Peristaltic Flow Research Articles

Impact of heat and mass transfer on the Peristaltic flow of non-Newtonian Casson fluid inside an elliptic conduit: Exact solutions through novel technique

The physics of peristaltic flow in elliptic duct with heat and mass transfer effects is mathematically investigated. A non-Newtonian Casson fluid model is considered for this mathematical analysis. The partial differential equations appearing in the non-dimensional form are interpreted by using a novel mathematical technique that provides exact analytical solution for temperature, concentration and velocity profile. Further, the graphical solutions are provided for the verification of mathematical computations. The declining axial pressure gradient for increasing flow rate indicates that this increase in the flow rate is basically assisting the fluid movement. It is also evident from the velocity profile graphs that the increasing flow rate results in an increased flow profile. The flow profile inside this vertically set duct is visualized through streamline graphs. Clearly streamlines are not crossing each other since the velocity at any spot can have only a unique value. Some closed contours are also evident near the central region in these streamline graphs that highlight the trapping phenomenon. A slight increment in trapping is noted for increasing flow rate. Except streamlines the flow profile can also be visualized through streaklines or pathlines but there is no need to plot streaklines or pathlines here since in case of a steady flow they are all identical.

Impact of inclined magnetic field on peristaltic flow of blood fluid in an inclined asymmetric channel in the presence of heat and mass transfer

The present investigation studies the peristaltic flow of the Newtonian fluid model through an inclined asymmetric channel. Mathematical analysis has been carried out in the presence of an inclined magnetic field and heat and mass transfer in the peristaltic flow of blood fluid in an inclined asymmetric channel. The flow is examined in a wave frame of references moving with the velocity of the wave. The physical problem is the first model, and then, the analytical solution is carried out under long-wavelength and low Reynolds number approximation. Expressions of the velocity, temperature, concentration, pressure gradient, tangential stress, and heat transfer coefficient are obtained. The results in the pressure rise and frictional force have also been computed numerically. The effects of thermal radiation, Hartman number, thermal slip, Grashof number, phase difference, aligned magnetic field, and inclination of the asymmetric channel to the vertical are studied. Numerical results are graphically discussed for various values of physical parameters of interest and the phenomenon of trapping is also discussed.

Theoretical study of transport of MHD peristaltic flow of fluid under the impact of viscous dissipation

ABSTRACT This article studies irreversibility analysis in the peristaltic transport of a non-Newtonian fluid. Jeffrey fluid is treated as the blood transport through a flexible artery/vessel. A peristaltic wave travels on the porous opposite wall of the inclined channel under the magnetic environment. Heating effects cause the shear thinning in the viscosity of the base liquid, transferring tiny particles. The efficiency of peristalsis is improved by reducing the irreversibility factor by means of entropy generation. The perturbation technique is applied to understand the nonlinear flow dynamics of heat and mass transfer with Jeffrey fluid with the help of convective boundary conditions. Comparative analysis is carried out with the available literature for the limiting case and found to have complete coherence. A detailed parametric study is carried out to comprehend the contribution of significant parameters which reveals that magnetic fields and slippery walls induce a resistive force on the nanoflow. The motion of the base liquid expedites subject to variation in Darcy number and shear-thinning effects. The energy is contributed to the nanofluid system in response to the Brinkman number. More, the number density of nanospecies reduces in the region of higher concentration subject to the Soret number and Schmidt number, respectively.

Dynamics and bifurcations of non-Newtonian Au–Cu/blood hybrid nanofluid model of electrokinetic flow in asymmetrically tapered wave microchannel

The present paper investigates the dynamic behavior of streamline patterns with their bifurcations for heat transfer in a peristaltic flow model. This model represents an incompressible Casson hybrid nanofluid Au–Cu/blood flowing through a porous saturated tapered asymmetric microchannel in the presence of electroosmotic body force, velocity slip, and temperature jump conditions. Analytical and numerical tools are used to perform a thorough bifurcation and stability analysis of the various stagnation point positions. The global dynamics behavior around these points generates invariant sets and attractors, such as a surface of heteroclinic connections between saddle stagnation points, which is used to predict the various flow modes and topologies that control stream flow. The impact of the physical parameters associated with flow problems is also thoroughly investigated and graphically illustrated.

