Laminar entry length problem for power law fluids

Unified entry length for newtonian and power–law fluids in laminar pipe flow

“…The entrance region flow of power-law fluids in pipes was investigated by Bogue (1959), Collins and Schowalter (1963), and Matras and Nowak (1983). Power-law fluids belong to a special group of non-Newtonian fluids that obey the following Ostwald-de Waele relationship: The parameters K and n in Equation (2) are referred to as the fluid consistency index and the flow behaviour index, respectively.…”

“…Many fluids of interest to chemical engineers exhibit the powerlaw behaviour. Bogue (1959) reported the entry length, to decrease with increasing n. The Metzner-Reed (1955) expression for Reynolds number ( [ R e ] M -R ) , that was used by Bogue (1959) and Matras and Nowak (1983) in defining [99 for power-law fluids, is: At 9"C, the bitumen is a dilatant fluid with n = 1.18 but the value of n decreases steadily with an increase in temperature.…”

“…It is noted that the ratio of the two expressions for Reynolds number of power-law fluids, given as Equations (3) and (4) From an integral transformation method utilizing a "pseudo-Newtonian" model, the following expression for was derived by Matras and Nowak (1983):…”

“…Collins and Schowalter (1963) calculated the entry length for pseudoplastic fluids, whereas Bogue (1959) gave results for both pseudoplastic and dilatant fluids. Bogue (1959) reported the entry length, to decrease with increasing n. The Metzner-Reed (1955) expression for Reynolds number ( [ R e ] M -R ) , that was used by Bogue (1959) and Matras and Nowak (1983) in defining [99 for power-law fluids, is:…”

“…From an integral transformation method utilizing a "pseudo-Newtonian" model, the following expression for was derived by Matras and Nowak (1983):…”