Mixed convective heat transfer analysis for the peristaltic transport of viscoplastic fluid: Perturbation and numerical study

Zaheer Asghar,Nasir Ali

doi:10.1063/1.5118846

Abstract

Mixed convective peristaltic flow of incompressible viscoplastic fluid is investigated in a two-dimensional symmetric channel. The rheology of viscoplastic material is characterized by the constitutive equation for Bingham plastic model. The coupling between momentum and energy equations is achieved through Boussinesq approximation. The coupled nonlinear partial differential equations are transformed in wave frame using Galilean transformation and then simplified under realistic assumptions of long wavelength and low Reynolds number. Approximate solution is obtained using regular perturbation method which is restricted to the smaller values of Grashof and Bingham numbers. The validity of approximate solution is established by comparing it with the numerical solution obtained via Matlab built-in routine bvp4c. Based on the numerical solution an extensive analysis is performed in order to analyze the effects of various parameters of interest on flow characteristics, pumping and trapping phenomena. It is found that velocity decreases at the center by increasing Bingham number showing a boundary layer character for large values. However, it increases by increasing Brinkman and Grashof numbers. Moreover, pressure rise per wavelength increases with Bingham number, Brinkman number and Grashof number, in the pumping region. The result further indicate that larger values of Bingham number circumvent bolus growth.

Highlights

Peristalsis is a process in which a progressive wave of contraction or expansion propagates along the wall(s) of tube/channel resulting in the movement of contents of tube/channel
Graphical results are displayed in order to see the effects of various emerging parameters such as by increasing plasticity parameter (Bn), Grashof number (Gr) and Brinkman number (Br) on velocity and temperature profiles, pressure rise per wavelength, frictional forces and trapping phenomenon
In these parameters Bn shows the effects of plasticity, Gr quantifies the buoyancy effect and Br is the measure of energy dissipated to the fluid due to friction

Summary

Introduction

Peristalsis is a process in which a progressive wave of contraction or expansion propagates along the wall(s) of tube/channel resulting in the movement of contents of tube/channel. The movements of small intestine are due to peristalsis. The transport of urine from kidney to bladder through ureter, vassomotion of small blood vessels such as arterioles, venules and capillaries and bile in the bile duct occur due to peristalsis. Peristalsis has been greatly exploited for the industrial and engineering purposes e.g. peristaltic pumps are designed on the principle of peristalsis. Peristaltic pumps can be used in mining slurries, waste water slurries, sodium bromide and lime slurry pumping. The vast applications of peristalsis has been attracting the interests of researchers after the seminal work of Latham.

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