Influence of Triple Diffusive Convection in Peristaltic Flow of Jeffrey Nanofluid Through Non-Uniform Channel

In this investigation, we considered the effect of triple diffusive convection on peristaltic flow through a non-uniform Channel. We also considered the incompressible non-Newtonian Jeffrey nanofluid. On the assumption of a long wavelength and low Reynolds number, the governing equations were transformed into a non-dimensional form. The reduced non-dimensional highly nonlinear partial differential equations are solved using the Homotopy Perturbation Sumudu transformation method (HPSTM). The influence of different physical parameters on dimensionless velocity, pressure gradient, temperature, the concentration of salt 1 and salt 2, and volume fraction was graphically represented. The Dufour solutal Lewis number of salt 1 and salt 2 on the velocity profile increases. The Dufour solutal Lewis number and modified Dufour parameter of salt 1 rises on nanoparticle volume fraction profile. It is found that the presence of the triple diffusing components with small diffusivity can change the convection in the system. The change in density in a triple diffusive is caused by the thermal and solutal diffusivities of two separate chemical species. So this study is applicable in engineering and scientific fields like geology, astrophysics, disposal of nuclear waste, deoxyribonucleic acid (DNA), and chemical engineering. This work is compared with the exact solution, and it is in good agreement with this method.

Mathematical model of convective heat transfer for peristaltic flow of Rabinowitsch fluid in a wavy rectangular duct with entropy generation

This research article unfolds a novel mathematical model that interprets the ‘peristaltic flow of Heated Rabinowitsch fluid’ inside a wavy rectangular duct. The fluid flow characteristics are thoroughly examined for Pseudo-plastic in addition to Dilatant nature, (i.e. α > 0 for pseudo-plastic nature and α < 0 for dilatant nature respectively). Peristaltic flow inside a wavy rectangular duct is widely being studied due to immense number of biomedical and engineering applications. We have derived the dimensionless nonlinear partial differential equations in coupled form after applying certain relevant dimensionless quantities, the lubrication technique of low Reynolds number and long wavelength estimations (i.e., ). The dimensionless energy equation is solved by dividing it into two additional equations and after employing suitable procedures, an exact temperature profile solution is computed. The present study has been developed by using hit and trial method to solve the single partial differential equation having two dependent variables in form of extra stress tensors. The solution of temperature profile provides a detailed solution method to exactly solve such complex partial differential equations. For both dilatant and Pseudo-plastic fluids, effective physical parameters are used to depict velocity distribution, pressure gradient and pressure rise, convection and entropy phenomena. When compared with Pseudo-plastic fluid, the Dilatant nature of fluid has a high convection rate. Finally, the phenomenon of entrapment is examined through streamlines that provide a flow visualization inside the wavy sinusoidal duct. Peristaltic pumps are being used for transportation of many fluids like toxic chemicals in nuclear industry, food processing, heart-lung machines, roller and finger pumps and transportation of slurries etc. These usage of these pumps leads to an upgraded mechanical efficiency and lower cost for transportation purposes.

Mathematical computations for the physiological flow of Casson fluid in a vertical elliptic duct with ciliated heated wavy walls

This mathematical investigation discloses the peristaltic flow of non-Newtonian fluid in a vertical duct with an elliptic cross-section and ciliated walls. The Casson fluid’s non-Newtonian model is utilized for an elliptic duct with heated ciliated walls. The physical aspects of cilia-driven metachronal wave combined with sinusoidal wavy wall movement are highlighted. A set of dimensionless partial differential equations with relevant boundary conditions is obtained after simplifying the dimensional form of governing equations using appropriate transformations. A complete mathematical method is conveyed to get exact solutions for this convection heat transfer problem. The final solutions are further analyzed through graphical results. The increase in the value of changes the mechanism from non-Newtonian to a Newtonian flow. Moreover, if is increased to infinity, then it becomes a complete Newtonian fluid flow problem. Moreover, the velocity increases with an increasing value of .

Wall properties and Joule heating effects on MHD peristaltic transport of Bingham non-Newtonian nanofluid

We analysed Soret and Dufour effects on peristaltic flow of magnetohydrodynamic (MHD) non-Newtonian nanofluid in a uniform symmetric channel with wall properties. Moreover, we involved effects of Joule heating, chemical reaction. Furthermore, we considered Brownian motion and thermophoresis. Then, we simplified the governing equations to a system of partial differential equations by applying low Reynolds number and long wavelength approximations and we solved them by using Homotopy Perturbation Method (HPM). We sketched the influence of various parameters on the stream function, velocity, temperature and nanoparticles concentration in graphs and we discussed them physically. Also, we obtained graphs for heat transfer coefficient, skin friction coefficient, Nusselt number and Sherwood number at the upper wall of the channel. Finding revealed that as the wall proprieties parameters E1 and E2 increased the velocity and temperature increased, but the stream function increased and decreased. While, Bingham number Bn had an opposite relative to the wall proprieties parameters E1 and E2.

