The Peristaltic Motion inside a Vertical Cylindrical Tube Surrounded Vapour Bubble with Two-Phase Density Flow

S A Mohammadein

doi:10.11648/j.abb.20170504.14

Abstract

The paper presents the growth of vapour bubble in a viscous, superheated liquid. The growth of vapour bubble between two-phase density flow in a vertical cylindrical tube under the effect of peristaltic motion of long wavelength and low Reynolds number is studied. The mathematical model is formulated by mass, momentum, and heat equations. The analytical solution is obtained for temperature and velocity distribution under the effect of different physical parameters. The growth process is studied under the affected of density ratio ε and amplitude ratio e. Moreover, the relation between the bubble radius R with the density ratio E, and amplitude ratio eare obtained. Theseresults agreement with some previous theoretical efforts.

Highlights

The transportation of bio-fluid by continuous wave like muscle contraction and relaxation of the wall of physiological vessels such as esophagus, stomach, intestines, sometimes in ureters, blood vessels and other hollow tubes is known as peristaltic transport [1, 2]
On the basis of continuity Eq (2), we find that, the velocity of cylindrical coordinates of the vapour bubble [22, 24], can be written as
The growth of vapour bubble of Newtonian fluids in a vertical cylindrical tube as shown in Figure 1 with two-phase density and it is obtained by relation (24).The physical values are calculated by Haar et al [28] as given by Table 1.In Figure 2, the velocity distribution in terms of for two different values of density ratio V = 0.6, 0.7, it is clearly, the velocity distribution is proportional inversely with the increasing of density ratio V

Summary

Introduction

The transportation of bio-fluid by continuous wave like muscle contraction and relaxation of the wall of physiological vessels such as esophagus, stomach, intestines, sometimes in ureters, blood vessels and other hollow tubes is known as peristaltic transport [1, 2]. The asymptotic solution, presented by Plesset and Zwick [15], considered thermal diffusion controlled growth, neglecting liquid inertia, and provided a zero-order approximate solution for the bubble wall temperature with the assumption of a thin thermal boundary layer with error of less than 10% [3]. Their solution [16] was in good agreement with the experimental data of Degarabedian [18] in moderately superheated water up to 6°C. The analytical solution of the heat and momentum equations are used to obtain a relation between bubble radius and time , which takes into account the effect of some physical parameter

Analysis

Discussion and Results

Conclusion