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The paper deals with a theoretical study of the transport of a fluid in achannel, which takes place by the phenomenon of peristalsis. A mathematicalanalysis of the said problem has been presented. The analysis involves theapplication of a suitable perturbation technique. The velocity profile and thecritical pressure for the occurrence of reflux are investigated with particularemphasis by using appropriate numerical methods. The effects of variousparameters, such as Reynolds number, pressure gradient, porosity parameter,Darcy number, slip parameter, amplitude ratio and wave number on velocity andcritical pressure for reflux are investigated in detail. The computed resultsare compared with a previous analytical work and an experimental investigationreported earlier in existing scientific literatures. The results of the presentstudy are in conformity to both of them. The study has got some relevance tothe physiological flow of bile in the common bile duct in a pathological state.It reveals that in the presence of gallstones, bile velocity increases as thevalue of the porosity parameter increases, while the critical pressure forreflux decreases as porosity increases.

Peristaltic flow of a fluid in a porous channel: A study having relevance to flow of bile within ducts in a pathological state