Applied Bionics and Biomechanics

Volume 2016 (2016), Article ID 4123741, 15 pages

http://dx.doi.org/10.1155/2016/4123741

## Analysis of Peristaltic Motion of a Nanofluid with Wall Shear Stress, Microrotation, and Thermal Radiation Effects

^{1}Department of Science and Humanities, Adhiparasakthi College of Engineering, Kalavai 632506, India^{2}Bharathiar University, Coimbatore 641046, India^{3}Department of Mathematics, Priyadarshini Engineering College, Vaniyambadi, Tamil Nadu 635751, India^{4}Department of Mathematics, Agni College of Technology, Thalambur, Chennai 600130, India^{5}Department of Mathematics, University College of Engineering Arni, Arni, Tamil Nadu 632326, India

Received 26 April 2016; Revised 10 July 2016; Accepted 11 July 2016

Academic Editor: Saverio Affatato

Copyright © 2016 C. Dhanapal et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper analyzes the peristaltic flow of an incompressible micropolar nanofluid in a tapered asymmetric channel in the presence of thermal radiation and heat sources parameters. The rotation of the nanoparticles is incorporated in the flow model. The equations governing the nanofluid flow are modeled and exact solutions are managed under long wavelength and flow Reynolds number and long wavelength approximations. Explicit expressions of axial velocity, stream function, microrotation, nanoparticle temperature, and concentration have been derived. The phenomena of shear stress and trapping have also been discussed. Finally, the influences of various parameters of interest on flow variables have been discussed numerically and explained graphically. Besides, the results obtained in this paper will be helpful to those who are working on the development of various realms like fluid mechanics, the rotation, Brownian motion, thermophoresis, coupling number, micropolar parameter, and the nondimensional geometry parameters.

#### 1. Introduction

Peristaltic pumping is one of the keystones for the development of science and engineering research in modern years. Peristalsis also plays an indispensable role in transporting physiological fluids inside living bodies, and many biomechanical and engineering devices have been designed on the basis of the principle of peristaltic pumping to transport fluids without internal moving parts. The problem of the mechanism of peristaltic transport has attracted the attention of many investigators since the first exploration of Latham [1]. A number of analytical, numerical, and experimental studies on peristaltic motion of different fluids have been described under various conditions with reference to physiological and mechanical environment [2–8].

Micropolar fluids have been a subject of great interest to research workers and a number of research papers have been published on this flow model. Physically, micropolar fluids may represent fluids consisting of rigid, randomly oriented (or spherical) particles suspended in a viscous medium, where the deformation of fluid particles is ignored. This constitutes a substantial generalization of the Navier-Stokes model and opens a new field of potential applications including a large number of complex fluids. Animal bloods and liquid crystals (with dumbbell type molecules) are few examples of micropolar fluids. Local conservation laws of mass, linear, and angular momentum and the energy for polar fluids were received by Grad [9] by using the method of statistical thermodynamics. Eringen [10] proposed the theory of micropolar fluids in which the microscopic effect arises from local structure and fluid elements of micromotion are taken into account. Later, Eringen [11] generalized the micropolar fluids theory to include thermal effects. Using quasi-linearization finite difference technique, an impact of temperature dependent heat sources and frictional heating on the fully developed free convection micropolar fluid flow between two porous parallel plates was analyzed by Agarwal and Dhanapal [12]. Devi and Devanathan [13] premeditated the peristaltic motion of a micropolar fluid in a cylindrical tube with sinusoidal waves of small amplitude travelling down in its flexible wall for the case of low Reynolds number. Srinivasacharya et al. [14] recently examined the peristaltic transport of a micropolar fluid in a circular tube using low Reynolds number and long wavelength assumptions.

Nowadays, there is a continuous focus of the researchers in the flow analysis of nanofluids because of its large number of applications in biomedical and industrial engineering. Choi [15] was the first who initiated this nanofluid technology. A detailed analysis of nanofluids was discussed by Buongiorno [16]. Sheikholeslami et al. [17] studied the natural convection in a concentric annulus between a cold outer square and heated inner circular cylinders in the presence of static radial magnetic field. After initiating a study of nanofluids flow under the effect of peristalsis by Akbar and Nadeem [18], Akbar et al. [19] discussed the slip effects on the peristaltic transport of nanofluid in an asymmetric channel. Recently, Mustafa et al. [20] examined the influence of wall properties on the peristaltic flow of a nanofluid. Mixed convection peristaltic flows of magnetohydrodynamic (MHD) nanofluids were analyzed by Hayat et al. [21]. The effects of wall properties on the peristaltic flow of an incompressible pseudoplastic fluid in a curved channel were investigated by Hina et al. [22]. Hayat et al. [23] studied the peristaltic transport of viscous nanofluid in an asymmetric channel. The channel walls satisfy the convective conditions and also effects of Brownian motion and thermophoresis have also been taken into account. The influence of nanofluid characteristic on peristaltic heat transfer in a two-dimensional axisymmetric channel was discussed analytically by Tripathi and Bég [24]. Moreover, the tremendous applications of nanofluids and the interaction of nanoparticles in peristaltic flows have obtained attentions of many researchers [25, 26].

In the recent years, it is well known by physiologists [27, 28] that the intrauterine fluid flow due to myometrial contractions displays peristalsis and myometrial contractions may occur in both symmetric and asymmetric directions and also noted that blood behaves like as a non-Newtonian fluid in microcirculation [10–12]. Motivated from the above analysis and the importance of peristaltic flows, the purpose of the present paper is to investigate the effects of thermal radiation and heat source/sink on the peristaltic flow of micropolar nanofluids in the tapered asymmetric channel. Therefore, such a consideration of peristaltic transport may be used to evaluate intrauterine fluid flow in a nonpregnant uterus [29]. To the best of the author’s knowledge, no attempt is available in the literature which deals with the peristalsis flow of micropolar nanofluid in the tapered asymmetric channel. The present analysis of peristaltic flow is confined to large wavelength and low Reynolds number assumptions. Explicit solutions are developed for axial velocity, axial pressure gradient, stream function, microrotation of the nanofluids, nanofluid temperature, and nanoparticle concentration. The numerical discussion of the pressure rise, shear stresses, and trapping are also obtained and the results are discussed through graphs.

#### 2. Mathematical Formulation

Let us consider the motion of peristaltic transport of an incompressible micropolar nanofluid through a tapered channel induced by sinusoidal wave trains propagating with constant speed but with different amplitudes and phases; see Figure 1. The governing equations of motion for the present investigation are [13, 16, 30] where , are the components of velocity along and directions, respectively, is the dimensional time, the volumetric volume expansion coefficient is , is the density of the fluid, is the density of the particle, is the acceleration due to gravity, is the pressure, , , and are the martial parameters [9–12], is the temperature, is the nanoparticle concentration, is the thermal expansion coefficient, represents the material time derivative, is the coefficient of expansion with concentration, is the microrotation of the nanofluid, is the microgyration parameter, is the fluid mean temperature, is the ratio of the effective heat capacity of nanoparticle material and heat capacity of the fluid with being the density, is the thermal conductivity of the nanofluids, is the Brownian diffusion coefficient, is the thermophoretic diffusion coefficient, is the constant heat addition/absorption, and the radioactive heat flux is .