. Heat transfer coefficient and temperature have decreasing effects against radiation parameter.

In this paper, we have analyzed the bifurcation of stagnation points in the non-Newtonian flow of the FENE-P fluid through a channel induced by peristalsis. The stream function for the flow under consideration is developed under negligible inertia and streamline curvature effects. A nonlinear autonomous system is developed for scrutiny of the critical points. A dynamical system approach is used to examine the stability of bifurcation points. Streamline patterns, and local and global bifurcation diagrams are plotted for analysis of the backward flow, trapping, and augmented flow regions. The impacts of important embedded parameters, i.e., extensibility parameter and Deborah number on local and global bifurcation diagrams, are also examined. The whole analysis reveals that two critical conditions appear in the flow field that are actually responsible for the conversion of backward flow to trapping and trapping to augmented flow. It is further seen that bifurcations occur at lower flow rates for increasing Deborah’s number while an opposite trend prevails for increasing the extensibility parameter. A comparison of bifurcations between planar and axisymmetric flows is also performed. It is observed that a greater area of the trapping region is encountered for axisymmetric flow than that for planar flow.

Nanofluids with peristaltic flows are being studied in depth because they can be used in so many different ways, such as to diagnose and treat diseases. In this paper, the peristaltic flow of a nanofluid with viscosity and electric conductivity that change with temperature is used. There are different base fluids and nanoparticles that are being thought about. First, the governing equations are modeled, and then they are made easier to understand by assuming that the wavelength is long and the Reynolds number is small. To make a dimensionless differential system, the right dimensionless numbers are added. Mathematica’s built-on function NDSolve is used to figure out the numerical solution of the resulting system. To figure out how fast heat moves, researchers compare different combinations of base fluids and nanoparticles.

The primary aim of this study was to examine the peristaltic flow of an unsteady non-Newtonian TiO₂ nanofluid through a uniformly symmetric channel under the influence of electro-osmosis. The fluid behavior was modeled by the Sutterby model. Furthermore, the flow took place through a porous medium, following a modified form of Darcy’s law. Additionally, the impacts of Dufour and Soret effects, chemical reaction, activation energy, viscous dissipation, heat generation, and thermal radiation were considered. A wave transformation was used to simplify the governing equations describing the velocity, temperature, and nanoparticle concentration. These simplified equations were then solved analytically using the homotopy perturbation method. Additionally, set figures were employed to illustrate and discuss the impact of the physical parameters involved in the problem on the obtained solutions. It is found that the presence of a modified Darcy’s medium in the Navier–Stokes equation results in a porous term that is dependent on the index of the Sutterby model. Furthermore, it is found that as the thermophoresis parameter increases, the nanoparticles are more concentrated, and their flow from the hot region to the cold region is more effective. Additionally, it is observed that in the presence of thermal radiation, the activation energy and the Brownian motion parameter have similar effects on the concentration profile.

This study focuses on the analysis of peristaltic transport of a hybrid nanofluid comprising deionized water as a base fluid and the multi-walled carbon nanotubes (MWCNTs) and copper oxide (CuO) as nanoparticles within a sinusoidal wavy porous duct, taking into consideration the influence of heat generation or absorption. The inaugural literature piece addresses the utilization of hybrid nanofluid in the context of peristaltic flow within ducts. To simplify the analysis, we have converted the non-dimensional equations into a two-dimensional (2D) coordinate system using the assumptions of a very long wavelength $(\delta <1)$ and low Reynolds number (Re). The non-dimensional equations governing the behavior of the hybrid nanofluid are then solved numerically using the finite volume method. Numerical solutions for temperature and the 2D peristaltic flow are obtained with the assistance of the Mathematics software MATLAB. These solutions are subsequently represented graphically using MATLAB software. The graphical results highlight several key findings for important parameters. First, it is observed that the pressure rise, temperature profile, and pressure gradient in the hybrid nanofluid (CuMWCNTs/H₂O) flow increases as heat generation increases. Furthermore, an increase in the nanoparticle volume fraction of both nanoparticles leads to a decrease in the pressure rise and pressure gradient in the hybrid nanofluid flow. Additionally, the widening of the channel reduces the pressure gradient and pressure rise in the CuMWCNTs/H₂O hybrid nanofluid. The analysis also includes the visualization of streamlines for peristaltic transport. These streamlines reveal that an increase in amplitude results in larger bolus sizes, while heightened heat generation has the opposite effect, decreasing bolus sizes. The results of this investigation can be found in various cooling devices as flows in the ducts are very frequently utilized for the cooling process of engines. A further topic is common in applications related to microfluidics, heat exchangers, and biomedical devices where peristaltic pumping is employed. Our results are in 100% agreement with the existing literature in special cases.

