The Peristaltic Flow of Eyring Powell Nanofluid in a porous channel

Abstract

µPeristalsis is a transport generated by the µwave-like contraction and expansion of a duct containing fluid. If there is no peristaltic movement then food bolus cannot be pushed through the digestive tract, urine cannot be moved through the urinary duct and spermatozoon, ovum, embryos and eggs cannot be moved and transferred into a reproductive duct. A person faces diarrhea or constipation in the absence of peristaltic motion. Also, the movement of lymph through lymphatic vessels and the motion of capillaries, arterioles and venules is peristaltic. Peristaltic pumping also acts as a cleansing agent that removes bacteria and gas and controls bacterial growth in large intestines. The peristaltic mechanism is applicable in engineering and biomathematics like the design of µfinger pumps and roller pumps , µdialysis and µblood pump machines . The First theoretical and experimental study on the topic of peristalsis in which the author derives the relation between motion of fluid and the amplitude ratio of the peristaltic transport KDV EHHQ GRQH ³ Peristaltic transport , by Fung and Yih [1] and further work on this topic is proceeded by Latham [2] in detail as Fluid motions in Peristaltic Pump in MIT-Press, Cambridge. There are many investigations studied mathematically for µNewtonian and µNon Newtonian fluids . Since there is a vast use of fluids like water, air, glue, paint and blood in our daily life, this domain of research has sought the attention of researchers. Jaffrin and Shapiro have done many investigations like [3] Peristaltic transport in which he uses a sinusoidal channel to describe the transport of mass and finds the mean average velocity of the transport and [4] he study about arbitrary Reynold number, wave number and amplitude ratio for peristaltic pumping. Srivastava at el. [5] KDV LQYHVWLJDWHG ³3 eristaltic transport in the blood (Casson fluid) and [6] ³7he perturbation solutions of peristaltic flow in a channel filled with Newtonian fluid for a small amplitude ratio . The flow of Maxwell fluids in porous media and peristaltic domain is examined by Whitaker et al. [7]. Husseny et al. [8] have looked into the ³(IIHFWV of porous boundary walls on peristaltic walls through a porous medium and gives the effects on the velocity of the channel by changing various parameters by using Newtonian fluids DQG DOVR WKH\ ZRUNHG RQ WKH ³, mpacts of poiseuille flow on peristaltic channel [9]. Moreover, Al-Arabi et al. [10] also show their interest in the domain of peristaltic flow and H[SORUHG ³ Non-linear peristaltic channel of Magnetohydrodynamic flow . DRSML QAU 6 Moreover, T. Hayat [11] along with some other researchers look over the field of peristalsis and research about the Peristaltic flow of an MHD by using Johnson-Segalman fluid and he also worked on Exact peristaltic flow in tubes by applying the characteristic properties on parameters of an endoscope [12]. Further, Abd et al. [13] ZRUNHG RQ WKH ³( ffect of MHD and heat transfer on the peristaltic movement of a Newtonian fluid in a vertical annulus . Mamand [14] investigated applied sciences Thermal Conductivity Calculations for Nanoparticles Embedded in a Base Fluid . The analytic research on peristalsis by considering the Peristaltic flow in a transport having corrugated walls by using Maxwell fluid has been done by Hayat et al. [15]. Also Nadeem take interest in this class of fluid mechanics like the Peristaltic flow of a Williamson fluid in an asymmetric channel [16], Peristaltic Flow of a Maxwell fluid Mode through Porous Boundaries in a Porous Medium [17] and Peristaltic flow of carreau fluid in a rectangular duct through a porous medium [18]. Moreover, the effect of wall properties on the peristaltic flow of a non-Newtonian fluid [19] is analysed by Hayat et al. and also worked on Peristaltic transport of a Maxwell fluid in a porous asymmetric channel through a porous medium [20]. Further KH LQYHVWLJDWHG ³ the consequence of nanofluid on peristaltic transport of a hyperbolic tangent fluid model in the occurrence of apt (tending) magnetic field [21]. Further, Corrugated walls analysis in microchannels through a porous medium under EMHD HIIHFWV´ [22] are examined by Nadeem with other researchers. Many investigators from all over the world have done analysis on mass and heat transfer along peristalsis or porous medium as Kwon et al. worked on Heat Transfer and Pressure Drop Characteristics of Nanofluids in a Plate Heat Exchanger [23] and Naven Kumar et al. [24] studied about the Heat and Mass Transfer Influence of wall properties on the peristaltic flow of a nanofluid . In addition, McGrail with his colleagues examined Metal-organic heat carrier nanofluids [25]. Peristaltic Motion of Non-Newtonian Fluid with Heat and Mass Transfer through a Porous Medium under a Uniform MHD is investigated by Edaib [26]. Further, Aly et al. [27] researched An Exact analytical solution for the peristaltic flow of