Effect of Thermal Radiation and Double-Diffusion Convective Peristaltic Flow of a Magneto-Jeffrey Nanofluid through a Flexible Channel

The noteworthiness of double-diffusive convection with magneto-Jeffrey nanofluid on a peristaltic motion under the effect of MHD and porous medium through a flexible channel with the permeable wall has been theoretically examined. A non-linearized Rosseland approximation is utilized to show the thermal radiation effect. The governing equations are converted to standard non-linear partial differential equations by using suitable non-dimensional parameters. Solutions of emerging equations are obtained by using the multi-step differential transformation method (Ms-DTM). The differential transformation method (DTM) can be applied directly to nonlinear differential equations without requiring linearization and discretization; therefore, it is not affected by errors associated with discretization. The role of influential factors on concentration, temperature, volume fraction, and velocity are determined using graphs. A significant outcome of the present article is that the presence of double-diffusive convection can change the nature of convection in the system. The present results have a wide biological applicability, including for biomicrofluidic devices that regulate the fluid flow through a flexible endoscope and other medical pumping systems.

Channel flow of non-Newtonian fluid due to peristalsis under external electric and magnetic field

The overall objective of the current analysis is to examine how electroosmotic flow combined with peristaltic pumping phenomenon could ably contribute to intracellular fluid flow. The biofluid is taken as non-Newtonian Couple stress fluid, while micro-passage is approximated as two-dimensional inclined channel comprehending complex peristaltic walls. Following a traditional approach of peristaltic fluid flow problem balance of mass and momentum is utilized. Beside channel waves, flow is also generated by Lorentz force triggered by electric and magnetic fields. To integrate electric potential term Poisson-Boltzmann and Nernst Planck equation are utilized. Finally, a sixth order BVP in term of stream function is obtained by employing creeping flow, long wavelength and Debye-Hückel assumptions. A numerical solution is calculated and analyzed by plotting fluid velocity and level curves in MATLAB 2021b. It is observed that couple stress fluid flows with greater speed (in central region of the channel) as compared to Newtonian fluid. Moreover, electro-osmotic parameter and Debye-Hückel length are assistive factors to the fluid velocity in the lower half of the passage.

Entropy generation analysis for magnetized peristaltic movement of nanofluid through a non-uniform asymmetric channel with variable thermal conductivity

This study examines the effects of entropy generation on MHD peristaltic flow of nanofluid through a non-uniform asymmetric channel by considering its rheological aspects. Thermal conductivity of the nanofluid is considered to vary with temperature. Thermophoresis, viscous heating, Brownian motion and Joule dissipation are involved in the mass species and thermal expressions. Mathematical modeling is carried out by making use of lubrication approximation. The resulting nonlinear system is solved using the Homotopy Analysis Method (HAM) which has rarely been used for such problems. Numerical results are also obtained by the Shooting method and comparison of both results is also provided. Nature of embedded constraints on momentum, thermal, concentration, Bejan number and entropy generation is reported. The presented results indicate that the strong magnetic field reduces the Bejan number. Moreover, entropy generation is less for flow through a divergent channel.

Analysis of electroosmotic flow of silver-water nanofluid regulated by peristalsis using two different approaches for nanofluid

This article deals with mathematical modeling of the electroosmotically boosted peristaltic propulsion of water-based silver nanofluid through an asymmetric channel. The inherent Joule heating phenomenon is also included in the mathematical modeling of the flow problem. The no-slip boundary conditions are utilized for velocity and temperature of the fluid and conditions of zero mass flux are considered for nanoparticle volume fraction. The electric potential generated by electroosmosis is formulated by Poisson-Boltzmann ionic distribution. The aim here is to compare the properties of nanofluid flow as predicted by the modified Buongiorno model in combination with the Corcione model for thermal conductivity and that estimated by a combination of the traditional Tiwari-Das model and the Corcione model under the same physical conditions. The numerical solution is computed for the emerging set of nonlinear coupled equations through the built-in command in Maple 17 which uses the finite difference technique in combination with Richardson extrapolation to solve a boundary value problem. Important attributes of electroosmotically controlled peristaltic fluid flow are illustrated subject to variation in different physical parameters. The analysis exhibits that under the same physical conditions, the modified Buongiorno model predicts the nanofluid properties more efficiently than the Tiwari-Das model. It is found that for larger temperature differences within a fluid medium, the Nusselt number declines in the case where the modified Buongiorno model is utilized whereas the Tiwari-Das model does not include the effect of temperature difference. Moreover, peristaltic pumping is boosted by forwarding electric field and opposed by backward electroosmosis, and the magnitude of the Nusselt number tends to raise for larger Joule heating parameter.

