Modelling of lubrication mechanism in human joints using micropolar fluid theory

The paper aims at presentation of modelling of human joints withinthe framework micropolar fluid theory. A mathematical model of two converging spheres represents the biobearings. In the model the boundaries of the spheres are considered to be rigid and the lubricant (synovial fluid) is represented by a micropolar fluid. Basing on the asymptotic solution obtained for squeezing motion of converging spheres (Kucaba-Piętal, 1999), the velocity vector in a gap is determined and asymptotic values of the forceare calculated. The effects or rheological constants variation on the flow field in a gap are disscussed.Przedmiotem pracy jest opis smarowania w stawach na bazie teorii płynów mikropolarnych. Rozpatrywany jest ruch ciśnieniowy (squeezing). Staw (biodrowy) modelowany jest za pomocą układu dwóch kul o twardych powierzchniach. Zakłada się, że przepływ opisany jest równaniem Stokesa. Na bazie rozwiązania asymptotycznego obliczono rozkład prędkości w szczelinie stawowej oraz wartość działającej asyptotycznie siły. Stałe reologiczne mazi stawowej oszacowano na podstawie danych eksperymentalnych

Squeeze flow modeling with the use of micropolar fluid theory

The aim of this paper is to study the applicability of micropolar fluid theory to modeling and to calculating tribological squeeze flow characteristics depending on the geometrical dimension of the flow field. Based on analytical solutions in the lubrication regime of squeeze flow between parallel plates, calculations of the load capacity and time required to squeeze the film are performed and compared – as a function of the distance between the plates – for both fluid models: the micropolar model and the Newtonian model. In particular, maximum distance between the plates for which the micropolar effects of the fluid become significant will be established. Values of rheological constants of the fluids, both those experimentally determined and predicted by means of using equilibrium molecular dynamics, have been used in the calculations. The same analysis was performed as a function of dimensionless microstructural parameters

Flow past a sphere moving towards a wall in micropolar fluid

The paper presents the first "exact" solution to the problem of creeping flow past a sphere mowing towards a wall in micropolar fluid. The analytical-numerical method is presented, that is a development of the boundary collocation technique previously used for solving many corresponding problems for a Newtonian fluid. The initial study of the method has been carried out and the results for a force acting on a sphere compared with their counterparts for a Newtonial fluid are presented. It is worth while to note that the drag force on a sphere depends on material constants of the micropolea fluid and the distance from the wall.Rozwiązane zostało zagadnienie wyznaczenia pola przepływu i działającej siły na cząstkę kulistą poruszającą się w kierunki ścianki w płynie mikropolarnym. Skonstruowano metodę analityczno-- --numeryczną w oparciu o metodę kolokacji. Rozpatrzono przepływ quasistacjonarny w przybliżeniu Stokesa

Numerical investigation of local heat transfer distribution on surfaces with a non-uniform temperature under an array of impinging jets with various nozzle shapes

Numerical calculations of heat transfer characteristics of an impingement cooling system with a non-uniform temperature on a cooled surface using ANSYS CFX have been performed. The influence of a surface heat flux qw(x) and a nozzle shape on the Nusselt number distribution on the cooled surface has been studied. The setup consisted of a cylindrical plenum with an inline array of ten impingement jets. Cylindrical, convergent divergent shapes of nozzles and linear temperature distribution on the cooled surface have been considered for various heat fluxes qw (x). Results indicate that geometry of the cylindrical nozzles resulted in the highest Nusselt numbers along the cooled surface. The line of the averaged Nusselt number has a trend to increase in the direction of the flow for the cooling system with increasing values of the surface heat flux q(x). This tendency can be observed for all presented shapes of jets. On the other hand, for decreasing functions of the heat flux qw (x), the Nusselt number distribution is more uniform. It can be observed for all types of nozzles. Very similar values of the Nusselt number occur especially for the non-uniform heat flux 5000-2500W/m². For constant values of the heat flux q(x) = 5000W/m², the line of the average Nusselt number has a trend to increase slightly in the direction of the flow. Numerical analysis of different mesh density results in good convergence of the GCI index, what excludes mesh size dependency. The presented study is an extension of the paper (Marzec and Kucaba-Piętal, 2016) and aims at answering the question how the Nusselt number distribution on the cooled surface is affected by various geometries of nozzles for a non-uniform surface heat flux qw (x)

