Heat transfer to non-Newtonian flows over a cylinder in cross flow

Over a range of 102<Re^*<5800, 6.5<Pr^*<79, and 0.6<n<1, circumferential wall temperatures for water and aqueous polymer (purely viscous) solution flows over a smooth cylinder were measured experimentally. The cylinder was heated by passing direct electric current through it. Aqueous solutions of Carbopol 934 and EZ1 were used as power-law non-Newtonian fluids. The peripherally averaged heat transfer coefficient for purely viscous non-Newtonian fluids, at any fixed flow rate, decreases with increasing polymer concentration. A new correlation is proposed for predicting the peripherally averaged Nusselt number for power-law fluid flows over a heated cylinder in cross flow.     

An efficient matrix solver for finite-element analysis of non-Newtonian fluid flow problems

When the Galerkin finite-element method with a nine-node isoparametric Lagrangian element is applied to solve non-Newtonian fluid flow problems, a considerable amount of computing time is required to solve the discretized non-linear system of equations by Newton's method. A method proposed by Broyden has been modified to compute the Jacobian matrix associated with Newton's method. This modified Broyden's method can be combined with the frontal method to efficiently solve the linearized finite-element equations during the iteration. Numerical results of a sample problem concerning the determination of the pressure-drop/flow-rate relationship for power-law fluids in rectangular ducts show that the application of this new method can reduce computing time substantially.     

On predicting unsteady non-Newtonian blood flow

The influence of the non-Newtonian stress–strain relation of blood on the oscillatory shear index (OSI) and mean wall shear stress (WSS) are described. A mathematical non-dimensional model based on the momentum equation for a modified Casson’s fluid is formulated in terms of the dimensionless yield shear stress . An original direct numerical procedure is presented to predict the flow patterns. Results obtained by using a finite difference approach show a difference in OSI when blood is assumed to be a Newtonian fluid instead of a modified Casson’s fluid. The calculation of the OSI in human normal conditions under the Newtonian approach differs in 5% from the result obtained from using the Casson model.     

Simulation of polymeric flows in the injection moulding process

Recent progress in the simulation of polymeric flows of two key problems in the injection moulding process, carried out by a team at Cornell University, is briefly described. For the filling of cooled thin cavities, the fluid is characterized by a power-law viscosity with exponential temperature dependence, and interaction between the transient thermal boundary-layer and the core flow in a domain with moving boundary is essential. The earlier procedure of Hieber and Shen is modified in two aspects: a boundary-integral formulation replaces the finite-element treatment of the pressure, and an ‘energy integral’ approach is used for the transient temperature. The second problem is the steady visco-elastic flow in the juncture region where sudden changes of the geometry and large strain rates occur. The constitutive equation is postulated according to the Leonov model. The main features in the numerical implementation are: integration along a streamline to determine the elastic deformation tensors for a given velocity field, and finite-element treatment (in time-dependent form) of the pressure and fields for given stresses. In an example where the contraction ratio is 7:1, results for nominal Deborah number exceeding 100 show no numerical instability. (However, for this problem, the true Weissenberg number, i.e. the ratio of local first-normal-stress difference to shear stress turns out to be generally O(10).) The predictions also correlate very well with experimental birefringence measurements.     

Travelling waves in dilatant non-Newtonian thin films

We prove the existence of a travelling wave solution for a gravity-driven thin film of a viscous and incompressible dilatant fluid coated with an insoluble surfactant. The governing system of second order partial differential equations for the film's height h and the surfactant's concentration γ are derived by means of lubrication theory applied to the non-Newtonian Navier–Stokes equations.     

Interior gradient estimate for steady flows of electrorheological fluids

In this paper, we consider the equations of stationary motion of electrorheological fluids in any dimension $n\ge 2$. We show that the first gradient of local solutions to the system has optimal $L^q$-regularity with some $q>1$ with respect to the one of the external force. This is achieved by comparison principle and a good $\lambda$-estimate.     

Coherent thermodynamic model for solid,liquid and gas phases of elements and simple compounds in wide ranges of pressure and temperature

Thermodynamic modeling of fluids (liquids and gases) uses mostly series expansions which diverge at low temperatures and do not fit to the behavior of metastable quenched fluids (amorphous, glass like solids). These divergences are removed in the present approach by the use of reasonable forms for the “cold” potential energy and for the thermal pressure of the fluid system. Both terms are related to the potential energy and to the thermal pressure of the crystalline phase in a coherent way, which leads to simpler and non diverging series expansions for the thermal pressure and thermal energy of the fluid system. Data for solid and fluid argon are used to illustrate the potential of the present approach.     

Strong Inhibition of Ice Growth by Biomimetic Crowding Coacervates

The freezing of biological fluids is intensively studied but remains elusive as it is affected not only by the various components but also by the crowding nature of the biological fluids. Herein, we constructed spherical crowders, fibrous crowders, and coacervates by various components ranging from surfactants to polymers and proteins, to mimic three typical crowders in biological fluids, i.e., globular proteins, fibrous networks, and condensates of biomolecules. It is elucidated that the three crowders exhibit low, moderate, and strong ice growth inhibition activity, respectively, resulting from their different abilities in slowing down water dynamics. Intriguingly, the coacervate consisting of molecules without obvious ice growth inhibition activity strongly inhibits ice growth, which is firstly employed as a highly-potent cryoprotectant. This work provides new insights into the survival of freezing-tolerant organisms and opens an avenue for the design of ice-controlling materials.     

A remark on similarity analysis of boundary layer equations of a class of non-Newtonian fluids

A similarity analysis of three-dimensional boundary layer equations of a class of non-Newtonian fluid in which the stress, an arbitrary function of rates of strain, is studied. It is shown that under any group of transformation, for an arbitrary stress function, not all non-Newtonian fluids possess a similarity solution for the flow past a wedge inclined at arbitrary angle except Ostwald-de-Waele power-law fluid. Further it is observed, for non-Newtonian fluids of any model only $90°$ of wedge flow leads to similarity solutions. Our results contain a correction to some flaws in Pakdemirli׳s [14] (1994) paper on similarity analysis of boundary layer equations of a class of non-Newtonian fluids.     

The convergence of non-Newtonian fluids to Navier-Stokes equations

In this paper, the convergence of solutions for incompressible dipolar viscous non-Newtonian fluids is investigated. We obtain the conclusion that the solutions of non-Newtonian fluids converge to the solutions of Navier-Stokes equations in the sense of L²-norm (resp. H¹-norm), as the viscosities tend to zero and the initial data belong to H¹(Ω) (resp. H²(Ω)). Moreover, we obtain L^∞-norm convergence of solutions if the initial data belong to H²(Ω).