Scaling analysis of the unsteady natural convection boundary layer adjacent to an inclined plate for Pr > 1 following instantaneous heating

The unsteady natural convection boundary layer adjacent to an instantaneously heated inclined plate is investigated using an improved scaling analysis and direct numerical simulations. The development of the unsteady natural convection boundary layer following instantaneous heating may be classified into three distinct stages including a start-up stage, a transitional stage and a steady state stage, which can be clearly identified in the analytical and numerical results. Major scaling relations of the velocity and thicknesses and the flow development time of the natural convection boundary layer are obtained using triple-layer integral solutions and verified by direct numerical simulations over a wide range of flow parameters.

An implicit RBF meshless approach for time fractional diffusion equations

This paper aims to develop an implicit meshless approach based on the radial basis function (RBF) for numerical simulation of time fractional diffusion equations. The meshless RBF interpolation is firstly briefed. The discrete equations for two-dimensional time fractional diffusion equation (FDE) are obtained by using the meshless RBF shape functions and the strong-forms of the time FDE. The stability and convergence of this meshless approach are discussed and theoretically proven. Numerical examples with different problem domains and different nodal distributions are studied to validate and investigate accuracy and efficiency of the newly developed meshless approach. It has proven that the present meshless formulation is very effective for modeling and simulation of fractional differential equations.

Novel numerical methods for time-space fractional reaction diffusion equations in two dimensions

We consider time-space fractional reaction diffusion equations in two dimensions. This equation is obtained from the standard reaction diffusion equation by replacing the first order time derivative with the Caputo fractional derivative, and the second order space derivatives with the fractional Laplacian. Using the matrix transfer technique proposed by Ilic, Liu, Turner and Anh [Fract. Calc. Appl. Anal., 9:333--349, 2006] and the numerical solution strategy used by Yang, Turner, Liu, and Ilic [SIAM J. Scientific Computing, 33:1159--1180, 2011], the solution of the time-space fractional reaction diffusion equations in two dimensions can be written in terms of a matrix function vector product $f(A)b$ at each time step, where $A$ is an approximate matrix representation of the standard Laplacian. We use the finite volume method over unstructured triangular meshes to generate the matrix $A$, which is therefore non-symmetric. However, the standard Lanczos method for approximating $f(A)b$ requires that $A$ is symmetric. We propose a simple and novel transformation in which the standard Lanczos method is still applicable to find $f(A)b$, despite the loss of symmetry. Numerical results are presented to verify the accuracy and efficiency of our newly proposed numerical solution strategy.

An analytical solution for diffusion and nonlinear uptake of oxygen in a spherical cell

We develop a new analytical solution for a reactive transport model that describes the steady-state distribution of oxygen subject to diffusive transport and nonlinear uptake in a sphere. This model was originally reported by Lin (Journal of Theoretical Biology, 1976 v60, pp449–457) to represent the distribution of oxygen inside a cell and has since been studied extensively by both the numerical analysis and formal analysis communities. Here we extend these previous studies by deriving an analytical solution to a generalized reaction-diffusion equation that encompasses Lin’s model as a particular case. We evaluate the solution for the parameter combinations presented by Lin and show that the new solutions are identical to a grid-independent numerical approximation.

Responding to rapid change in higher education : enabling university departments responsible for work related programs through boundary spanning

Boundary spanning links organisations to one another in order to create mutually beneficial relationships; it is a concept developed and used in organisational theory but rarely used to understand organisational structures in higher education (Pruitt & Schwartz, 1999). Yet understanding boundary spanning activity has the capacity to help universities respond to demands for continuous quality improvement, and to increase capacity to react to environmental uncertainty. At a time of rapid change characterised by a fluctuating economic environment, globalisation, increased mobility, and ecological issues, boundary spanning could be viewed as a key element in assisting institutions in effectively understanding and responding to such change. The literature suggests that effective boundary spanning could help universities improve organisational performance, use of infrastructure and resources, intergroup relations, leadership styles, performance and levels of job satisfaction, technology transfer, knowledge creation, and feedback processes, amongst other things. Our research aims to put a face on boundary spanning (Miller, 2008) by contextualising it within organisational systems and structures in university departments responsible for work related programs i.e. Work Integrated Learning (WIL) and Co-operative Education (Co-op). In this paper these approaches are referred to collectively as work related programs. The authors formed a research team in Victoria, British Columbia in 2009 at a sponsored international research forum, Two Days in June. The purpose of the invitation-only forum was to investigate commonalities and differences across programs and to formulate an international research agenda for work related programs over the next five to ten years. Researchers from Queensland University of Technology, University of Cincinnati, Baden-Wuerttemberg Cooperative State University, University of Ottawa,and Dublin City University agreed that further research was needed into the impact stakeholders, organisational systems, structures, policies, and practices have on departments delivering work related programs. This paper illustrates how policy and practice across the five institutions can be better understood through the lens of boundary spanning. It is argued that boundary spanning is an area of theory and practice with great applicability to a better understanding of the activity of these departments. The paper concludes by proposing topics for future research to examine how boundary spanning can be used to better understand practice and change in work related programs.

