Entropy analysis in cilia driven pumping flow of hyperbolic tangent fluid with magnetic field effects

A mathematical model is developed to analyse the entropy generation in two-dimensional flow of hydromagnetic hyperbolic tangent fluid through an inclined symmetric channel lining cilia. Cilia (distributed at equal intervals) tend to beat in a coordinate rhythm to mobilise propulsive metachronal waves along the channel surface by obeying elliptic trajectory movement in the parallel direction of flow. The entire analysis is conducted in wave frame of reference. Under the lubrication approach, the governing equations of the present flow problem are simplified and solved by perturbation technique. Effects of various physical parameters of interest on various flow and heat transfer quantities, the total entropy generation number and the Bejan number are illustrated graphically and discussed. It is noted that the fluid velocity (in contracted channel part) and temperature are accelerated for small values of cilia length and higher values of eccentricity parameter. Overall, the entropy is an increasing function of eccentricity parameters and decreasing function of cilia length. Irreversibility due to fluid friction is seen to be dominant at the channel centre, however, at the channel boundary the irreversibility due to heat transfer is considerable.