Influence of slim obstacle geometry on the flow and heat transfer in microchannels

This paper presents a computational study on hydrodynamic and heat transfer characteristics of the laminar flow inside a rectangular 2D microchannel of height H, which includes a slim micro obstacle of height h and width w placed on the lower wall of the channel. The Reynolds number varies between 20 and 200. Three different values of height h and two different shapes of the slim obstacles: triangular and rectangular one, are considered. Thus, a total of 24 geometrical configurations of fluid flow are analyzed. Fluid flow equations are solved using the commercial CFD package of ADINA R&D, Inc. 9.1. Detailed analysis of the fluid velocity field and streamlines is carried out to investigate the flows in recirculation zone behind the obstacle. Results obtained show that the rectangular obstacle caused larger vortex formation in fluid flow. For flows with larger value of the (h/H) ratio, an increase in the value of loss coefficient factors is observed. Meanwhile, the increased Reynolds number causes the vortex zone behind the rectangular obstacle to be larger than behind the triangular one

Nanovortex evolution in entrance part of the 2D open type long nanocavity

Non-equilibrium molecular dynamics method (NEMD) is applied to investigate a formation process of water nanovortex in 7 nm wide nanocavity (aspect ratio of which was equal to 3.6). The flow in the nanocavity was induced by Poiseuille 2D water nanoflow in a main nanochannel, to which the nanocavity is situated perpendicularly. The wall of main channel and the nanocavity is made from quartz. Flow is induced by applying constant force to molecules inside the main channel. Based on NEMD simulation data, the sequence of images representing water velocity vector fields was obtained at constant time intervals equal to 1 ns, which shows vortex formation mechanism. Flow field images analysis indicates that the shape and centre position of the nanovortex vary slightly each nanosecond, nevertheless, the structure remains stable in the flow field at the entrance to the nanocavity

Numerical investigation of local heat transfer distribution on surfaces with a non-uniform temperature under an array of impinging jets with various nozzle shapes

Numerical calculations of heat transfer characteristics of an impingement cooling system with a non-uniform temperature on a cooled surface using ANSYS CFX have been performed. The influence of a surface heat flux qw(x) and a nozzle shape on the Nusselt number distribution on the cooled surface has been studied. The setup consisted of a cylindrical plenum with an inline array of ten impingement jets. Cylindrical, convergent divergent shapes of nozzles and linear temperature distribution on the cooled surface have been considered for various heat fluxes qw (x). Results indicate that geometry of the cylindrical nozzles resulted in the highest Nusselt numbers along the cooled surface. The line of the averaged Nusselt number has a trend to increase in the direction of the flow for the cooling system with increasing values of the surface heat flux q(x). This tendency can be observed for all presented shapes of jets. On the other hand, for decreasing functions of the heat flux qw (x), the Nusselt number distribution is more uniform. It can be observed for all types of nozzles. Very similar values of the Nusselt number occur especially for the non-uniform heat flux 5000-2500W/m². For constant values of the heat flux q(x) = 5000W/m², the line of the average Nusselt number has a trend to increase slightly in the direction of the flow. Numerical analysis of different mesh density results in good convergence of the GCI index, what excludes mesh size dependency. The presented study is an extension of the paper (Marzec and Kucaba-Piętal, 2016) and aims at answering the question how the Nusselt number distribution on the cooled surface is affected by various geometries of nozzles for a non-uniform surface heat flux qw (x)

Flows in microchannels

The aim of this paper is to present a survey of the results for the flows of simple gases and liquids with substructure through narrow channels, obtained with the Direct Monte-Carlo and Molecular Dynamics Simulation methods