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.

Some novel techniques of parameter estimation for the dynamical models in biological systems

Inverse problems based on using experimental data to estimate unknown parameters of a system often arise in biological and chaotic systems. In this paper, we consider parameter estimation in systems biology involving linear and non-linear complex dynamical models, including the Michaelis–Menten enzyme kinetic system, a dynamical model of competence induction in Bacillus subtilis bacteria and a model of feedback bypass in B. subtilis bacteria. We propose some novel techniques for inverse problems. Firstly, we establish an approximation of a non-linear differential algebraic equation that corresponds to the given biological systems. Secondly, we use the Picard contraction mapping, collage methods and numerical integration techniques to convert the parameter estimation into a minimization problem of the parameters. We propose two optimization techniques: a grid approximation method and a modified hybrid Nelder–Mead simplex search and particle swarm optimization (MH-NMSS-PSO) for non-linear parameter estimation. The two techniques are used for parameter estimation in a model of competence induction in B. subtilis bacteria with noisy data. The MH-NMSS-PSO scheme is applied to a dynamical model of competence induction in B. subtilis bacteria based on experimental data and the model for feedback bypass. Numerical results demonstrate the effectiveness of our approach.

Exploring the parameter space of a rabbit ventricular action potential model to investigate the effect of variation on action potential and calcium transients

Computational models for cardiomyocyte action potentials (AP) often make use of a large parameter set. This parameter set can contain some elements that are fitted to experimental data independently of any other element, some elements that are derived concurrently with other elements to match experimental data, and some elements that are derived purely from phenomenological fitting to produce the desired AP output. Furthermore, models can make use of several different data sets, not always derived for the same conditions or even the same species. It is consequently uncertain whether the parameter set for a given model is physiologically accurate. Furthermore, it is only recently that the possibility of degeneracy in parameter values in producing a given simulation output has started to be addressed. In this study, we examine the effects of varying two parameters (the L-type calcium current (I(CaL)) and the delayed rectifier potassium current (I(Ks))) in a computational model of a rabbit ventricular cardiomyocyte AP on both the membrane potential (V(m)) and calcium (Ca(2+)) transient. It will subsequently be determined if there is degeneracy in this model to these parameter values, which will have important implications on the stability of these models to cell-to-cell parameter variation, and also whether the current methodology for generating parameter values is flawed. The accuracy of AP duration (APD) as an indicator of AP shape will also be assessed.

Parameter estimation for a phenomenological model of the cardiac action potential

The action potential (ap) of a cardiac cell is made up of a complex balance of ionic currents which flow across the cell membrane in response to electrical excitation of the cell. Biophysically detailed mathematical models of the ap have grown larger in terms of the variables and parameters required to model new findings in subcellular ionic mechanisms. The fitting of parameters to such models has seen a large degree of parameter and module re-use from earlier models. An alternative method for modelling electrically exciteable cardiac tissue is a phenomenological model, which reconstructs tissue level ap wave behaviour without subcellular details. A new parameter estimation technique to fit the morphology of the ap in a four variable phenomenological model is presented. An approximation of a nonlinear ordinary differential equation model is established that corresponds to the given phenomenological model of the cardiac ap. The parameter estimation problem is converted into a minimisation problem for the unknown parameters. A modified hybrid Nelder–Mead simplex search and particle swarm optimization is then used to solve the minimisation problem for the unknown parameters. The successful fitting of data generated from a well known biophysically detailed model is demonstrated. A successful fit to an experimental ap recording that contains both noise and experimental artefacts is also produced. The parameter estimation method’s ability to fit a complex morphology to a model with substantially more parameters than previously used is established.

Natural convection flow in a porous enclosure with localized heating from below

Natural convection flow in a two-dimensional fluid saturated porous enclosure with localized heating from below, symmetrical cooling from the sides and the top and rest of the bottom walls are insulated, has been investigated numerically. Darcy’s law for porous media along with the energy equation based on the 1st law of thermodynamics has been considered. Implicit finite volume method with TDMA solver is used to solve the governing equations. Localized heating is simulated by a centrally located isothermal heat source on the bottom wall, and four different values of the dimensionless heat source length, 1/5, 2/5, 3/5 and 4/5 are considered. The effect of heat source length and the Rayleigh number on streamlines and isotherms are presented, as well as the variation of the local rate of heat transfer in terms of the local Nusselt number from the heated wall. Finally, the average Nusselt number at the heated part of the bottom wall has been shown against Rayleigh number for the non-dimensional heat source length.

