Similar solutions for the incompressible laminar boundary layer with pressure gradient in micropolar

This paper presents the similarity solution for the steady incompressible laminar boundary layer flow of a micropolar fluid past an infinite wedge. The governing equations have been solved numerically using fourth orderRunge-Kutta-Gill method. The results indicate the extent to which the velocity and microrotation profiles, and the surface shear stress are influenced by coupling, microrotation, and pressure gradient parameters. The important role played by the standard length of the micropolar fluid in determining the structure of the boundary layer has also been discussed.

A computer code for enclosed natural convection in the boundary layer regime

A computer code is developed for the numerical prediction of natural convection in rectangular two-dimensional cavities at high Rayleigh numbers. The governing equations are retained in the primitive variable form. The numerical method is based on finite differences and an ADI scheme. Convective terms may be approximated with either central or hybrid differencing for greater stability. A non-uniform grid distribution is possible for greater efficiency. The pressure is dealt with via a SIMPLE type algorithm and the use of a fast elliptic solver for the solenoidal velocity correction field significantly reduces computing times. Preliminary results indicate that the code is reasonably accurate, robust and fast compared with existing benchmarks and finite difference based codes, particularly at high Rayleigh numbers. Extension to three-dimensional problems and turbulence studies in similar geometries is readily possible and indicated.

The laminar boundary layer regime for natural convection of air in a square cavity

Numerical predictions are obtained for laminar natural convection of air in a square two dimensional cavity at high Rayleigh numbers. Proper resolution of the core reveals weak multi-cellular structure which varies in a complex manner as the effects of convection are increased. The end of the steady laminar regime is numerically estimated to occur at Ra=2.2x10^8.

Unsteady laminar boundary layers in a compressible stagnation flow

The unsteady laminar compressible boundary-layer flow in the immediate vicinity of a two-dimensional stagnation point due to an incident stream whose velocity varies arbitrarily with time is considered. The governing partial differential equations, involving both time and the independent similarity variable, are transformed into new co-ordinates with finite ranges by means of a transformation which maps an infinite interval into a finite one. The resulting equations are solved by converting them into a matrix equation through the application of implicit finite-difference formulae. Computations have been carried out for two particular unsteady free-stream velocity distributions: (1) a constantly accelerating stream and (2) a fluctuating stream. The results show that in the former case both the skin-friction and the heat-transfer parameter increase steadily with time after a certain instant, while in the latter they oscillate thus responding to the fluctuations in the free-stream velocity.

Agreeable Agreement : An Examination into the Quest for a Solid Consensus in Light of Bilateral Doctrinal Dialogues among Anglicans, Lutherans and Roman Catholics

The purpose of this study is to analyse the development and understanding of the idea of consensus in bilateral dialogues among Anglicans, Lutherans and Roman Catholics. The source material consists of representative dialogue documents from the international, regional and national dialogues from the 1960s until 2006. In general, the dialogue documents argue for agreement/consensus based on commonality or compatibility. Each of the three dialogue processes has specific characteristics and formulates its argument in a unique way. The Lutheran-Roman Catholic dialogue has a particular interest in hermeneutical questions. In the early phases, the documents endeavoured to describe the interpretative principles that would allow the churches to together proclaim the Gospel and to identify the foundation on which the agreement in the church is based. This investigation ended up proposing a notion of basic consensus , which later developed into a form of consensus that seeks to embrace, not to dismiss differences (so-called differentiated consensus ). The Lutheran-Roman Catholic agreement is based on a perspectival understanding of doctrine. The Anglican-Roman Catholic dialogue emphasises the correctness of interpretations. The documents consciously look towards a common future , not the separated past. The dialogue s primary interpretative concept is koinonia. The texts develop a hermeneutics of authoritative teaching that has been described as the rule of communion . The Anglican-Lutheran dialogue is characterised by an instrumental understanding of doctrine. Doctrinal agreement is facilitated by the ideas of coherence, continuity and substantial emphasis in doctrine. The Anglican-Lutheran dialogue proposes a form of sufficient consensus that considers a wide set of doctrinal statements and liturgical practices to determine whether an agreement has been reached to the degree that, although not complete , is sufficient for concrete steps towards unity. Chapter V discusses the current challenges of consensus as an ecumenically viable concept. In this part, I argue that the acceptability of consensus as an ecumenical goal is based not only the understanding of the church but more importantly on the understanding of the nature and function of the doctrine. The understanding of doctrine has undergone significant changes during the time of the ecumenical dialogues. The major shift has been from a modern paradigm towards a postmodern paradigm. I conclude with proposals towards a way to construct a form of consensus that would survive philosophical criticism, would be theologically valid and ecumenically acceptable.

Surface waves on the boundary of a magnetized plasma

Full dispersion curves including the effect of ions are presented for the electromagnetic surface waves propagating over a plasma-plasma interface in the direction perpendicular to the magnetic field which is parallel to the interface. The effect of ions and finite density ratio of the two media at the boundary give rise to various new features in the dispersion characteristics of these surface waves.

