Effects of slip and convective conditions on the peristaltic flow of couple stress fluid in an asymmetric channel through porous medium

Abstract

Background: Assessment of the fluid flow pattern in a non-pregnant uterus is important for understanding embryo transport in the uterus. Fertilization occurs in the fallopian tube and the embryo enters the uterine cavity within three days of ovulation. In the uterus, the embryo is conveyed by the uterine fluid for another three to four days to a successful implantation site at the upper part of the uterus. The movements of fluid within the uterus may be induced by several mechanisms, but they seem to be dominated by myometrial contractions. The intrauterine fluid flow due to these myometrial contractions is peristaltic type motion in nature and the myometrial contractions may occur in both symmetric and asymmetric directions.

Objective: The aim of the present article is to investigate the peristaltic transport of couple stress fluid in an asymmetric channel. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different wave amplitudes and phase differences. The fluid is filled with a homogeneous porous medium. The effects of slip and convective boundary conditions are also taken into consideration.

Method: The flow is investigated in the wave frame of reference moving with constant velocity with the wave. Long wavelength and low Reynolds number approximations are utilized in problem formulation. Exact solutions are presented for the stream function, pressure gradient and temperature.

Results: The graphical analysis is carried out to examine the effects of sundry parameters on flow quantities of interest. Comparative study is also made for couple stress fluid with Newtonian fluid.

Conclusions: The results revealed that the trapping fluid can be increased and the central line axial velocity can be raised to a considerable extent by increasing Darcy number. Increasing of slip parameter increases the velocity near the boundary of the walls and Brinkman number increases the temperature of the fluid.

Keywords: Asymmetric channel; Convective and slip conditions; Couple stress fluid; Peristaltic motion; Porous medium.