Analytical Solution for the MHD Flow of Non-Newtonian Fluids between Two Coaxial Cylinders

This paper deals with the MHD peristaltic flow of Williamson fluids through a porous medium between two joint cylinders. The fluid flow was considered to be that of a non-Newtonian fluid, i.e., a Williamson fluid. The inner tube was uniform, while the flexible outer tube had a Sine wave moving down its wall. The analytical solutions for velocity and temperature were obtained as functions (Bessell functions of the first and second types). The solution for velocity profile, temperature, and concentration distribution were obtained as functions of the physical parameters of the problem (Darcy number, magnetic parameter, Grasoff thermal number, Reynolds number, Prantl number, and Schmidt number) along with other physical parameters. The effect of the physical parameters was discussed graphically. A comparison with previously published graphical results was also carried out. The ambition of the present paper is to contribute to practical applications in geographical and physiological fluid dynamics, such as on sandstone, in the human lungs, on beach sand, on limestone, and in the bile duct. This study is based on theoretical research and can be helpful in the fields of fluid mechanics and mathematics.

Modeling of the Peristaltic Lithogeic Bile Flow in the Calculus Duct Under the Influence of Heat Transfer with Slip Boundary Conditions

This paper deals with a mathematical model that represents non-Newtonian bile flow through a calculus duct under the influence of heat transfer with wall slip conditions. The peristaltic flow of bile is characterized by a generalized Carreau's model. An ordinate transformation is initiated to map the cosine geometry of the stone into a rectangular grid. It allows evaluation velocity, pressure distribution, flow rate, and reflux occurrence conditions, adopting the perturbation technique, the analytical solution obtained under various parameters, such as Knudsen number, amplitude ratio, Grashof number, Weissenberg number, and power index. These mathematical expressions are analyzed by plotting the graph in MATLAB R2018b software and observed that the axial velocity and the pressure gradient are strongly affected by heat and wall slip parameters.

Influence of metachronal ciliary wave motion on peristaltic flow of nanofluid model of synovitis problem

In this article, we have considered the effect of metachronal ciliary wave motion on the peristaltic flow of the Buongiorno nanofluid model for the synovitis problem. This study is additionally limited by the assumption of a low Reynolds number and lubrication theory approximations. An internal energy generation is also taken into account. Shear-thinning (model I) and shear-thickening (model II) for the concentration fluids are considered. The obtained dimensionless rheological equation is solved by using the homotopy perturbation Sumudu transformation method. The influence of various physical parameters on the dimensionless velocity, pressure rise, temperature, volume fraction, multi-sinusoidal waves, triangular waves, and streamlines has been analyzed. A trapping phenomenon is thoroughly examined. It is observed from the investigation that the shear-thinning (model I) and shear-thickening (model II) have completely distinct characteristics. The synovial fluid parameter shows opposite behavior on velocity and pressure rise profiles for models I and II, whereas the multi-sinusoidal wave and triangular wave forms retain the same shape of the waves as in the pressure gradient. These models can be used to treat rheumatoid arthritis as synovial fluids are present in joints. Fluid transfer in biological organs is improved by metachronal ciliary motion. Patients with rheumatoid arthritis can be treated with nanoparticles and ciliary motion. It is primarily due to their biocompatibility, low toxicity, and controlled release as well as their capacity to boost bioavailability and bioactivity of treatments and enable targeting the injured joints through the use of nanoparticles. In the limited scenario, the current work is in good accord with the earlier research, and it is analyzed through a graph.

Thermal Diffusion and Diffusion Thermo Effects on Magnetohydrodynamics Transport of Non-Newtonian Nanofluid Through a Porous Media Between Two Wavy Co-Axial Tubes

Magnetohydrodynamics peristaltic flow of non-Newtonian nanofluid with heat and mass transfer is investigated. The fluid obeys third-grade model and flows through a porous medium inside a gap between two co- axial tubes, where the inner is rigid and the outer has a sinusoidal wave traveling down its wall. The effects of heat source and chemical reaction on the fluid are taken into account. The governing equations that describe the velocity, temperature, and nanoparticles concentration of the fluid are simplified under the assumptions of long wavelength and low Reynolds number. The homotopy perturbation method (HPM) is used to solve these equations, and the solutions are obtained as functions of the physical parameters entering the problem. The behavior of the obtained solutions for different values of these parameters is discussed in detail and illustrated graphically through a set of figures. It is shown that the velocity increases with the increase in the third-grade parameter, while it decreases with increasing the magnetic field parameter. Also, the temperature increases by increasing the Brownian motion parameter. Furthermore, the nanoparticles&#x2019; concentration decreases with the increase in the chemical reaction rate parameter.

