^{1}

^{2, 3}

^{1}

^{2}

^{3}

The exact solution for any physical model is of great importance in the applied science. Such exact solution leads to the correct physical interpretation and it is also useful in validating the approximate analytical or numerical methods. The exact solution for the peristaltic transport of a Jeffrey fluid with variable viscosity through a porous medium in an asymmetric channel has been achieved. The main advantage of such exact solution is the avoidance of any kind of restrictions on the viscosity parameter

The subject of peristaltic flow, first introduced and formulated by Latham [

Recently, the peristaltic flow in asymmetric channel has attracted much attention due to the physiological observations that the intrauterine fluid flow induced by myometrial contractions is peristaltic-type motion. These contractions occur in asymmetric directions during the secretory phase, when the embryo enters the uterus for implantation, de Vries et al. [

In such kind of problems, the authors usually expand the viscosity function in terms of a small viscosity parameter and hence consider the first two or three terms of Maclaurin series. This procedure helped them to use the regular perturbation method to solve the differential equations governing the flow. Consequently, the perturbation series solutions up to first order [

obtaining the exact solution for the differential equation governing the axial velocity;

obtaining the exact expressions for the pressure gradient and the pressure rise;

comparing the present exact results for the fluid velocity and the pressure rise with those approximately obtained by using the regular perturbation method [

Afsar Khan et al. [^{2} cP while the viscosity of the chyme varies as 10^{3}–10^{6} cP. In order to use the regular perturbation method to solve (

In [

On using the complete definition for

In the previous section, the exact solution for the axial velocity has been obtained. Consequently, exact analytical expressions have been obtained for the pressure gradient and the pressure rise. The availability of such exact solutions is of great importance, especially in validating other approximate results, and they certainly would lead to better understanding of the physical aspects of the model. Here, the obtained exact expressions are invested not only to explore the actual effects of various parameters on the velocity profiles and the pressure rise but also to validate the approximate results obtained in [

The pressure rise versus flow rate when_{1} = 0.8; Da = 0.6;

The pressure rise versus flow rate when _{1} = 0.4;

The pressure rise versus flow rate when _{1} = 0.4; Da = 0.5;

The pressure rise versus flow rate when

The pressure rise versus flow rate when _{1} = 0.5.

The pressure rise versus flow rate when _{1} = 0.4; Da = 0.5;

The pressure rise versus flow rate when _{1} = 0.4; Da = 0.5;

Figure

Regarding the exact effects of

Axial velocity versus_{1} = 1; Da = 1;

Axial velocity versus_{1} = 1; Da = 1;

Axial velocity versus_{1} = 1; Da = 1;

Axial velocity versus_{1} = 1;

Axial velocity versus_{1} = 1;

In this paper the physical model describing the influence of viscosity variation on peristaltic flow in an asymmetric channel has been reanalyzed in view of new exact solutions. The main advantage of these exact solutions is the avoidance of any kind of restrictions on the viscosity parameter, unlike the study [

The authors declare that there is no conflict of interests regarding the publication of this paper.