Boundary weaving : the social structure and processes of organizational boundaries

Boundaries are an important field of study because they mediate almost every aspect of organizational life. They are becoming increasingly more important as organizations change more frequently and yet, despite the endemic use of the boundary metaphor in common organizational parlance, they are poorly understood. Organizational boundaries are under-theorized and researchers in related fields often simply assume their existence, without defining them. The literature on organizational boundaries is fragmented with no unifying theoretical basis. As a result, when it is recognized that an organizational boundary is "dysfunctional". there is little recourse to models on which to base remediating action. This research sets out to develop just such a theoretical model and is guided by the general question: "What is the nature of organizational boundaries?" It is argued that organizational boundaries can be conceptualised through elements of both social structure and of social process. Elements of structure include objects, coupling, properties and identity. Social processes include objectification, identification, interaction and emergence. All of these elements are integrated by a core category, or basic social process, called boundary weaving. An organizational boundary is a complex system of objects and emergent properties that are woven together by people as they interact together, objectifying the world around them, identifying with these objects and creating couplings of varying strength and polarity as well as their own fragmented identity. Organizational boundaries are characterised by the multiplicity of interconnections, a particular domain of objects, varying levels of embodiment and patterns of interaction. The theory developed in this research emerged from an exploratory, qualitative research design employing grounded theory methodology. The field data was collected from the training headquarters of the New Zealand Army using semi-structured interviews and follow up observations. The unit of analysis is an organizational boundary. Only one research context was used because of the richness and multiplicity of organizational boundaries that were present. The model arose, grounded in the data collected, through a process of theoretical memoing and constant comparative analysis. Academic literature was used as a source of data to aid theory development and the saturation of some central categories. The final theory is classified as middle range, being substantive rather than formal, and is generalizable across medium to large organizations in low-context societies. The main limitation of the research arose from the breadth of the research with multiple lines of inquiry spanning several academic disciplines, with some relevant areas such as the role of identity and complexity being addressed at a necessarily high level. The organizational boundary theory developed by this research replaces the typology approaches, typical of previous theory on organizational boundaries and reconceptualises the nature of groups in organizations as well as the role of "boundary spanners". It also has implications for any theory that relies on the concept of boundaries, such as general systems theory. The main contribution of this research is the development of a holistic model of organizational boundaries including an explanation of the multiplicity of boundaries . no organization has a single definable boundary. A significant aspect of this contribution is the integration of aspects of complexity theory and identity theory to explain the emergence of higher-order properties of organizational boundaries and of organizational identity. The core category of "boundary weaving". is a powerful new metaphor that significantly reconceptualises the way organizational boundaries may be understood in organizations. It invokes secondary metaphors such as the weaving of an organization's "boundary fabric". and provides managers with other metaphorical perspectives, such as the management of boundary friction, boundary tension, boundary permeability and boundary stability. Opportunities for future research reside in formalising and testing the theory as well as developing analytical tools that would enable managers in organizations to apply the theory in practice.

An advanced meshless method for time fractional diffusion equation

Recently, because of the new developments in sustainable engineering and renewable energy, which are usually governed by a series of fractional partial differential equations (FPDEs), the numerical modelling and simulation for fractional calculus are attracting more and more attention from researchers. The current dominant numerical method for modeling FPDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings including difficulty in simulation of problems with the complex problem domain and in using irregularly distributed nodes. Because of its distinguished advantages, the meshless method has good potential in simulation of FPDEs. This paper aims to develop an implicit meshless collocation technique for FPDE. The discrete system of FPDEs is obtained by using the meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of fractional partial differential equations.

Turbulence characteristics of a small subtropical estuary during and after some moderate rainfall

In natural estuaries, scalar diffusion and dispersion are driven by turbulence. In the present study, detailed turbulence measurements were conducted in a small subtropical estuary with semi-diurnal tides under neap tide conditions. Three acoustic Doppler velocimeters were installed mid-estuary at fixed locations close together. The units were sampled simultaneously and continuously at relatively high frequency for 50 h. The results illustrated the influence of tidal forcing in the small estuary, although low frequency longitudinal velocity oscillations were observed and believed to be induced by external resonance. The boundary shear stress data implied that the turbulent shear in the lower flow region was one order of magnitude larger than the boundary shear itself. The observation differed from turbulence data in a laboratory channel, but a key feature of natural estuary flow was the significant three dimensional effects associated with strong secondary currents including transverse shear events. The velocity covariances and triple correlations, as well as the backscatter intensity and covariances, were calculated for the entire field study. The covariances of the longitudinal velocity component showed some tidal trend, while the covariances of the transverse horizontal velocity component exhibited trends that reflected changes in secondary current patterns between ebb and flood tides. The triple correlation data tended to show some differences between ebb and flood tides. The acoustic backscatter intensity data were characterised by large fluctuations during the entire study, with dimensionless fluctuation intensity I0b =Ib between 0.46 and 0.54. An unusual feature of the field study was some moderate rainfall prior to and during the first part of the sampling period. Visual observations showed some surface scars and marked channels, while some mini transient fronts were observed.

Free convection heat transfer through coupled thermal boundary layers in a partitioned triangular enclosure

A numerical investigation has been carried out for the coupled thermal boundary layers on both sides of a partition placed in an isosceles triangular enclosure along its middle symmetric line. The working fluid is considered as air which is initially quiescent. A sudden temperature difference between two zones of the enclosure has been imposed to trigger the natural convection. It is anticipated from the numerical simulations that the coupled thermal boundary layers development adjacent to the partition undergoes three distinct stages; namely an initial stage, a transitional stage and a steady state stage. Time dependent features of the coupled thermal boundary layers as well as the overall natural convection flow in the partitioned enclosure have been discussed and compared with the non-partitioned enclosure. Moreover, heat transfer as a form of local and overall average Nusselt number through the coupled thermal boundary layers and the inclined walls is also examined. The details results will be discussed in the full paper.