Transport of micro‐polar fluids in an exponentially diverging tube by means of peristaltic waves of dilating amplitude

Abstract

AbstractThe paper models a peristaltically driven flow when the cross section of the tube changes exponentially. This may resemble the shape of the oesophagus when it suffers from sliding hiatus hernia, that is, when the abdomen protrudes through the hiatus. The fluid transported is considered micro‐polar while the peristaltic waves propagating along wall too dilate exponentially. Bulging, caused by herniation, in tube is examined considering two different cases: (i) tube diverging entirely from the first end to the other, and (ii) tube diverging partly limited to the other end only. Effects of dilating amplitude, the coupling number and the micro‐polar parameter are also investigated. Non‐linear governing equations are linearized by the method of low Reynolds number and long wavelength approximations and computer simulation is used to estimate the numerical results. It is observed that whether the tube diverges entirely or partly, pressure required for carrying the fluid is less, hence facilitating easier swallowing, which causes sliding hiatus hernia to go unnoticed. Exponential divergence in the tube geometry makes swallowing easier than linear divergence. While pressure increases with the coupling number, it declines with the micropolar parameter. Reflux region is further found to shrink once the wave amplitude dilates.