Entrance flow of a yield-power law fluid

In the present work we have obtained the numerical solution of the momentum equation for a Yield-Pseudoplastic power-law fluid flowing in the entrance region of a tube. The accuracy of the numerical results is checked by comparing the asymptotic values of friction coefficients and velocity profiles with the corresponding results from the analytical solutions for the fully-developed region. The results of the entrance flow solution for the power-law exponent equal to unity (Bingham fluid) are also in agreement with the numerical solution for a Bingham fluid. Detailed results are presented for wide ranges of yield numbers and power law exponents.

Nomenclature

Nomenclature a constant - D diameter - F dimensionless pressure gradient in (4.3) - f_x friction factor in (5.1) - f_app total friction factor in (5.2) - K entrance pressure drop coefficient - n power law exponent - p pressure - r radial co-ordinate - R radius of a tube - Re Reynolds number (5.3) - s rate of shear, u/r - u axial velocity - average velocity - v velocity in radius direction - x axial co-ordinate - y normal co-ordinate - Y yield number in (4.4) - z dimensionless axial distance =(x/D)/Re - z₁ 1/zGreek Symbols plug flow radius in (4.6) - _eff effective viscosity - density - shear stress - _y yield stress - dimensionless stream function