Automatic phonetic transcription of Tamil in Roman script

Simple formalized rules are proposed for automatic phonetic transcription of Tamil words into Roman script. These rules are syntax-directed and require a one-symbol look-ahead facility and hence easily automated in a digital computer. Some suggestions are also put forth for the linearization of Tamil script for handling these by modern machinery.

Laminar compressible boundary layers with vectored mass transfer

The paper studies the influence of vectored suction or injection on the flow and heat transfer at the stagnation point of a two-dimensional body (a cylinder) and an axisymmetric body (a sphere) with allowance for the effects of variable gas properties. The analysis is based on the boundary-layer equations in dimensionless form for the steady compressible fluid with variable properties in the stagnation region of a two-dimensional or an axisymmetric body with tangential and normal surface mass transfer under similarity requirements. It is shown that the variation of the density-viscosity product across the boundary layer has a strong effect on the skin friction and heat transfer. This gives rise to a point of inflection which can be removed by suction and by increasing the wall temperature. The skin friction and heat transfer are significantly affected by the pressure gradient parameter.

The structure of turbulent boundary layers along mildly curved surfaces

This paper describes a detailed study of the structure of turbulence in boundary layers along mildly curved convex and concave surfaces. The surface curvature studied corresponds to δ/Rw = ± 0·01, δ being the boundary-layer thickness and Rw the radius of curvature of the wall, taken as positive for convex and negative for concave curvature. Measurements of turbulent energy balance, autocorrelations, auto- and cross-power spectra, amplitude probability distributions and conditional correlations are reported. It is observed that even mild curvature has very strong effects on the various aspects of the turbulent structure. For example, convex curvature suppresses the diffusion of turbulent energy away from the wall, reduces drastically the integral time scales and shifts the spectral distributions of turbulent energy and Reynolds shear stress towards high wavenumbers. Exactly opposite effects, though generally of a smaller magnitude, are produced by concave wall curvature. It is also found that curvature of either sign affects the v fluctuations more strongly than the u fluctuations and that curvature effects are more significant in the outer region of the boundary layer than in the region close to the wall. The data on the conditional correlations are used to study, in detail, the mechanism of turbulent transport in curved boundary layers. (Published Online April 12 2006)

Nonsimilar incompressible laminar boundary layers with magnetic field.

The solution of the steady laminar incompressible nonsimilar magneto-hydrodynamic boundary layer flow and heat transfer problem with viscous dissipation for electrically conducting fluids over two-dimensional and axisymmetric bodies with pressure gradient and magnetic field has been presented. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The computations have been carried out for flow over a cylinder and a sphere. The results indicate that the magnetic field tends to delay or prevent separation. The heat transfer strongly depends on the viscous dissipation parameter. When the dissipation parameter is positive (i.e. when the temperature of the wall is greater than the freestream temperature) and exceeds a certain value, the hot wall ceases to be cooled by the stream of cooler air because the ‘heat cushion’ provided by the frictional heat prevents cooling whereas the effect of the magnetic field is to remove the ‘heat cushion’ so that the wall continues to be cooled. The results are found to be in good agreement with those of the local similarity and local nonsimilarity methods except near the point of separation, but they are in excellent agreement with those of the difference-differential technique even near the point of separation.

Nonsimilar incompressible laminar boundary-layer flows in micropolar fluids

The solution of the steady laminar incompressible nonsimilar boundary-layer problem for micropolar fluids over two-dimensional and axisymmetric bodies has been presented. The partial differential equations governing the flow have been transformed into new co-ordinates having finite range. The resulting equations have been solved numerically using implicit finite-difference scheme. The computations have been carried out for a cylinder and a sphere. The results indicate that the separation in micropolar fluids occurs at earlier streamwise locations as compared to Newtonian fluids. The skin friction and velocity profiles depend on the shape of the body and are almost insensitive to microrotation or coupling parameter, provided the coupling parameter is small. On the other hand, the microrotation profiles and microrotation gradient depend on the microrotation parameter and they are insensitive to the coupling parameter.

Mean Flow Measurements in Turbulent Boundary Layers along Mildly Curved Surfaces

An experimental investigation of the mean flow characteristics of two-dimensional turbulent boundary layers over surfaces of mild longitudinal curvature is reported. The study covered both convex and concave walls of \d/Rw I « 0.013 (d being the boundary-layer thickness and Rw being the wall radius). It was found that, whereas the region close to the wall was not affected significantly by wall curvature, the outer region was very sensitive to even mild wall curvature. A detailed study of the wake region using present and other available data suggests a systematic effect of b/Rw on the wake structure. The paper also discusses in detail the effect of mild wall curvature on the boundary-layer development with particular emphasis on the difference in behavior of the boundary layer at short and long distances from the leading edge of the curved wall, an aspect which has not received sufficient attention in previous experimental investigations. An attempt has been made to explain this behavior from a consideration of the structure of turbulence in boundary layers over curved surfaces taken into account.

Laminar hypersonic boundary-layer flow at a three-dimensional stagnation point with slip and mass transfer

Abstract is not available.