Inverse Boundary Value Problem for the Magnetohydrodynamics Equations

In this paper, we consider the stationary magnetohydrodynamics (MHD) equations in a bounded domain of ℝ d d = 2 , 3 with viscosity and magnetic diffusing. By the linearization technique, we prove that the uniqueness of viscosity function and magnetic diffusing function in the MHD equations is determined from the knowledge of the Cauchy data measured on the boundary.

Capillary Rise and Oil Recovery under Primary Bjerknes Force Experienced by Bubbles

A numerical study of forced imbibition into capillary tubes under primary Bjerknes force is presented. A mathematical model is developed to predict the motion of a meniscus while an external force is applied. Remarkable enhancement in liquid flow attributed to the frequency and intensity of a waveform on primary Bjerknes force and to the viscosity of fluid was observed. It was found that imbibition optimal frequency for each equilibrium height depends on the time as ω(xeq)∼emt, where the recovery time is a viscosity function t(xeq)∼μH. The results are presented in a set of curves, which reveal the features of enhanced oil recovery of the system under consideration. Some physical implications are discussed.

Dimensional Analysis of Superplastic Processes with the Buckingham Π Theorem

This work applies the Buckingham Π theorem from dimensional analysis on superplastic processes in order to obtain laws of behaviour in a simple way. For this reason, a mathematical background is developed. The particular behaviour of superplastic materials makes it necessary to adapt the way in which these are treated, modelling them by a viscosity function of the strain-rate. Then, dimensional analysis is applied on a set of free-inflation tests in order to obtain a formula that defines the forming time as single function of geometric and material variables. Dimensional analysis allows us to reduce the number of variables to analyse from six to only three. Finally, two different forming time estimators are compared to measure the accuracy of our method, showing a significant improvement over previous methods.

Superplastic Materials Characterisation Based on Free-Bulge Tests

A new characterisation method based on free-bulge tests is proposed to find the characteristic parameters of the strainstress relation in superplastic alloys. The method is applied to experimental tests found in the literature and to new adhoc tests performed on aluminium, magnesium and titanium alloys. The parameters are then compared to independent values obtained from tensile test and computer-aided simulations. The characterisation of the material is evaluated as an apparent viscosity function of the strain-rate and is extracted from the height evolution at the apex dome during the forming process. Results show a good agreement between parameter estimation using this method and independent values. Moreover, this characterisation method exposes the non-newtonian fluid behaviour of these materials during superplastic processes known as shear-thinning or pseudoplasticity.

Monte Carlo simulation of nonlinear gravity driven Poiseuille–Couette flow in a dilute gas

Through the direct simulation Monte Carlo, the Boltzmann equation is solved numerically for dilute hard spheres gas between two infinite parallel plates in relative motion and at the same time the particles feel the action of a uniform body force along the same direction as the moving plate. The study is conducted on the effect of the external force on the nonlinear properties of the Poiseuille–Couette flow. We have been interested in the bulk properties, to inhibit the influence of finite-size effects, while ignoring linear effects like Knudsen boundary layer to investigate the generalised transport coefficients depending on the shear rate nonlinearly: the two nonlinear thermal conductivity function of normal heat flux and parallel one, the viscosity function, the tangential friction function, and the thermal curvature. The results indicate that the effect of the external force is significant on the nonlinear functions, where the viscosity function and normal thermal conductivity are increasing functions of this field.

A Graphical Technique for Solving the Couette-Poiseuille Problem for Generalized Newtonian Fluids

This paper addresses the mixed Couette-Poiseuille problem, that is the flow between two parallel plates, in the presence of simultaneous pressure gradient and wall motion. Instead of the wall-normal coordinate y, we use the local shear stress as our primary variable and rewrite the corresponding formulae for the velocity profile, flow rate, etc. This gives rise to a graphical technique for solving the problem in the case of arbitrary (possibly measured) generalized Newtonian fluid rheology. We demonstrate the use of the proposed technique on two problems: (a) Bingham fluid and (b) a non-Newtonian fluid with general, nonmonotonous viscosity function.

Weak solutions for generalized stationary Oldroyd-B fluid with a diffusive stress

This paper focuses on the analysis of the stationary case of incompressible viscoelastic generalized Oldroyd-B fluids derived in [2] by Bejaoui and Majdoub. The studied model is different from the classical Oldroyd-B fluid model in having a viscosity function which is shear-rate depending, and a diffusive stress added to the equation of the elastic part of the stress tensor. Under some conditions on the viscosity stress tensor and for a large class of models, we prove the existence of weak solutions in both two-dimensional and three-dimensional bounded domains for shear-thickening flows.