Modeling Coupled Heat and Mass Transfer in Peristaltic Cylindrical Flow of Robertson-Stiff Fluid

The Robertson–Stiff fluid (RS) is a yield-pseudo-plastic model which has been used to describe the rheological properties of drilling fluids, cement slurries and bentonite suspensions. Experimentally, several rheological data showed that this model provides more consistently accurate descriptions of the rheology of such fluids than other viscoplastic models. This result motivates us to study theoretically the peristaltic transport for this shear-thinning model and for other viscoplastic models in the presence of heat and mass transfer in a cylindrical tube. For long wavelength and low Reynolds number approximations, an analytical solution is obtained. The results showed that the velocity and the temperature decrease with increasing the yield parameter and the power index while they increase with the increase in the occlusion parameter. We also observed an opposite behavior of the concentration versus these physical parameters. Moreover, all these parameters enhance the mechanical efficiency of pumping. In addition, the comparison shows that the velocity, temperature and the absolute value of concentration are greater for the proposed model than those of Herschel–Bulkley, Bingham and Casson models, respectively.