A mathematical framework for peristaltic flow analysis of non-Newtonian Sisko fluid in an undulating porous curved channel with heat and mass transfer effects

doi:10.1016/j.cmpb.2019.105040

Computer Methods and Programs in Biomedicine

Volume 182, December 2019, 105040

https://doi.org/10.1016/j.cmpb.2019.105040 Get rights and content

Highlights

•
Analysis of non-Newtonian Sisko fluid in an undulating porous curved channel is reported.
•
Modified Darcy's law is implemented to capture the porosity effects.
•
Implicit finite difference scheme is used for simulations.
•
The size of circulating bolus of fluid reduces with increasing permeability parameter.

Abstract

Background and objective

Peristaltic is one of the most frequently occurring phenomenon in biological systems. These systems of the human body (especially digestive, reproductive, respiratory, renal system) generally involve effects of curvature, porosity, rheology and heat transfer. Thus, in the present investigation we integrate heat transfer phenomenon with Sisko fluid flowing through porous medium bounded within curved wavy walls. The theoretical analysis presented under long wavelength approximation serves as a model for the creeping non-isothermal flow of blood through a diseased segment of the artery due to vasomotion (peristaltic motion) in the artery.

Methods

The highly nonlinear ordinary differential equation with appropriate boundary conditions is solved using a well-tested implicit finite difference scheme. A comparison of velocity profile for Newtonian, power-law and Sisko fluids is also presented.

Results

The Sisko model predict higher values of velocity in the central core region than power-law and Newtonian model. The size of circulating bolus of fluid reduces with increasing permeability parameter. The symmetry in velocity and streamlines pattern is observed when dimensionless radius of curvature becomes very large.

Introduction

Peristaltic is nature's way of transportation of fluids in living organism. In this mechanism, the drag flow due to boundary is superimposed with pressure gradient. Diabetic pump, heart-lung machine, roller and finger pumps are few out of several applications of this mechanism in medical and nuclear industries. Inspired by this fact many researcher investigated the peristaltic phenomenon in different disciplines. Shapiro et al. [1] presented the first theoretical and experimental investigation on peristaltic flows under the assumption of negligible inertial and streamline curvature effects. Their analysis is generalized in several directions to include the non-Newtonian effects [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], curvature effects [15], [16], [17], [18], [19], magnetohydrodynamic effects [20], [21], electro-osmotic effects [22], slip effects [23], [24], [25] and porous media effects [25], [26], [27], [28], [29], [30]. The heat transfer analysis is also carried out in peristaltic flows by several researcher with motivation of its applications in hemodialysis, laser therapy and cryosurgery [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40]. Few latest references [42], [43], [44], [45], [46], [47], [48] related to bacterial gliding by means of peristaltic waves and swimming motion of spermatozoa are also worthwhile to mention.

From the above studies it is noted that, the geometry of the peristaltic flow model is usually considered as a planar channel, axisymmetric tube, curved channel or a duct. Moreover, the peristaltic flow through a porous-saturated straight vessel is modeled but no information is available for these physical conditions with curvature effects. Motivated by this fact the aim of this study to model the non-isothermal flow of biological fluid in a porous curved channel. The primary motivation of this study is application of porous media in small constricted curved blood vessel. In such vessels the diseased segment can be thought of a fictitious porous medium thorough which blood is transported by vasomotion (peristaltic) of the vessel. There are several other important applications of porous media in ground water hydrology, metallurgy and petroleum geoscience. The rheological behavior of blood is modeled by Sisko constitutive equation. This equation possess two material constants in addition to power-law index. It includes power-law and Newtonian equation as special cases. Sisko constitutive equation is capable of predicting the behavior of fluids which exhibit shear-thinning behavior at low shear rates while viscosity approach a constant value when shear rate becomes large. Blood is a typical example with such characteristics. In contrast to previous studies, the porous effects via

