Unsteady natural convection in a triangular enclosure under isothermal heating

The fluid flow and heat transfer inside a triangular enclosure due to instantaneous heating on the inclined walls are investigated using an improved scaling analysis and direct numerical simulations. The development of the unsteady natural convection boundary layer under the inclined walls 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. A new triple-layer integral approach of scaling analysis has been considered to obtain major scaling relations of the velocity, thicknesses, Nusselt number and the flow development time of the natural convection boundary layer and verified by direct numerical simulations over a wide range of flow parameters.

Scaling of free convection heat transfer in a triangular cavity for Pr>1

Unsteady natural convection inside a triangular cavity subject to a non-instantaneous heating on the inclined walls in the form of an imposed temperature which increases linearly up to a prescribed steady value over a prescribed time is reported. The development of the flow from start-up to a steady-state has been described based on scaling analyses and direct numerical simulations. The ramp temperature has been chosen in such a way that the boundary layer is reached a quasi-steady mode before the growth of the temperature is completed. In this mode the thermal boundary layer at first grows in thickness, then contracts with increasing time. However, if the imposed wall temperature growth period is sufficiently short, the boundary layer develops differently. It is seen that the shape of many houses are isosceles triangular cross-section. The heat transfer process through the roof of the attic-shaped space should be well understood. Because, in the building energy, one of the most important objectives for design and construction of houses is to provide thermal comfort for occupants. Moreover, in the present energy-conscious society it is also a requirement for houses to be energy efficient, i.e. the energy consumption for heating or air-conditioning houses must be minimized.

Natural convection in a triangular enclosure subject to periodic thermal forcing

The effects of periodic thermal forcing on the flow field and heat transfer through an attic space are examined numerically in this paper. We consider the case with a fixed aspect ratio of 0.5 and a fixed Grashof number of 1.33×106. The numerical results reveal that, during the daytime, the flow is stratified; whereas at the night-time, the flow becomes unstable. A number of regular plumes and vortices are observed in the contours of isotherms and stream functions respectively. Moreover, the flow appears to be symmetric during the daytime, and becomes asymmetric at the night-time. It is also found that the flow is weaker during the daytime than that at the night-time in the present case, and the calculated heat transfer rate at the night-time is approximately three times greater than the heat transfer rate during the daytime.

Triangular Linguistic Fuzzy based performance measurement model for supply chain to assess leanness attributes

Increasing global competitiveness worldwide has forced manufacturing organizations to produce high-quality products more quickly and at a competitive cost. In order to reach these goals, they need good quality components from suppliers at optimum price and lead time. This actually forced all the companies to adapt different improvement practices such as lean manufacturing, Just in Time (JIT) and effective supply chain management. Applying new improvement techniques and tools cause higher establishment costs and more Information Delay (ID). On the contrary, these new techniques may reduce the risk of stock outs and affect supply chain flexibility to give a better overall performance. But industry people are unable to measure the overall affects of those improvement techniques with a standard evaluation model .So an effective overall supply chain performance evaluation model is essential for suppliers as well as manufacturers to assess their companies under different supply chain strategies. However, literature on lean supply chain performance evaluation is comparatively limited. Moreover, most of the models assumed random values for performance variables. The purpose of this paper is to propose an effective supply chain performance evaluation model using triangular linguistic fuzzy numbers and to recommend optimum ranges for performance variables for lean implementation. The model initially considers all the supply chain performance criteria (input, output and flexibility), converts the values to triangular linguistic fuzzy numbers and evaluates overall supply chain performance under different situations. Results show that with the proposed performance measurement model, improvement area for each variable can be accurately identified.

Free convection in a triangular enclosure with fluid-saturated porous medium and internal heat generation

Unsteady natural convection inside a triangular cavity has been studied in this study. The cavity is filled with a saturated porous medium with non-isothermal left inclined wall while the bottom surface is isothermally heated and the right inclined surface is isothermally cold. An internal heat generation is also considered which is dependent of the fluid temperature. The governing equations are solved numerically by finite element method. The Prandtl number of the fluid is considered as 0.7 (air) while the aspect ratio and the Rayleigh number are considered as 0.5 and 105 respectively. The effect of the porosity of the medium and heat generation on the fluid flow and heat transfer have been presented as a form of streamlines and isotherms. The rate of heat transfer through three surfaces of the enclosure is also presented.

