In this paper the steady three-dimensional stagnation-point flow of an incompressible, homogeneous, electrically conducting micropolar fluid over a flat plate is numerically investigated. The fluid is permeated by a uniform external magnetic field. The effects of the magnetic field on the velocity and on the microrotation profiles are presented graphically and discussed. The results obtained indicate that the thickness of the boundary layer decreases when the magnetic field increases. Moreover the magnetic field tends to prevent the occurrence of the reverse flow and of the reverse microrotation

Abstract. The steady two-dimensional oblique stagnation-point flow of an electrically conducting Newtonian fluid in the presence of a uniform external electromagnetic field (E0, H0) is analyzed, and some physical situations are examined. In particular, if E0 vanishes, H0 lies in the plane of the flow, with a direction not parallel to the boundary, and the induced magnetic field is neglected, it is proved that the oblique stagnation-point flow exists if, and only if, the external magnetic field is parallel to the dividing streamline. In all cases it is shown that the governing nonlinear partial differential equations admit similarity solutions, and the resulting ordinary differential problems are solved numerically. Finally, the behaviour of the flow near the boundary is analyzed; this depends on the Hartmann number if H0 is parallel to the dividing streamline.

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Abstract. The steady two-dimensional oblique stagnation-point flow of an electrically conducting micropolar fluid in the presence of a uniform external electromagnetic field (E 0 , H 0 ) is analyzed and some physical situations are examined. In particular, if E 0 vanishes, H 0 lies in the plane of the flow, with a direction not parallel to the boundary, and the induced magnetic field is neglected. It is proved that the oblique stagnationpoint flow exists if, and only if, the external magnetic field is parallel to the dividing streamline. In all cases it is shown that the governing nonlinear partial differential equations admit similarity solutions and the resulting ordinary differential problems are solved numerically. Finally, the behaviour of the flow near the boundary is analyzed; this depends on the three dimensionless material parameters, and also on the Hartmann number if H 0 is parallel to the dividing streamline.76W05, 76D10. Micropolar fluids, MHD flow, oblique stagnation-point flow.

We derive the homogenized governing equations for a double porosity system where the fluid flow within the individual compartments is governed by the coupling between the Darcy and the Darcy–Brinkman equations at the microscale , and are subjected to inhomogeneous body forces. The homogenized macroscale results are obtained by means of the asymptotic homogenization technique and read as a double Darcy differential model with mass exchange between phases. The role of the microstructure is encoded in the effective hydraulic conductivities which are obtained by solving periodic cell problems whose properties are illustrated and compared. We conclude by solving the new model by means of a semi-analytical approach under the assumption of azimuthal axisymmetry to model the movement of fluid within a lymph node.

We present a continuum model for the mechanical behavior of the skeletal muscle tissue when its functionality is reduced due to aging. The loss of ability of activating is typical of the geriatric syndrome called sarcopenia. The material is described by a hyperelastic, polyconvex, transverse isotropic strain energy function. The three material parameters appearing in the energy are fitted by least square optimization on experimental data, while incompressibility is assumed through a Lagrange multiplier representing the hydrostatic pressure. The activation of the muscle fibers, which is related to the contraction of the sarcomere, is modeled by the so called active strain approach. The loss of performance of an elder muscle is then obtained by lowering of some percentage the active part of the stress. The model is implemented numerically and the obtained results are discussed and graphically represented. arXiv:1701.07823v1 [q-bio.TO]

Active materials are media for which deformations can occur in absence of loads, given an external stimulus. Two approaches to the modeling of such materials are mainly used in literature, both based on the introduction of a new tensor: an additive stress Pact in the active stress case and a multiplicative strain Fa in the active strain one. Aim of this paper is the comparison between the two approaches on simple shears.Considering an incompressible and transversely isotropic material, we design constitutive relations for Pact and Fa so that they produce the same results for a uniaxial deformation along the symmetry axis. We then study the two approaches in the case of a simple shear deformation. In a hyperelastic setting, we show that the two approaches produce different stress components along a simple shear, unless some necessary conditions on the strain energy density are fulfilled. However, such conditions are very restrictive and rule out the usual elastic strain energy functionals. Active stress and active strain therefore produce different results in shear, even if they both fit uniaxial data.Our results show that experimental data on the stress-stretch response on uniaxial deformations are not enough to establish which activation approach can capture better the mechanics of active materials. We conclude that other types of deformations, beyond the uniaxial one, should be taken into consideration in the modeling of such materials. Date

In this paper the steady three-dimensional stagnation-point flow of an incompressible, homogeneous, electrically conducting Newtonian fluid over a flat plate is investigated numerically. The fluid is permeated by a uniform external magnetic field H 0 . The effects of the magnetic field on the velocity profiles are presented graphically and discussed. This paper completes the analysis concerning the Newtonian fluids devoleped in [4].The obtained results indicate that the thickness of the boundary layer decreases when the magnetic field increases. Moreover H 0 tends to prevent the occurrence of the reverse flow.By virtue of the numerical integration, the stagnation-point is classified as nodal or saddle point and as attachment or separation point.