Variational formulation of hyperbolic heat conduction problems applying Laplace transform technique

In this paper, a non-Fourier heat conduction problem is analyzed by employing newly developed theory. Application of conventional numerical schemes leads to strong oscillations of the results around discontinuities in solution domain. To overcome this difficulty the variational formulation of the Laplace-transformed hyperbolic heat conduction equation is developed. The results were used for evaluation of parameters used in approximate transformed temperature profiles. To validate the approach the results were compared with the exact analytical solution solved at special case and with an approach previously reported in the literature. Both showed a close agreement with the proposed approach.     

Mother wavelet selection in the discrete wavelet transform for condition monitoring of wind turbine drivetrain bearings

Although the discrete wavelet transform has been used for diagnosing bearing faults for two decades, most work in this field has been done with test rig data. Since field data starts to be made more available, there is a need to shift into application studies. The choice of mother wavelet, ie, the predefined shape used to analyse the signal, has previously been investigated with simulated and test rig data without consensus of optimal choice in literature. Common between these investigations is the use of the wavelet coefficients' Shannon entropy to find which mother wavelet can yield the most useful features for condition monitoring. This study attempts to find the optimal mother wavelet selection using the discrete wavelet transform. Datasets from wind turbine gearbox accelerometers, consisting of enveloped vibration measurements monitoring both healthy and faulty bearings, have been analysed. The bearing fault frequencies' excitation level has been analysed with 130 different mother wavelets, yielding a definitive measure on their performance. Also, the applicability of Shannon entropy as a ranking method of mother wavelets has been investigated. The results show the discrete wavelet transforms ability to identify faults regardless of mother wavelet used, with the excitation level varying no more than 4%. By analysing the Shannon entropy, broad predictions to the excitation level could be drawn within the mother wavelet families but no direct correlation to the main results. Also, the high computational effort of high order Symlet wavelets, without increased performance, makes them unsuitable.     

Investigating heat conduction in a sphere with heat absorption using generalized Caputo fractional derivative

In this paper, we study the ρ-Laplace transform and the finite sin-Fourier transform as powerful tools in solving fractional differential equations with generalized Caputo derivative. We use these transforms to solve the time-fractional heat equation with a generalized Caputo fractional derivative associated with heat absorption in spherical coordinates. We obtain the solutions in two cases of Dirichlet boundary conditions. The effect of the parameter $\rho$, which characterizes the generalized Caputo derivative is illustrated through some numerical examples.     

Integral transform solution for hyperbolic heat conduction in a finite slab

An analytical integral transformation of the thermal wave propagation problem in a finite slab is obtained through the generalized integral transform technique (GITT). The use of the GITT approach in the analysis of the hyperbolic heat conduction equation leads to a coupled system of second order ordinary differential equations in the time variable. The resulting transformed ODE system is then numerically solved by Gear's method for stiff initial value problems. Numerical results are presented for the local and average temperatures with different Biot numbers and dimensionless thermal relaxation times, permitting a critical evaluation of the technique performance. A comparison is also performed with previously reported results in the literature for special cases and with those produced through the application of the Laplace transform method (LTM), and the finite volume-Gear method (FVGM).     

Fast fluid and ground temperature computation for geothermal ground-loop heat exchanger systems

Heat pumps (HPs) coupled to ground-loop heat exchangers (GLHEs) have become increasingly popular for heating and cooling purposes in the context of growing energy costs. Precise design of GLHEs requires the computation of hourly fluid and ground temperatures, especially when the geothermal system is coupled to another system (e.g. boiler, cooling tower). However, because of the computational burden, hourly computation is often simplified in actual designs by rules of thumb or approximations that can cause over- or under-design of the GLHE system. The hourly temperature computation can be seen as a convolution in the time domain that is most efficiently evaluated by fast Fourier transform (FFT). An additional substantial reduction in computing time is obtained by subsampling the analytical function at a few selected times according to a geometric sequence and then using a good quality interpolant such as the cubic spline. This combined “FFT-S approach” enables one to obtain a 30-year hourly simulation in less than a second on a standard laptop computer, even for the computationally intensive finite line-source model. This reduction of one to two orders of magnitude in computing time compared to time-domain approaches with load aggregation should help promote the use of hourly temperature simulation for GLHE design purposes.     