nanofluids in an asymmetric channel with a slip . The effect of water-based nanofluid incorporating Al2O3 Nanoparticle on heat pipe performance is discussed and enhanced by M. I. H. et al. [28]. Convection is a subclass of mass and heat transfer most papers cover this class too like Natural convection in a wavy porous cavity with sinusoidal and internal heat generation by Cheong et al. [29] and Analytical investigation of peristaltic nanofluid flow and heat transfer in an asymmetric wavy wall channel by Hatami et al. [30]. Impacts of Hall Current and Ohmic DRSML QAU 7 Heating on Non-Newtonian Fluid Flow due to Peristaltic Wave has been examined by Hasan et al. in [31]. Since mass and heat transfer is a wide class of not only mathematics but also physics and engineering so there is a wide range of works in this field but only a few are mentioned and discussed here. µEyring Powell fluid is a µnon-Newtonian viscoelastic fluid which has been studied by Eyring Powell in 1944. Although µEyring Powell fluid is discussed by some researchers but still it is not very common in the area of research. The studies on this topic include the Boundary layer flow of an Eyring-Powell fluid due to a stretching cylinder with variable viscosity by Nadeem et al. [32], the Effect of joule heating and MHD on peristaltic blood flow of an Eyring Powell nanofluid in a non-uniform channel by Asha and Sunitha [33], A numerical study of unsteady non-Newtonian Eyring Powell nanofluid flow over a shrinking sheet with heat generation and thermal radiation is done by Mondal et al. [34]. Further, Numerical and scale analysis of Eyring Powell nanofluid towards a magnetized stretched Riga surface with entropy generation and internal resistance is investigated by Nazeer et al. [35]. Also, an Analysis of Eyring Powell fluid flow was used as a coating material for wire with variable viscosity effect along with thermal radiation and joule heating by Khan et al. [36]. In addition, Boundary layer flow of non-Newtonian Eyring Powell nanofluid over a moving flat plate in Darcy porous medium with a parallel free-stream: Multiple solutions and stability analysis by Verma et al. [37] and Darcy Forchheimer higher-order slip flow of Eyring Powell nanofluid with nonlinear thermal radiation and bioconvection phenomenon by Bhatti et al. [38]. The Nanoparticles metals, oxides, carbides, ܣ݈ଶܱଷ or carbon nanotubes are mostly used in Nanofluids. These are mostly used as coolants and have many applications worldwide. Also, Nanofluids have a wide range of literature in µfluid mechanics as McGrail et al. studied Metal organic heat carrier nanofluids [25]. Aly and Ebaid investigated the Exact analytical solution for the peristaltic flow of nanofluids in an asymmetric channel with the slip effect of the velocity, WHPSHUDWXUH DQG FRQFHQWUDWLRQ´ [27]. Moreover, Riaz and Ellahi [39] studied the Role of hybrid nanoparticles in the thermal performance of the peristaltic flow of Eyring Powell fluid . Transport properties of non-Newtonian nanofluids and applications is studied by the Sivaraj et al [40]. Fluid for a permeable medium has a broad scope and importance for engineering technologies. In our daily life, permeable media includes wood, foam, and rocks. Industrial and domestic applications of a thin permeable layer are cells, batteries, filters and printing papers. Permeable DRSML QAU 8 media had drawn the attention of many researchers such as the Flow of Maxwell fluids in porous media [7] has been examined by De Haro et al., Effects of porous boundaries on peristaltic transport through a porous medium [8] is studied by Shehawey and Husseny. Nonlinear peristaltic transport of MHD flow through a porous medium was investigated by Mekheimer [10]. In addition, many researchers worked on this domain with their fellows but just a few researches of interest are mentioned above. In Chapter 1, we discussed some elementary definitions, relations, formulae, characteristics and equations. Further, in Chapter 2, we studied the viscoelastic non-Newtonian Eyring Powell fluid and presented its results for various parameters like Eyring Powell fluid parameter M, porosity V and Permeability W. Lastly, in Chapter 3, the aim of the study is to check the mathematical behaviour of non-Newtonian viscoelastic Eyring Powell Nanofluid having incorporated ܣ݈ଶܱଷfor Eyring Powell Parameter M, the porosity V and the permeability parameter W. In our investigation, we have considered the transport bounded by two porous peristaltic plates in which the rate at which fluid is coming in the flow portion through one plate and the rate at which it is exiting the flow region through another plate is the same. This rate is called the porosity V of the boundaries. Also, a free pumping case is considered. Physically, our aim is to check the effect of various physical parameters like porosity, permeability and viscosity on the µvelocity and µtemperature of the fluid that is moving in human peristaltic membranes or any other physical system.