Effect of differentially heating and consequent transient behaviour for natural convection within an enclosure of sinusoidal corrugated side walls

Unsteady natural convection due to differentially heating of the sinusoidal corrugated side walls of a modified square enclosure has been numerically investigated. The fluid inside the enclosure is air, initially as quiescent. The flat top and bottom surfaces are considered as adiabatic. The numerical scheme is based on the finite element method adapted to triangular non-uniform mesh element by a non-linear parametric solution algorithm. The results are obtained for the Rayleigh number, Ra ranging from 1e+05 to 1e+08 for different corrugation amplitude and frequency with constant physical properties for the fluid medium considered. The streamlines, isotherms and average Nusselt numbers are presented to observe the effect of sudden heating and its consequent transient behavior on fluid flow and heat transfer characteristics for the range of governing parameters. The present results show that the transient phenomena are greatly influenced by the variation of the aforementioned parameters.

An improved boundary layer scaling with ramp heating on a sloping plate

A scaling analysis for the natural convection boundary layer adjacent to an inclined semi-infinite plate subject to a non-instantaneous heating in the form of an imposed wall temperature which increases linearly up to a prescribed steady value over a prescribed time is reported. The development of the boundary layer flow from start-up to a steady-state has been described based on scaling analyses and verified by numerical simulations. The analysis reveals that, if the period of temperature growth on the wall is sufficiently long, the boundary layer reaches a quasi-steady mode before the growth of the temperature is completed. In this mode the thermal boundary layer at first grows in thickness and then contracts with increasing time. However, if the imposed wall temperature growth period is sufficiently short, the boundary layer develops differently, but after the wall temperature growth is completed, the boundary layer develops as though the startup had been instantaneous. The steady state values of the boundary layer for both cases are ultimately the same.

Effect of soil parameter uncertainty on seismic response of buried segmented pipeline

Pipelines are important lifeline facilities spread over a large area and they generally encounter a range of seismic hazards and different soil conditions. The seismic response of a buried segmented pipe depends on various parameters such as the type of buried pipe material and joints, end restraint conditions, soil characteristics, burial depths, and earthquake ground motion, etc. This study highlights the effect of the variation of geotechnical properties of the surrounding soil on seismic response of a buried pipeline. The variations of the properties of the surrounding soil along the pipe are described by sampling them from predefined probability distribution. The soil-pipe interaction model is developed in OpenSEES. Nonlinear earthquake time-history analysis is performed to study the effect of soil parameters variability on the response of pipeline. Based on the results, it is found that uncertainty in soil parameters may result in significant response variability of the pipeline.

Heating effects in nanofocusing metal wedges

This paper investigates theoretically and numerically local heating effects in plasmon nanofocusing structures with a particular focus on the sharp free-standing metal wedges. The developed model separates plasmon propagation in the wedge from the resultant heating effects. Therefore, this model is only applicable where the temperature increments in a nanofocusing structure are sufficiently small not to result in significant variations of the metal permittivity in the wedge. The problem is reduced to a one-dimensional heating model with a distributed heat source resulting from plasmon dissipation in the metal wedge. A simple heat conduction equation governing the local heating effects in a nanofocusing structure is derived and solved numerically for plasmonic pulses of different lengths and reasonable energies. Both the possibility of achieving substantial local temperature increments in the wedge (with a significant self-influence of the heating plasmonic pulses), and the possibility of relatively weak heating (to ensure the validity of the previously developed nanofocusing theory) are demonstrated and discussed, including the future applications of the obtained results. Applicability conditions for the developed model are also derived and discussed.

Vertical vegetation design decisions and their impact on energy consumption in subtropical cities

Vertical vegetation is vegetation growing on, or adjacent to, the unused sunlit exterior surfaces of buildings in cities. Vertical vegetation can improve the energy efficiency of the building on which it is installed mainly by insulating, shading and transpiring moisture from foliage and substrate. Several design parameters may affect the extent of the vertical vegetation's improvement of energy performance. Examples are choice of vegetation, growing medium geometry, north/south aspect and others. The purpose of this study is to quantitatively map out the contribution of several parameters to energy savings in a subtropical setting. The method is thermal simulation based on EnergyPlus configured to reflect the special characteristics of vertical vegetation. Thermal simulation results show that yearly cooling energy savings can reach 25% with realistic design choices in subtropical environments. Heating energy savings are negligible. The most important parameter is the aspect of walls covered by vegetation. Vertical vegetation covering walls facing north (south for the northern hemisphere) will result in the highest energy savings. In making plant selections, the most significant parameter is Leaf Area Index (LAI). Plants with larger LAI, preferably LAI>4, contribute to greater savings whereas vertical vegetation with LAI<2 can actually consume energy. The choice of growing media and its thickness influence both heating and cooling energy consumption. Change of growing medium thickness from 6cm to 8cm causes dramatic increase in energy savings from 2% to 18%. For cooling, it is best to use a growing material with high water retention, due to the importance of evapotranspiration for cooling. Similarly, for increased savings in cooling energy, sufficient irrigation is required. Insufficient irrigation results in the vertical vegetation requiring more energy to cool the building. To conclude, the choice of design parameters for vertical vegetation is crucial in making sure that it contributes to energy savings rather than energy consumption. Optimal design decisions can create a dramatic sustainability enhancement for the built environment in subtropical climates.