This study investigates the impact of electroosmosis on the peristaltic flow of unsteady micropolar nanofluid with heat transfer. The findings could enhance the design of peristaltic pumps, potentially improving drug delivery systems, simulations of blood flow in medical devices, and cancer treatments. The fluid under investigation adheres to a micropolar model and flows through a microchannel that exhibits peristalsis along its walls. Moreover, the system is subjected to various external effects, including a uniform magnetic field, the electroosmotic phenomenon, heat absorption, and a chemical reaction with activation energy. Consequently, the problem is mathematically modulated by a system of nonlinear partial differential equations governing the velocity, temperature, and nanoparticle concentration. By employing wave transformation, these governing equations are reduced to ordinary differential equations (ODEs). The reduced equations were solved both analytically, using the homotopy perturbation method, and numerically, using the Runge–Kutta–Merson method. A comparison was made between the solutions, which were found to be closely aligned. Furthermore, a series of figures were employed to provide visual representation and discussion of the implications of the physical properties. The calculations reveal that the electroosmotic flow (EOF) enhances the axial flow of the micropolar fluid along the direction of the applied electric field. It is also observed that the increase in the activation energy (which indicates a low reaction rate) increases the concentration profile whereas the increase in the reaction rate parameter reduces the concentration profile. Additionally, the spin velocity of the particles is diminished by either an increase in the magnetic parameter or the coupling parameter.

The effect of a third-order fluid on the peristaltic transport is analysed in a circular cylindrical tube, such as some organs in the living body. The third-order flow of an incompressible fluid in a circular cylindrical tube, on which an axisymmetric travelling sinusoidal wave is imposed, is considered. The wavelength of the peristaltic waves is assumed to be large compared to the tube average radius, whereas the amplitude of the wave need not be small compared to the average radius. Both analytic (perturbation) and numerical solutions are given. For the perturbation solution, a systematic approach based on an asymptotic expansion of the solution in terms of a small Deborah number is used and solutions up to the first order are presented in closed forms. The numerical solution, valid for any Deborah number, represents a new approach to peristaltic flows, and its features illuminate the physical behaviour much more than the analytical research on this problem. Comparison is made between the analytic (perturbation) and numerical results. Furthermore, the obtained results could also have applications to a range of peristaltic flows for a variety of non-Newtonian fluids such as aqueous solutions of high-molecular weight polyethylene oxide and polyacrylamide.

The present investigation is devoted to study a theoretical investigation of the peristaltic flow of a couple-stress conducting fluids in a porous channel under the influence of slip boundary condition. This study is applicable to the physiological flow of blood in the micro-circulatory system, by taking account of the particle size effect. The expressions for axial velocity, pressure gradient, stream function, frictional force and mechanical efficiency are obtained under the small Reynolds number and the large wavelength approximations. Effects of different physical parameters reflecting permeability parameter, couple-stress parameter, Hartmann number as well as amplitude ratio on pumping characteristics, frictional force, mechanical efficiency and trapping of peristaltic flow pattern are studied. The computational and numerical results are presented in graphical form. On the basis of our discussion, it is concluded that pressure reduces by increasing the magnitude of couple-stress parameter, permeability parameter, slip parameter, whereas it enhances by increasing the magnitude of magnetic field and amplitude ratio.

In a previous paper,¹ we proposed an optofluidic modulator based on peristaltic flow. A microchannel made of polydimethylsiloxane is filled with nematic liquid crystal molecules that align homeotropically in the steady state. Once we apply a periodic peristaltic flow through mechanical deformation of the channel, liquid crystal molecules tend to realign with the gradient velocity field and thus change their optical properties. In this paper, we focus on the channel deformation with the finite elements program Comsol^®, and we highlight the limitations in frequency of such optofluidic components.