Influence of the Induced Magnetic and Rotation on Mixed Convection Heat Transfer for the Peristaltic Transport of Bingham plastic Fluid in an Asymmetric Channel

In this paper, the peristaltic flow under the impact of heat transfer, rotation and induced magnetic field of a two dimensional for the Bingham plastic fluid is discussed. The coupling among of momentum with rotational, energy and the induced magnetic field equations are achieved by the perturbation approximation method and the mathematica software to solve equations that are nonlinear partial differential equations. The fluid moves in an asymmetric channel, and assumption the long wavelength and low Reynolds number, approximation are used for deriving a solution of the flow. Expression of the axial velocity, temperature, pressure gradient, induced magnetic field, magnetic force, current density are developed the effect of rotation, a stress on the lower and upper channel and stream function. The quantities flow have been tested for variant parameters. The impact of the Bingham, Brinkman, Hartman and Grashof numbers are also tested for different values to indicate the effect on the move of flow fluid. The applications can be seen through many graphics.

Effect of Joule heating and entropy generation on multi-slip condition of peristaltic flow of Casson nanofluid in an asymmetric channel.

In the present investigation, the effect of multi-slip condition on peristaltic flow through asymmetric channel with Joule heating effect is considered. We also considered the incompressible non-Newtonian Casson nanofluid model for blood, which is electrically conducting. Second law of thermodynamics is used to examine the entropy generation. Multi-slip condition is used at the boundary of the wall and the analysis is also restricted under the low Reynolds number and long wavelength assumption. The governing equations were transformed into a non-dimensional form by using suitable terms. The reduced non-dimensional highly nonlinear partial differential equations are solved by using the Homotopy Perturbation Sumudu transformation method (HPSTM). The influence of different physical parameters on dimensionless velocity, pressure gradient, temperature, concentration and nanoparticle is graphically presented. From the results, one can understand that the Joule heating effect controls the heat transfer in the system and as the magnetic parameter is increased, there will be decay in the velocity of fluid. The outcomes of the present investigation can be applicable in examining the chyme motion in the gastrointestinal tract and controlling the blood flow during surgery. Present study shows an excellent agreement with the previously available studies in the limiting case.

3D printed PLA enzyme microreactors: Characterization and application for the modification of bioactive compounds

Process sustainability of biocatalytic processes is significantly empowered with the use of continuous-flow technologies that offer high productivity, minimal wastes and low volumetric consumption. Combining microreactor design with 3D printing technology can broaden the engineering potentials. This work proposes a protocol to modify the surface of 3D-printed PLA scaffolds, based on chitosan deposition. Mimicking the concept of microplates, multi-well plates were designed to facilitate parameter testing. Immobilization of laccase from Trametes versicolor was successfully performed, while chitosan and cross-linker concentration and incubation time were optimized. Τhe developed protocol was applied for the continuous flow bioconversion of hydroxyyrosol, yielding a TTN of 438.6 × 103 for a total of 10 h continuous use. Also, a peristaltic flow pattern seemed to favor the system performance, reaching 95% bioconversion efficiency in a total of 1 h reaction time. The potential of the developed system was further evaluated for the biotransformation of different biophenols from dietary sources, proving the efficiency of the system as a versatile biotechnological tool.

Study of Pseudoplastic and Dilatant Behavior of Nanofluid in Peristaltic Flow: Reiner-Philippoff Models

The main goal of this article is to study the effects of pseudoplastic and dilatant behavior of nanofluid on peristaltic flow. This behavior is analyzed along with heat transfer analysis in an asymmetric, non-uniform channel. The Reiner-Philippoff (RPh) fluid model is considered for this study to depict the non-Newtonian characteristics of the fluid. The Reiner-Philippoff fluid model represents the implicit relation between stress and deformation rate. The governing equations for the Reiner-Philippoff peristaltic nanofluid motion are simplified by using the small Reynolds-number and long wavelength estimations. The sound effects of Reiner-Philippoff nanofluid on the behavior of axial velocity, volume fraction of nanoparticles, pressure gradient fields, temperature of fluid, heat transfer rate and streamline functions are discussed in detail. The interesting behavior of Reiner-Philippoff fluid for two limiting cases when shear stress parameter is very small and very large is verified. The heat transfer analysis of dilatants and pseudoplastic fluids is also discussed in detail.