Incompressible Poiseuille flows of Newtonian liquids with a pressure-dependent viscosity

Asymptotic solutions of weakly compressible Newtonian Poiseuille flows with pressure-dependent viscosity

“…The above solution coincides with that derived by Kalogirou et al [22] who considered the flow domain −1 ≤ z ≤ 0 and imposed a zero datum pressure at the center of the tube exit; as a result, the expression of the pressure (and the viscosity) is slightly different. In Eq.…”

“…for the zero-order and the orders ε, δ, ε 2 , δ 2 , and εδ. Since the derivation of the zeroorder solution is trivial, the solutions at orders ε and ε 2 are given in [14], and the solutions at orders δ and δ 2 are Taylor expansions of the analytical solution provided in [22], the lengthy but straightforward derivation of the perturbation solution is briefly discussed below.…”

“…Results for A as a function of δa have been presented in [22]. In particular, it has been shown that A is an increasing function of δa.…”

“…where A is the root of The above solution is the same as that of Kalogirou et al [22], if the differences in the definitions of the axial coordinate and the datum pressure are taken into account. The average pressure drop is given by: …”

“…Recently, Kalogirou et al [22] compiled analytical solutions for unidirectional plane, round, and annular Poiseuille flows of a Newtonian liquid assuming that the viscosity obeys Eq. (2).…”