Modified Darcy law is modeled through the effective viscosity of the Sisko model. The present study serves as a first theoretical model which analyses the heat and mass transfer effects in peristaltic flow through a curved porous-saturated channel. Our objective is to explore the effects of permeability of the porous medium on creeping flow generated by wavy walls under mass and heat variation. To this end, the constitutive equations are modeled for the case when viscous effects dominate the inertial effects. The highly nonlinear system of equations with appropriate boundary conditions is solved using a well-tested implicit finite difference scheme. The velocity of the Sisko fluid, pressure rise, temperature profile, heat transfer coefficient, concentration profile and Sherwood number are analyzed for several values of rheological, curvature, porosity parameters and Brinkmann number. Few recent studies related to such thermal analysis of the fluid flow problems can be found in the refs. [49], [50], [51], [52], [53], [54], [55].

Section snippets

Mathematical formulation

Assume a curved passage of width 2 w having radius R₀ and center O. The gap between the channel walls is filled with homogenous porous medium and Sisko fluid. The flow inside the porous-saturated channel is due to the sinusoidal deformation of the channel walls. Let c be the speed and a be the amplitude of sinusoidal waves in curved boundaries. Let T₁ and T₀ be the constant temperature at lower and upper peristaltic walls, respectively. Similarly, C₀ and C₁ specify the mass concentration at

Computational results and interpretation

In this section, we interpret the graphical results provided in Fig. 2, Fig. 3, Fig. 4, Fig. 5, Fig. 6, Fig. 7, Fig. 8, Fig. 9, Fig. 10, Fig. 11, Fig. 12, Fig. 13, Fig. 14, Fig. 15, Fig. 16, Fig. 17, Fig. 18, Fig. 19, Fig. 20, Fig. 21 to analyze some significant features of the peristaltic motion such as flow characteristics, pumping characteristics, temperature distribution, mass concentration, and streamlines for different paramters. The variation of heat and mass transfer coefficients at

Concluding remarks

A creeping flow generated by undulating curved porous walls is numerically investigated under long wavelength assumption. The non-Newtonian Sisko model is used in the analysis. The behavior of velocity, pressure, temperature, mass concentration and streamlines is shown through graphs. The key findings of the analysis are:

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The flow velocity diminishes with increasing K*.
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Increasing K* assist the pressure rise.
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The radial distribution of temperature and mass concentration inside the channel follow

Declaration of Competing Interest

It is declared that we have no conflict of interest.

