Solution of Heat Transfer and Fluid Flow problems using meshless Radial Basis Function method

In the past, the world of numerical solutions for Heat Transfer and Fluid Flow problems has been dominated by Finite Element Method, Finite Difference Method, Finite Volume Method, and more recently the Boundary Element Method. These methods revolve around using a mesh or grid to solve problems. However, problems with irregular boundaries and domains can be difficult to properly discretize; In this thesis, heat transfer and fluid flow problems are solved using Radial Basis Functions. This method is meshless, easy to understand, and even easier to implement. Radial Basis Functions are used to solve lid-driven cavity flow, natural convection in a square enclosure, flow with forced convection over backward facing step and flow over an airfoil. Codes are developed using MATLAB. The results are compared with COMSOL and FLUENT, two popular commercial codes widely used. COMSOL is a finite element model while FLUENT is a finite volume-based code

Continuous cellular automata on irregular tessellations : mimicking steady-state heat flow

Leaving a few exceptions aside, cellular automata (CA) and the intimately related coupled-map lattices (CML), commonly known as continuous cellular automata (CCA), as well as models that are based upon one of these paradigms, employ a regular tessellation of an Euclidean space in spite of the various drawbacks this kind of tessellation entails such as its inability to cover surfaces with an intricate geometry, or the anisotropy it causes in the simulation results. Recently, a CCA-based model describing steady-state heat flow has been proposed as an alternative to Laplace's equation that is, among other things, commonly used to describe this process, yet, also this model suffers from the aforementioned drawbacks since it is based on the classical CCA paradigm. To overcome these problems, we first conceive CCA on irregular tessellations of an Euclidean space after which we show how the presented approach allows a straightforward simulation of steady-state heat flow on surfaces with an intricate geometry, and, as such, constitutes an full-fledged alternative for the commonly used and easy-to-implement finite difference method, and the more intricate finite element method

Fluid flow and conjugated heat transfer in arbitrarily shaped channels via single domain formulation and integral transforms

The present work advances a recently introduced approach based on combining the Generalized Integral Transform Technique (GITT) and a single domain reformulation strategy, aimed at providing hybrid numerical–analytical solutions to convection–diffusion problems in complex physical configurations and irregular geometries. The methodology has been previously considered in the analysis of conjugated conduction–convection heat transfer problems, simultaneously modeling the heat transfer phenomena at both the fluid streams and the channels walls, by making use of coefficients represented as space variable functions with abrupt transitions occurring at the fluid–wall interfaces. The present work is aimed at extending this methodology to deal with both fluid flow and conjugated heat transfer within arbitrarily shaped channels and complex multichannel configurations, so that the solution of a cumbersome system of coupled partial differential equations defined for each individual sub-domain of the problem is avoided, with the proposition of the single-domain formulation. The reformulated problem is integral transformed through the adoption of eigenvalue problems containing the space variable coefficients, which provide the basis of the eigenfunction expansions and are responsible for recovering the transitional behavior among the different regions in the original formulation. For demonstration purposes, an application is first considered consisting of a microchannel with an irregular cross-section shape, representing a typical channel micro-fabricated through laser ablation, in which heat and fluid flow are investigated, taking into account the conjugation with the polymeric substrate. Then, a complex configuration consisting of multiple irregularly shaped channels is more closely analyzed, in order to illustrate the flexibility and robustness of the advanced hybrid approach. In both cases, the convergence behavior of the proposed expansions is presented and critical comparisons against purely numerical approaches are provided.Indisponível

Numerical investigation of the energy performance of a guideless irregular heat and mass exchanger with corrugated heat transfer surface for dew point cooling

© 2016 The Author(s) The paper presents an investigation into the energy performance of a novel irregular heat and mass exchanger for dew point cooling which, compared to the existing flat-plate heat exchangers, removed the use of the channel supporting guides and implemented the corrugated heat transfer surface, thus expecting to achieve the reduced air flow resistance, increased heat transfer area, and improved energy efficiency (i.e. Coefficient of Performance (COP)) of the air cooling process. CFD simulation was carried out to determine the flow resistance (K) factors of various elements within the dry and wet channels of the exchanger, while the ‘finite-element’ based ‘Newton-iteration’ numerical simulation was undertaken to investigate its cooling capacity, cooling effectiveness and COP at various geometrical and operational conditions. Compared to the existing flat-plate heat and mass exchangers with the same geometrical dimensions and operational conditions, the new irregular exchanger could achieve 32.9%–37% higher cooling capacity, dew-point and wet-bulb effectiveness, 29.7%–33.3% higher COP, and 55.8%–56.2% lower pressure drop. While undertaking dew point air cooling, the irregular heat and mass exchanger had the optimum air velocity of 1 m/s within the flow channels and working-to-intake air ratio of 0.3, which allowed the highest cooling capacity and COP to be achieved. In terms of the exchanger dimensions, the optimum height of the channel was 5 mm while its length was in the range 1–2 m. Overall, the proposed irregular heat and mass exchanger could lead to significant enhanced energy performance compared to the existing flat-plate dew point cooling heat exchanger of the same geometrical dimensions. To achieve the same amount cooling output, the irregular heat and mass exchanger had the reduced size and cost against the flat-plate ones

Convection in Corrugated Slots

This thesis consists of two parts. The first part deals with the development of proper methodology, i.e. a spectrally accurate algorithm suitable for analysis of convection problems in corrugated slots. The second part is devoted to the study of natural convection in corrugated slots. The algorithm uses the immersed boundary conditions (IBC) concept to deal with the irregular form of the solution domain associated with the presence of corrugated plates. The field equations are discretized on a regular domain surrounding the flow domain using Fourier expansions in the horizontal direction and Chebyshev expansions in the vertical direction. The boundary conditions are expressed in the form of constraints and the spectrally accurate discretization of these constraints has been proposed. The buoyancy forces associated with the temperature difference between isothermal plates drive the natural convection. This temperature difference is expressed in terms of the Rayleigh number Ra and the analysis is limited to its subcritical values where no secondary motion takes place in the absence of corrugation. Corrugations have a sinusoidal form characterized by the wave number a, the upper and lower amplitudes and the phase difference between the upper and lower corrugation systems. They create horizontal temperature gradients which lead to the formation of vertical and horizontal pressure gradients which drive the motion regardless of the intensity of the heating. Presence of corrugations affects the conductive heat flow and creates the convective heat flow. The increase of the heat flow induced by the corrugations has been determined. The convection is qualitatively similar for all Prandtl numbers with the intensity of convection increasing for smaller Pr’s and with the heat transfer augmentation increasing for larger Pr’s

On Using Physical Analogies for Feature and Shape Extraction in Computer Vision

There is a rich literature of approaches to image feature extraction in computer vision. Many sophisticated approaches exist for low- and high-level feature extraction but can be complex to implement with parameter choice guided by experimentation, but impeded by speed of computation. We have developed new ways to extract features based on notional use of physical paradigms, with parameterisation that is more familiar to a scientifically-trained user, aiming to make best use of computational resource. We describe how analogies based on gravitational force can be used for low-level analysis, whilst analogies of water flow and heat can be deployed to achieve high-level smooth shape detection. These new approaches to arbitrary shape extraction are compared with standard state-of-art approaches by curve evolution. There is no comparator operator to our use of gravitational force. We also aim to show that the implementation is consistent with the original motivations for these techniques and so contend that the exploration of physical paradigms offers a promising new avenue for new approaches to feature extraction in computer vision