基于小波变换与Elman神经网络的短期风速组合预测

风速的准确预测对风电场发电系统的经济和安全运行有着重要的作用。为了克服风速随机性强的缺点,提高短期风速预测的精度,提出了一种将小波变换与Elman神经网络相结合的短期风速组合预测模型。该模型由小波预处理模块和神经网络预测模块组成。首先利用小波预处理模块将风速序列作多尺度分解,重构得到不同频段的子序列,然后利用Elman神经网络模块分别对其训练和预测。实际风速预测结果表明,与单一的Elman和ARMA法相比,该组合预测模型的预测精度有较大的改善,可以用于风电场短期风速的预测。     

热网管道保温与热化发电之间的相互关系分析

热网管道的保温设计，尤其是长距离热风管道的保温设计，对热网管道设计成功与否显得十分重要。而热电厂供热参数的高低不仅与经济发电相关，更主要的是跟热网的保温、散热损失有关。一般热能工程设计手册中，仅有经济厚度等计算方法介绍，而没有考虑保温散热损失对热化发电的影响。这对集中供热来说是合理的，但对于热电联产来说，似乎有点欠缺。本文试图通过实例分析计算，来说明保温厚度、散热损失、热化发电的相互关系。以期重视热网管道的保温设计、施工，正确处理经济厚度与热化发电的联系，进一步降低消耗，节约能源。     

An analytical solution for two-dimensional inverse heat conduction problems using Laplace transform

An analytical method has been developed for two-dimensional inverse heat conduction problems by using the Laplace transform technique. The inverse solutions are obtained under two simple boundary conditions in a finite rectangular body, with one and two unknowns, respectively. The method first approximates the temperature changes measured in the body with a half polynomial power series of time and Fourier series of eigenfunction. The expressions for the surface temperature and heat flux are explicitly obtained in a form of power series of time and Fourier series. The verifications for two representative testing cases have shown that the predicted surface temperature distribution is in good agreement with the prescribed surface condition, as well as the surface heat flux.     

Study of two-phase flow regime identification in horizontal tube bundles under vertical upward cross-flow condition using wavelet transform

A wavelet-transform based approach for flow regime identification in horizontal tube bundles under vertical upward cross-flow condition was presented. Tests on two-phase flow pattern of R134a were conducted under low mass velocity and flow boiling conditions over ranges of mass flux 4–25 kg/m²·s, vapor quality 0.02–0.90. Time series of differential pressure fluctuations were measured and analyzed with discrete wavelet transform. Different time-scale characteristics in bubbly flow, churn flow and annular flow were analyzed. The wavelet energy distributions over scales were found to be appropriate for flow regime identification. Based on the wavelet energy distribution over characteristic scales, a criterion of flow regime identification was proposed. The comparison with experiment results show that it is feasible to use the discrete wavelet transform as the tool of flow regime identification in horizontal tube bundles under vertical upward cross-flow condition. __________ Translated from Journal of Shanghai Jiaotong University, 2007, 41(3): 337–341, 346 [译自: 上海交通大学学报]     

Fractional analysis of radiative blood transport through a porous channel containing multishaped cobalt nanoparticles: An application to hemodynamics

In this work, impacts of dispersing nonspherical shaped cobalt nanoparticles in the blood are analyzed for magnetohydrodynamic radiative transport of blood inside a vertical porous channel. An Oldroyd-B model is used to feature flow characteristics of blood along with Fourier's principle of heat transmission for the mathematical modeling of the problem. A fractional system is constructed by employing the idea of the Caputo–Fabrizio derivative on subsequent differential equations. The Laplace transform method is adopted to solve the fractional flow and energy equations subject to generalized boundary conditions, which involve time-dependent functions $h\left(\tau \right)$ and $g\left(\tau \right)$, respectively. Instead of promoting the analytic velocity and energy expressions, Zakian's numerical algorithm is operated to achieve the reverse transformation purpose of Laplace domain functions. To certify the obtained solutions, two additional numerical algorithms named Stehfest's algorithm and Durbin's algorithm are inculcated in this study, and comparative illustrations are drawn. For the extensive investigation of shear stress and heat transfer phenomenon, numerical simulations for the coefficient of skin friction and Nusselt number are performed, and outcomes are communicated through various tables. The impacts of shape-dependent viscosity and other significant parameters on flow patterns are investigated through graphs for multiple motion types of the left channel wall. Meanwhile, the thermal performance of nanofluid is examined for platelet, brick, cylinder, and blade shape nanoparticles, along with other thermal parameters. In addition, some recently reported results and flow profiles for Maxwell, second-grade, and viscous fluids are deduced graphically as special cases of the current study.     

