Effects of chemical reaction and space porosity on MHD mixed convective flow in a vertical asymmetric channel with peristalsis

Peristaltic motion of Jeffrey fluid with nonlinear mixed convection

Since previous few decays the consideration of non-Newtonian liquids motion due to its immense usages in medicine, biology, industrial procedures, chemistry of catalysts and in environment. Various studies examine the significance of bio-materials flow in physiological procedures to explore the cure of diagnosed symptoms of disease appearing during movement in a human physiological system. To illustrate the characteristics of physiological liquids various non-Newtonian models have been proposed, but yet no such single liquid model is exploited which describes all the properties of nonlinear behaving liquids. Among these several non-Newtonian models, Jeffery liquid model should be reduced to its base fluid case (i.e. viscous liquid) by choosing λ₁ = λ₂ = 0. Various physiological materials which represents both linear and nonlinear characteristics respectively blood is one of these. Jeffery fluid and peristaltic motion have some common properties such as radii, relaxation time and retardation time. Moreover heat and mass transfer is also an important phenomenon which is suitable for various physiological processes such as hemodialysis and oxygenation etc. Thus due to such motivating facts this research is conducted to investigate the peristaltic motion of electrically conducting Jeffery liquid. The peristaltic propagating channel walls are asymmetric and inclined. Joule heating and magnetic field effects are considered by applying magnetic field in transverse direction to the flow. Further conservation laws modelled the flow situation via considering quadric mix convection, thermos diffusion and diffusion-thermos, heat generation and absorption, chemical reaction with activation energy features. Moreover, creeping flow and long wavelength assumptions are used to simplify the mathematical modelling. The reduced system of equation is solved numerically through built-in technique in Mathematica software. This built-in technique is working through ND Solve command and shooting and RK-Felburg numerical schemes are behind this technique. These numerical results are used to discuss the flow quantities i.e., velocity, temperature and concentration against the sundry dimensionless quantities. Examining the results it comes to know that both thermal and concentration nonlinear mix convection have oppositely affecting the axial velocity. Both heat and mass transfer are escalating function of thermo-diffusion/diffusion-thermo aspects.

Darcy–Boussinesq Model of Cilia-Assisted Transport of a Non-Newtonian Magneto-Biofluid with Chemical Reactions

The model developed in this study presents a mathematical approach to the physiological transport of seminal liquid due to ciliary movements, which are attached with the lumen of the ductile efferent in the male reproductive system. The rheological properties of the seminal liquids were described using the Jeffrey liquid model. The problem described an electromagnetic mixed convective flow of a Jeffrey liquid through a vertical channel with heat and mass transfers. The effects of chemical reactions and the external heat generation were included in the formulation. The flow took place through an active porous medium (due to thick cilia mat and other deposits) and was influenced by the Lorentz magnetic force. Four basic conservation laws of mass, momentum, energy, and concentration were utilized in the mathematical modeling. These are highly nonlinear equations, which were simplified due to a physiologically valid approach known as LAT (lubrication approximation theory). Analytical solutions for temperature, concentration, and velocity profiles were evaluated. The expressions describing the pressure–volume flow rate relationships were also obtained. Analysis of various physical and geometrical factors affecting the pressure–volume (pumping) characteristics was also presented. One of the main findings of our study is that the difference between our calculated values of the flow rate and the estimated values of the flow rate in the ductile efferent was negligibly small. Moreover, our results can be implemented in the artificial cilia pumping systems in microchannels.

Soret and Dufour effects on MHD peristaltic transport of Jeffrey fluid in a curved channel with convective boundary conditions

The purpose of present article is to examine the peristaltic flow of Jeffrey fluid in a curved channel. An electrically conducting fluid in the presence of radial applied magnetic field is considered. Analysis of heat and mass transfer is carried out. More generalized realistic constraints namely the convective conditions are utilized. Soret and Dufour effects are retained. Problems formulation is given for long wavelength and low Reynolds number assumptions. The expressions of velocity, temperature, heat transfer coefficient, concentration and stream function are computed. Effects of emerging parameters arising in solutions are analyzed in detail. It is found that velocity is not symmetric about centreline for curvature parameter. Also maximum velocity decreases with an increase in the strength of magnetic field. Further it is noticed that Soret and Dufour numbers have opposite behavior for temperature and concentration.

Numerical simulation for peristalsis of Carreau-Yasuda nanofluid in curved channel with mixed convection and porous space

Main theme of present investigation is to model and analyze the peristaltic activity of Carraeu-Yasuda nanofluid saturating porous space in a curved channel. Unlike the traditional approach, the porous medium effects are characterized by employing modified Darcy’s law for Carreau-Yasuda fluid. To our knowledge this is first attempt in this direction for Carreau-Yasuda fluid. Heat and mass transfer are further considered. Simultaneous effects of heat and mass transfer are examined in presence of mixed convection, viscous dissipation and thermal radiation. The compliant characteristics for channel walls are taken into account. The resulting complex mathematical system has been discussed for small Reynolds number and large wavelength concepts. Numerical approximation to solutions are thus plotted in graphs and the physical description is presented. It is concluded that larger porosity in a medium cause an enhancement in fluid velocity and reduction in concentration.

