There are several factors that can cause the excessive accumulation of biofluid in human tissue, such as pregnancy, local traumas, allergic responses or the use of certain therapeutic medications. This study aims to further investigate the shear-dependent peristaltic flow of Phan–Thien–Tanner (PTT) fluid within a planar channel by incorporating the phenomenon of electro-osmosis. This research is driven by the potential biomedical applications of this knowledge. The non-Newtonian fluid features of the PTT fluid model are considered as physiological fluid in a symmetric planar channel. This study is significant, as it demonstrates that the chyme in the small intestine can be modelled as a PTT fluid. The governing equations for the flow of the ionic liquid, thermal radiation and heat transfer, along with the Poisson–Boltzmann equation within the electrical double layer, are discussed. The long-wavelength ($\delta \ll 1$) and low-Reynolds-number approximations ($Re \to 0$) are used to simplify the simultaneous equations. The solutions analyse the Debye electronic length parameter, Helmholtz–Smoluchowski velocity, Prandtl number and thermal radiation. Additionally, streamlines are used to examine the phenomenon of entrapment. Graphs are used to explain the influence of different parameters on the flow and temperature. The findings of the current model have practical implications in the design of microfluidic devices for different particle transport phenomena at the micro level. Additionally, the noteworthy results highlight the advantages of electro-osmosis in controlling both flow and heat transfer. Ultimately, our objective is to use these findings as a guide for the advancement of lab-on-a-chip systems.

The peristaltic flow of nanofluids under the effect of slip conditions was theoretically investigated. The mathematical model was governed by a system of linear and non-linear partial differential equations with prescribed boundary conditions. Then, the exact solutions were successfully obtained and reported for the first time in the present work. These exact solutions were then used for studying the effects of the slip, thermophoresis, Brownian motion parameters and many others on the pressure rise, velocity profiles, temperature distribution, nanoparticle concentration and pressure gradient. In addition, it is proved that the obtained exact solutions are reduced to the literature results in the special cases.

In the general case, it was found that on comparing the current solutions with the approximate ones obtained using the homotopy perturbation method in literature, remarkable differences have been detected for behaviour of the pressure rise, velocity profiles, temperature distribution, nanoparticle concentration and finally the pressure gradient. An example of these differences is about effect of the Brownian motion parameter on the velocity profile; where it was shown in this paper that the small values of this parameter have not a significant effect on the velocity, while this situation was completely different in the published work. Many other significant differences have been also discussed. Therefore, these observed differences recommend the necessity of including the convergence issue when applying the homotopy perturbation method or any other series solution method to solve a physical model. In conclusion. The current results may be considered as a base for any future analysis and/or comparisons.

In this paper, we studied the peristaltic flow and heat transfer of an incompressible, electrically conducting Bingham Non-Newtonian fluid in an eccentric uniform annulus in the presence of external uniform magnetic field with slip velocity and temperature jump at the wall conditions. The viscous and Joule dissipations are taken into account. The inner tube is rigid and moving with a constant axial velocity, while the outer tube has a sinusoidal wave traveling down its wall. Under zero Reynolds number condition with the long wavelength approximation, the axial velocity and the stream function are obtained analytically. A numerical solution for the governing partial differential equation of energy is performed in order to analyze the temperature distribution. The effects of all parameters of the problem are numerically discussed and graphically explained.