Inherent errors in pollutant build-up estimation in considering urban land use as a lumped parameter

Stormwater quality modelling results is subject to uncertainty. The variability of input parameters is an important source of overall model error. An in-depth understanding of the variability associated with input parameters can provide knowledge on the uncertainty associated with these parameters and consequently assist in uncertainty analysis of stormwater quality models and the decision making based on modelling outcomes. This paper discusses the outcomes of a research study undertaken to analyse the variability related to pollutant build-up parameters in stormwater quality modelling. The study was based on the analysis of pollutant build-up samples collected from 12 road surfaces in residential, commercial and industrial land uses. It was found that build-up characteristics vary appreciably even within the same land use. Therefore, using land use as a lumped parameter would contribute significant uncertainties in stormwater quality modelling. Additionally, it was also found that the variability in pollutant build-up can also be significant depending on the pollutant type. This underlines the importance of taking into account specific land use characteristics and targeted pollutant species when undertaking uncertainty analysis of stormwater quality models or in interpreting the modelling outcomes.

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.

Enhanced photocatalytic activity of titanium oxide nanotubes after heating treatment

Titanium oxide nanotubes were obtained by an electrochemical anodization method. Scanning electron microscope results demonstrate that the diameter of the tubes is about 120 nm and the length of the tubes is around 13 μm. Transmission electron microscope results indicate that the nanotubes are assembled by numerous nanoparticles and tube-like structure remains well after heat treatment at 400-600 °C. The photocatalysis performance of the nanotubes was evaluated in terms of the decomposition rate of methyl orange under UV irradiation. The results show that the photocatalytic activity was enhanced through the heating treatment of the nanotubes, and the nanotubes heated at 600 °C exhibits the best photocatalytic activity. X-ray diffraction patterns indicate that there is no phase transformation during the heat treatment. Therefore, the enhanced activity can be attributed to the improvement of nanotubes crystallinity, which may provide more insights about the effect of the crystallinity on the photocatalytic performance.

Spectroscopic studies of the adsorption and reactions of chlorofluorocarbons (CFC-11 and CFC-12) and hydrochlorofluorocarbon (HCFC-22) on oxide surfaces

Raman and Fourier transform infrared (FT-IR) spectroscopy have been applied to a systematic investigation of the adsorption and decomposition of dichlorodifluoromethane (CCl2F2, CFC-12), fluorotrichloromethane (CCl3F, CFC-11), chlorodifluoromethane (CHClF2, HCFC-22) and molecular chlorine on oxide surfaces. Additionally, the effects of heating and ultraviolet photolysis of the CFC and HCFCs adsorbed on the oxide surfaces have been investigated. Spectral features for these species indicated a small wavenumber shift (1-6 cm-1) associated with the adsorbed phase. Some evidence, specifically the appearance of the Raman band at 507 cm-1, is presented to show that chlorine decomposition species are associated with these oxide surfaces. It was concluded that the new spectral feature (at ca. 507 cm-1) related with the decomposition of the CFC and HCFC molecules was an important indicator of the extent to which the reaction between the adsorbed CFC and HCFC and oxide surface has taken place. The extent of CFC-surface interaction has been quantified in terms of a maximum (Raman) frequency shift parameter (AM). Wavenumber shifts suggest both cation-adsorbate and non-specific adsorption interactions are occurring in the internal channels of the zeolites. Slow decomposition of the adsorbed CFCs under ultraviolet-visible photolysis (at ? > 300 nm) and/or thermal treatment was observed spectroscopically. Using FT-IR spectroscopy, the formation of gas-phase products (CO, CO2, HCl) both onyn photolysis and heating was evident. Results of these measurements are compared with the observed atmospheric reactivity of these compounds.