Unsteady solute dispersion in non-Newtonian fluid flow in a tube with wall absorption—Deviation from the Gaussianity

Unsteady solute dispersion in a pulsatile Herschel–Bulkley fluid flow in a tube is reinvestigated to examine the significance of the skewness and kurtosis on the concentration distribution using Aris' method of moments considering Hermite polynomials. This study is also an initiation in the direction of solute dispersion in a pulsatile non-Newtonian flow considering the first five moments. This investigation not only brings in the accuracy in the estimation but also measures the deflection and decrease in the axial mean concentration distribution of a solute in a tube. Significant variations in the skewness and kurtosis coefficients against various values of the flow governing parameters, such as the yield stress τy, the wall absorption parameter β, the power law index a, the Womersley frequency parameter α, and the amplitude of fluctuating pressure component e, are presented graphically along with the variations in the mean concentration distribution of the solute in the tube. For larger values of the Womersley frequency parameter, the occurrence of double frequency period for the convection and dispersion coefficients is noticed, which has significant influence on the skewness and kurtosis coefficients. The results for solute dispersion in Newtonian fluid, Bingham fluid, and power law fluid flows are also reported as special cases of this analysis.