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

An exact analytical solution for viscoelastic fluids with pressure-dependent viscosity

“…(A2), (A3) coincide with that derived by Kalogirou et al [36] if the differences in the domain definition and the boundary condition for the pressure are taken into account, and, also, they are the same with those reported by Pojiadji et al [40].…”

“…Numerical simulations for generalized shear-thinning Newtonian liquids have been performed by Lanzendörfer [28], Lanzendörfer and Stebel [38] and Hirn et al [39]. Asymptotic solutions of weakly compressible Newtonian Poiseuille flows with pressure dependent viscosity have been derived by Poyiadji et al [40], while the effect of the pressure-dependent viscosity for the unbounded flow past a sphere has been studied by Housiadas et al [41].…”

Asymptotic Analysis of the Curved-Pipe Flow with a Pressure-Dependent Viscosity Satisfying Barus Law

“…Tools from Differential Geometry. In order to write the transformed equations (19)- (20) in the curvilinear coordinates ( ), we need to introduce some advanced notions from differential geometry. We begin by introducing the covariant basis defined as a ( ) = Φ ( ) , = 1,2,3.…”

“…Analytical solutions have been reported only in some simplified situations like unidirectional and planeparallel flows and under the assumption of the linear law ( ) = or ( ) = 0 (1 + ). We refer the reader to [16][17][18][19][20]. However, a year ago, the straight-pipe flow has been successfully addressed by Marušić-Paloka and Pažanin [21] in the case of exponential law (1).…”

Asymptotic Behavior of Solutions to Free Boundary Problem with Tresca Boundary Conditions

“…There are many phenomena in nature and industry exhibiting the behavior of the Herschel-Bulkley fluid medium and has been used in various publications to describe the flow of metals, plastic solids, and some polymers. The literature concerning this topic is extensive (see e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13][14]). Further, let us mention the works which is realized by many authors in this area, for example, (see [2,4,9,10,[13][14][15][16][17][18][19][20][21]).…”