Natural convection in a triangular enclosure due to non-uniform cooling on top

Natural convection in a triangular enclosure subject to non-uniformly cooling at the inclined surfaces and uniformly heating at the base is investigated numerically. The numerical simulations of the unsteady flows over a range of Rayleigh numbers and aspect ratios are carried out using Finite Volume Method. Since the upper surface is cooled and the bottom surface is heated, the air flow in the enclosure is potentially unstable to Rayleigh Benard instability. It is revealed that the transient flow development in the enclosure can be classified into three distinct stages; an early stage, a transitional stage and a steady stage. It is also found that the flow inside the enclosure strongly depends on the governing parameters, Rayleigh number and aspect ratio. The asymmetric behaviour of the flow about the geometric centre line is discussed in detailed. The heat transfer through the roof and the ceiling as a form of Nusselt number is also reported in this study.

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.

Natural convection in a triangular enclosure due to non-uniform cooling on top

Natural convection in a triangular enclosure subject to non-uniformly cooling at the inclined surfaces and uniformly heating at the base is investigated numerically. The numerical simulations of the unsteady flows over a range of Rayleigh numbers and aspect ratios are carried out using Finite Volume Method. Since the upper surface is cooled and the bottom surface is heated, the air flow in the enclosure is potentially unstable to Rayleigh Benard instability. It is revealed that the transient flow development in the enclosure can be classified into three distinct stages; an early stage, a transitional stage and a steady stage. It is also found that the flow inside the enclosure strongly depends on the governing parameters; Rayleigh number and aspect ratio. The asymmetric behaviour of the flow about the geometric centre line is discussed in detailed. The heat transfer through the roof and the ceiling as a form of Nusselt number is also reported in this study.

Free convection in a triangular enclosure with fluid-saturated porous medium and internal heat generation

Unsteady natural convection inside a triangular cavity has been studied in this study. The cavity is filled with a saturated porous medium with non-isothermal left inclined wall while the bottom surface is isothermally heated and the right inclined surface is isothermally cooled. An internal heat generation is also considered which is dependent on the fluid temperature. The governing equations are solved numerically by finite volume method. The Prandtl number, Pr of the fluid is considered as 0.7 (air) while the aspect ratio and the Rayleigh number, Ra are considered as 0.5 and 105 respectively. The effect of heat generation on the fluid flow and heat transfer have been presented as a form of streamlines and isotherms. The rate of heat transfer through three surfaces of the enclosure is also presented.

Models of collective cell behaviour with crowding effects : comparing lattice-based and lattice-free approaches

Individual-based models describing the migration and proliferation of a population of cells frequently restrict the cells to a predefined lattice. An implicit assumption of this type of lattice based model is that a proliferative population will always eventually fill the lattice. Here we develop a new lattice-free individual-based model that incorporates cell-to-cell crowding effects. We also derive approximate mean-field descriptions for the lattice-free model in two special cases motivated by commonly used experimental setups. Lattice-free simulation results are compared to these mean-field descriptions and to a corresponding lattice-based model. Data from a proliferation experiment is used to estimate the parameters for the new model, including the cell proliferation rate, showing that the model fits the data well. An important aspect of the lattice-free model is that the confluent cell density is not predefined, as with lattice-based models, but an emergent model property. As a consequence of the more realistic, irregular configuration of cells in the lattice-free model, the population growth rate is much slower at high cell densities and the population cannot reach the same confluent density as an equivalent lattice-based model.