The present studies deal with the peristaltic motion of an incompressible Williamson fluid model in an endoscope. The governing equations of Williamson fluid model are first simplify using the assumptions of long wavelength and low Reynolds number. The four types of solutions have been presented for velocity profile named (i) exact solution, (ii) perturbation solution, (iii) HAM solution, and (iv) numerical solutions. The comparisons of four solutions have been found a very good agreement between all the solutions. In addition, the expressions for pressure rise and velocity against various physical parameters are discussed through graphs.

In the present article, we have discussed the closed-form analytical and numerical solutions of the peristaltic flow of a Jeffrey fluid in an inclined tube with different viscosities and with different wave shapes. The closed-form analytical solutions have been computed by Adomian decomposition method and the numerical solutions have been calculated using finite difference technique. A comparison of numerical and analytical solutions have been presented and found a very good agreement between the two solutions. The expressions for pressure rise and friction forces are computed using numerical integration with the help of mathematics software. At the end various physical parameters appearing in the problem are shown pictorially and the results have been discussed in detail. The phenomena for different wave shape are also discussed.

In this article, we considered the peristaltic flow of Newtonian incompressible fluid of chyme in small intestine. The analysis has been performed using an endoscope. The peristaltic flow of chyme is modeled by assuming that the peristaltic wave is formed in non-periodic mode comprising two sinusoidal waves of different wave lengths propagating with same speed along the outer wall of the tube. Heat transfer mechanisms have been taken into account, such that the constant temperature and are assigned to inner and outer tubes, respectively. A complex system of equations has been simplified using long wavelength and low Reynolds number approximation because such assumptions exist in small intestine. Exact solutions have been carried out for velocity temperature and pressure gradient. Graphical results have been discussed for pressure rise, frictional forces, temperature, and velocity profile. Comparison of present results with the results of the existing literature have been presented through figures. Trapping phenomena have been presented at the conclusion of the article.

The peristaltic flow of Jeffrey fluid in a microchannel with compliant wall has been investigated. The rheological effects and compressibility of the fluid are given proper attention. Perturbation approach has been employed when the ratio of the wave amplitude to the radius of the pore is small. Expressions of perturbation function, mean axial velocity distribution, mean velocity at the boundaries and critical values are derived. The variations of various interesting parameters are shown and examined very carefully.

This article studies the hydromagnetic peristaltic flow of couple stress fluids through the gap between two concentric channels containing a Darcian porous medium, with the inner channel being rigid. A sinusoidal wave propagates along the outer channel. Long wavelength and low Reynolds number assumptions are used. The effects of couple stress parameter, magnetic field, permeability, and the channel ratio width on pressure and frictional forces on the inner and outer channels are depicted graphically. Mechanical efficiency and trapping are also studied. Pressure diminishes with increasing coupling and permeability parameters whereas it increases with Hartmann number and channel width ratio. Applications of the model include transport of complex bio-waste fluids and magnetic field control of gastro-intestinal disorders.

In this study, the mathematical observations for the peristaltic flow of a Williamson fluid model (e.g., chyme) in a cross-section of a rectangular duct having compliant walls were considered. The flow was assumed incompressible and unsteady. The constitutive equations were reduced under the assumptions of low Reynolds number and long wavelength approximations. The resulting dimensionless governing equations were solved using the homotopy perturbation method (HPM) and eigenfunction expansion method. The results obtained were explained graphically. The velocity distribution was plotted for physical parameters both in two and three dimensions. The streamline graphs are presented in the end, which explain the trapping bolus phenomenon. All theoretical and graphical results are then discussed simultaneously.

Analysis is performed for the simultaneous effects of heat and mass transfer on the peristaltic transport of an electrically conducting couple-stress fluid in a compliant walls channel. The study may be useful in understanding the physiological flow of blood through micro-circulatory system in the presence of particle-size effect. Long wavelength and low Reynolds number aspects are taken into consideration. Exact solutions for stream function, temperature and concentration are derived. Impact of pertinent parameters like the couple-stress fluid parameter (γ), Hartman number (M), amplitude ratio (ϵ), elastic parameters (E₁, E₂, E₃, E₄, E₅), Brinkman number (Br) and Schmidt number (Sc). It is observed that velocity and temperature distributions are greater for couple stress fluid when compared with the Newtonian fluid.