Radiative Peristaltic Flow of Jeffrey Nanofluid with Slip Conditions and Joule Heating

Mixed convection peristaltic flow of Jeffrey nanofluid in a channel with compliant walls is addressed here. The present investigation includes the viscous dissipation, thermal radiation and Joule heating. Whole analysis is performed for velocity, thermal and concentration slip conditions. Related problems through long wavelength and low Reynolds number are examined for stream function, temperature and concentration. Impacts of thermal radiation, Hartman number, Brownian motion parameter, thermophoresis, Joule heating and slip parameters are explored in detail. Clearly temperature is a decreasing function of Hartman number and radiation parameter.

PERISTALTIC FLOW OF COUPLE-STRESS FLUID WITH HEAT AND MASS TRANSFER: AN APPLICATION IN BIOMEDICINE

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.

Influence of Hall Current and Viscous Dissipation on Pressure Driven Flow of Pseudoplastic Fluid with Heat Generation: A Mathematical Study

In this paper, we study the influence of heat sink (or source) on the peristaltic motion of pseudoplastic fluid in the presence of Hall current, where channel walls are non-conducting in nature. Flow analysis has been carried out under the approximations of a low Reynolds number and long wavelength. Coupled equations are solved using shooting method for numerical solution for the axial velocity function, temperature and pressure gradient distributions. We analyze the influence of various interesting parameters on flow quantities. The present study can be considered as a mathematical presentation of the dynamics of physiological organs with stones.

Effects of Heat and Mass Transfer on the Peristaltic Transport of MHD Couple Stress Fluid through Porous Medium in a Vertical Asymmetric Channel

The intrauterine fluid flow due to myometrial contractions is peristaltic type motion and the myometrial contractions may occur in both symmetric and asymmetric directions. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitude, and phase due to the variation of channel width, wave amplitudes and phase differences. In this paper, we study the effects of heat and mass transfer on the peristaltic transport of magnetohydrodynamic couple stress fluid through homogeneous porous medium in a vertical asymmetric channel. The flow is investigated in the wave frame of reference moving with constant velocity with the wave. The governing equations of couple stress fluid have been simplified under the long wave length approximation. The exact solutions of the resultant governing equations have been derived for the stream function, temperature, concentration, pressure gradient, and heat transfer coefficients. The pressure difference and frictional forces at both the walls are calculated using numerical integration. The influence of diverse flow parameters on the fluid velocity, pressure gradient, temperature, concentration, pressure difference, frictional forces, heat transfer coefficients, and trapping has been discussed. The graphical results are also discussed for four different wave shapes. It is noticed that increasing of couple stresses and heat generation parameter increases the size of the trapped bolus. The heat generation parameter increases the peristaltic pumping and temperature.

Peristaltic transport of pseudoplastic fluid in a curved channel with wall properties and slip conditions

Effects of wall properties and slip condition on the peristaltic flow of an incompressible pseudoplastic fluid in a curved channel are studied. Series solution of the governing problem is obtained after applying long wavelength and low Reynolds number approximations. The results are validated with the numerical solutions through the built-in routine for solving nonlinear boundary value problems via software Mathematica. The variations of different parameters on axial velocity are carefully analyzed. Behaviors of embedding parameters on the dimensionless stream function are also discussed. It is noted that the axial velocity and size of trapped bolus increases with an increase in slip parameter. It is also observed that the profiles of axial velocity are not symmetric about the central line of the curved channel which is different from the case of planar channel.

Exact analytical solution of the peristaltic nanofluids flow in an asymmetric channel with flexible walls and slip condition: application to the cancer treatment

In the cancer treatment, magnetic nanoparticles are injected into the blood vessel nearest to the cancer's tissues. The dynamic of these nanoparticles occurs under the action of the peristaltic waves generated on the flexible walls of the blood vessel. Studying such nanofluid flow under this action is therefore useful in treating tissues of the cancer. In this paper, the mathematical model describing the slip peristaltic flow of nanofluid was analytically investigated. Exact expressions were deduced for the temperature distribution and nano-particle concentration. In addition, the effects of the slip, thermophoresis, and Brownian motion parameters on the temperature and nano-particle concentration profiles were discussed and further compared with other approximate results in the literatures. In particular, these results have been obtained at the same values of the physical examined parameters that was considered in Akbar et al., "Peristaltic flow of a nanofluid with slip effects," 2012. The results reveal that remarkable differences are detected between the exact current results and those approximately obtained in the literatures for behaviour of the temperature profile and nano-particles concentration. Accordingly, the current analysis and results are considered as optimal and therefore may be taken as a base for any future comparisons.