Surface effects on the dual-mode vibration of <110> silver nanowires with different cross-sections

Dual-mode vibration of nanowires has been reported experimentally through actuation of the nanowire at its resonance frequency, which is expected to open up a variety of new modalities for the NEMS that could operate in the nonlinear regime. In the present work, we utilize large scale molecular dynamics simulations to investigate the dual-mode vibration of <110> Ag nanowires with triangular, rhombic and truncated rhombic cross-sections. By incorporating the generalized Young-Laplace equation into Euler-Bernoulli beam theory, the influence of surface effects on the dual-mode vibration is studied. Due to the different lattice spacing in principal axes of inertia of the {110} atomic layers, the NW is also modeled as a discrete system to reveal the influence from such specific atomic arrangement. It is found that the <110> Ag NW will under a dual-mode vibration if the actuation direction is deviated from the two principal axes of inertia. The predictions of the two first mode natural frequencies by the classical beam model appear underestimated comparing with the MD results, which are found to be enhanced by the discrete model. Particularly, the predictions by the beam theory with the contribution of surface effects are uniformly larger than the classical beam model, which exhibit better agreement with MD results for larger cross-sectional size. However, for ultrathin NWs, current consideration of surface effects is still experiencing certain inaccuracy. In all, for all different cross-sections, the inclusion of surface effects is found to reduce the difference between the two first mode natural frequencies. This trend is observed consistent with MD results. This study provides a first comprehensive investigation on the dual-mode vibration of <110> oriented Ag NWs, which is supposed to benefit the applications of NWs that acting as a resonating beam.

Analysis of heat transfer and fluid flow in a triangular enclosure in presence of an adiabatic fin

Natural convection thermal boundary layer adjacent to the heated inclined wall of a right angled triangle with an adiabatic fin attached to that surface is investigated by numerical simulations. The finite volume based unsteady numerical model is adopted for the simulation. It is revealed from the numerical results that the development of the boundary layer along the inclined surface is characterized by three distinct stages, i.e. a start-up stage, a transitional stage and a steady stage. These three stages can be clearly identified from the numerical simulations. Moreover, in presence of adiabatic fin, the thermal boundary layer adjacent to the inclined wall breaks initially. However, it is reattached with the downstream boundary layer next to the fin. More attention has been given to the boundary layer development near the fin area.

Finite volume approach of natural convection in a triangular enclosure with localized heating from below

In this study, natural convection heat transfer and buoyancy driven flows have been investigated in a right angled triangular enclosure. The heater located on the bottom wall while the inclined wall is colder and the remaining walls are maintained as adiabatic. Governing equations of natural convection are solved through the finite volume approach, in which buoyancy is modeled via the Boussinesq approximation. Effects of different parameters such as Rayleigh number, aspect ratio, prantdl number and heater location are considered. Results show that heat transfer increases when the heater is moved toward the right corner of the enclosure. It is also revealed that increasing the Rayleigh number, increases the strength of free convection regime and consequently increases the value of heat transfer rate. Moreover, larger aspect ratio enclosure has larger Nusselt number value. In order to have better insight, streamline and isotherms are shown.

Improved estimates of percolation and anisotropic permeability from 3-D X-ray microtomography using stochastic analyses and visualization

X-ray microtomography (micro-CT) with micron resolution enables new ways of characterizing microstructures and opens pathways for forward calculations of multiscale rock properties. A quantitative characterization of the microstructure is the first step in this challenge. We developed a new approach to extract scale-dependent characteristics of porosity, percolation, and anisotropic permeability from 3-D microstructural models of rocks. The Hoshen-Kopelman algorithm of percolation theory is employed for a standard percolation analysis. The anisotropy of permeability is calculated by means of the star volume distribution approach. The local porosity distribution and local percolation probability are obtained by using the local porosity theory. Additionally, the local anisotropy distribution is defined and analyzed through two empirical probability density functions, the isotropy index and the elongation index. For such a high-resolution data set, the typical data sizes of the CT images are on the order of gigabytes to tens of gigabytes; thus an extremely large number of calculations are required. To resolve this large memory problem parallelization in OpenMP was used to optimally harness the shared memory infrastructure on cache coherent Non-Uniform Memory Access architecture machines such as the iVEC SGI Altix 3700Bx2 Supercomputer. We see adequate visualization of the results as an important element in this first pioneering study.