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The influence of an external normal electric field on peristalsis involving Sisko fluid on convection flow between two coaxial cylinders is explored. The resulting system of equations is analytically solved using the regular perturbation technique with low parameters. This approach is dependent on two factors: a small wave number and a small Sisko fluid parameter. Analytical solutions for radial and axial velocities, temperature, electric potential, and pressure are produced based on the use of appropriate non-dimensional quantities. Graphical representations of the impacts of various parameters on the pertinent physiological factors. The results show that when there is an electric field present, the effects of the endoscope velocity on the axial velocity are more noticeable and distinct than when there isn't. It is discovered that the endoscope radius plays a dual role on the electrical potential. The electrical potential decreases with an increase in the endoscope velocity, amplitude ratio, Reynolds number, and Prandtl number while the opposite occurs when electrical potential, temperature parameter, and power index are increased. Additionally, with respect to shear thickening fluid, the temperature, electrical potential, and pressure are all higher compared to in the case of Newtonian fluid. The Rayleigh number, electrical potential, endoscopic velocity and radius, temperature parameter, Reynolds number, and power law index all raise the size of the trapped bolus while the amplitude ratio diminishes it. The study's findings will assist in a better understanding of biomedical engineering and technology.
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This research article investigated the effects of dual-phase chemical reactions on the unsteady flow of Sisko fluid. Utilizing Caputo's fractional derivatives, the model captured the fractional behavior of the fluid and integrated relaxation times to reflect the viscoelastic nature of the Sisko fluid. The model also considered unequal diffusivities of the chemical species. The resulting equations were discretized using the finite difference method, complemented by the $L_{1}$ algorithm. Our simulations underscored how memory parameters, $β$ and $γ$ , significantly shaped the concentration trajectories by emphasizing the impact of past flow behaviors. Moreover, the study identified the heterogeneous reaction parameter and the diffusion coefficients ratio as critical determinants in the reaction dynamics, underscoring their role in the system's behavior. This study illuminates the intricate matrix of relationships in the realm of chemical reactions and viscoelastic fluid flow, offering valuable insights for fields ranging from chemical processing to environmental remediation.
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Citation Excerpt :
They saw that the both temperature profile and heat transfer coefficient boosted by increasing the following involved parameter, for example: bi-viscosity parameter, Hartmann number and porosity parameter. Asghar et al. [12] investigated the influences of heat transfer phenomena on the Sisko liquid via sinusoidal contraction and relaxation of the outer walls in the curved porous medium. They deliberated the comparison between viscous fluid, power-law fluid and Sisko fluid.
The applications of hybrid nanomaterials report excellent thermal performances and convey applications in various processes like energy production, extrusion processes, nuclear reaction, manufacturing and engineering processes, industrial domains, aero-spaces etc. Additionally, the impacts of magnetic devices in advance endoscopy and biological transport phenomena are also a hot topic of research in the current era. This study deals with the physical influences of magnetic device on the peristaltic transport of a viscoplastic nanofluid between the two-dimensional curved concentric tubes. The curved shape structure of flow geometry from the external side with a flexible complex nature of the peristaltic endoscope present inside that is similar to the endoscopy of a living organ. The non-Newtonian Casson liquid polymer is employed for assist the dynamic of viscoplastic materials. The concentration of silver $(A g)$ and alumina $(A l_{2} O_{3})$ nanoparticles are utilized in the clay as a base fluid. The governing equations are modeled by using the curvilinear coordinates. The conducting investigation is worked out for creeping pattern and under the high wavelength consideration. The analytical proceedings for flow features, for examples, axial velocity profile, pressure gradient, pressure rise, shearing stress tensor and temperature profile, are obtained by using integration technique. It is noted that the velocity magnitude for viscous fluid is larger in magnitude as compared with the viscoplastic fluid. The magnitude of temperature rate get slower variation for volumetric concentration parameter (range of concentration parameter is 0%–4%). The current model has been used in bio-engineering processes, industrial fluid mechanics, thermal processing, endoscopy of living organs and cooling systems.
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Utilization of variable thermal conductivity and diffusion coefficient on non-Newtonian Prandtl model with modified heat and mass fluxes
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A mathematical framework for peristaltic flow analysis of non-Newtonian Sisko fluid in an undulating porous curved channel with heat and mass transfer effects

Highlights

Abstract

Background and objective

Methods

Results

Introduction

Section snippets

Mathematical formulation

Computational results and interpretation

Concluding remarks

Declaration of Competing Interest

J. Biomech.

J. Non-Newtonian Fluid. Mech.

Comput. Mater. Sci.

J. Non Newtonian Fluid Mech.

Physica A

Commun. Nonlinear Sci. Numer. Simulat.

Nonlinear Anal.: Real World Appl.

Phys. Lett. A

Appl. Math. Model

Phys. Lett. A

Appl. Math. Comput.

Int. J. Heat Mass Transfer

Commun. Nonlinear Sci. Numer. Simul.

Int. J. Heat Mass Transfer

Int. J. Heat Mass Transfer

Int. J. Therm. Sci.

J. Theor. Biol.

Math. Biosci.

Results Phys.

J. Magn. Magn. Mater.

Results Phys.

Peristaltic pumping with long wavelength at low Reynolds number

J. Fluid Mech.

Peristaltic motion of non-Newtonian fluid

Acta

Peristaltic motion of non-Newtonian fluid II Viscoelastic

Fluid Rheol, Acta

Peristaltic flow of viscoelastic liquids

J. Fluid Mech.

Peristaltic pumping of second order fluid in a planar channel

Rheol. Acta

Peristaltic transport of third order fluid in a cylindrical tube

Math. Models Methods Appl. Sci.