Eigenvalue approach to fractional order generalized thermoelasticity with line heat source in an infinite medium

Applying the eigenvalue approach method along with Laplace transform, a general solution scheme for the thermoelastic deformation of an unbounded transversely isotropic medium has been developed on fractional order generalized thermoelasticity with an instantaneous heat source. Solution has been achieved in Laplace transform domain for the perturbed temperature field and other field variables. Several graphs have been presented, and analyses of the results have been made.     

Generator bearing fault diagnosis for wind turbine via empirical wavelet transform using measured vibration signals

The implementation of condition monitoring and fault diagnosis system (CMFDS) on wind turbine is significant to lower the unscheduled breakdown. Generator is one of the most important components in wind turbine, and generator bearing fault identification always draws lots of attention. However, non-stationary vibration signal of weak fault and compound fault with a large amount of background noise makes this task challenging in many cases. So, effective signal processing method is essential in the accurate diagnosis step of CMFDS. As a novel signal processing method, empirical Wavelet Transform (EWT) is used to extract inherent modulation information by decomposing signal into mono-components under an orthogonal basis, which is seen as a powerful tool for mechanical fault diagnosis. Moreover, in order to avoid the inaccurate identification the internal modes caused by the heavy noise, wavelet spatial neighboring coefficient denoising with data-driven threshold is applied to increase Signal to Noise Ratio (SNR) before EWT. The effectiveness of the proposed technique on weak fault and compound fault diagnosis is first validated by two experimental cases. Finally, the proposed method has been applied to identify fault feature of generator bearing on wind turbine in wind farm successfully.     

Field synergy equation for turbulent heat transfer and its application

A field synergy equation with a set of specified constraints for turbulent heat transfer developed based on the extremum entransy dissipation principle can be used to increase the field synergy between the time-averaged velocity and time-averaged temperature gradient fields over the entire fluid flow domain to optimize the heat transfer in turbulent flow. The solution of the field synergy equation gives the optimal flow field having the best field synergy for a given decrement of the mean kinetic energy, which maximizes the heat transfer. As an example, the field synergy analysis for turbulent heat transfer between parallel plates is presented. The analysis shows that a velocity field with small eddies near the boundary effectively enhances the heat transfer in turbulent flow especially when the eddy height which are perpendicular to the primary flow direction, are about half of the turbulent flow transition layer thickness. With the guide of this optimal velocity field, appropriate internal fins can be attached to the parallel plates to produce a velocity field close to the optimal one, so as to increase the field synergy and optimize the turbulent heat transfer.     

Fractional heat conduction in a space with a source varying harmonically in time and associated thermal stresses

Time-nonlocal generalization of the classical Fourier law with the “long-tail” power kernel can be interpreted in terms of fractional calculus (theory of integrals and derivatives of noninteger order) and leads to the time-fractional heat conduction equation with the Caputo derivative. Fractional heat conduction equation with the harmonic source term under zero initial conditions is studied. Different formulations of the problem for the standard parabolic heat conduction equation and for the hyperbolic wave equation appearing in thermoelasticity without energy dissipation are discussed. The integral transform technique is used. The corresponding thermal stresses are found using the displacement potential.     

循环流化床锅炉中灰循环倍率与燃烧产物热平衡方程式

循环流化床锅炉在炉膛、分离器和回料器组成的灰循环系统中 ,存在大量的循环灰量。它是载热体 ,从炉膛吸入或放出热量。虽然循环灰温降不大 ,然而循环灰量却极大 ,严重影响燃烧产物的热平衡。在循环流化床锅炉热力计算时 ,必须加以考虑     

Forecasting electricity price and demand using a hybrid approach based on wavelet transform,ARIMA and neural networks

Demand and price forecasting are extremely important for participants in energy markets. Most research work in the area predicts demand and price signals separately. In this paper, a model is presented which predicts electricity demand and price simultaneously. The model combines wavelet transforms, ARIMA models and neural networks. Both time domain and wavelet domain variables are considered in the feature set for price and demand forecasting. The best input set is selected by two‐step correlation analysis. The proposed model is better adapted to real conditions of an energy market since the forecast features for price and demand are not assumed as known values but are predicted by the model, thus accounting for the interactions of the demand and price forecast processes. The forecast accuracy of the proposed method is evaluated using data from the Finnish energy market, which is part of the Nordic Power Pool. The results show that the proposed model provides significant improvement in both demand and price prediction accuracy compared with models using a separate frameworks approach. Copyright © 2013 John Wiley & Sons, Ltd.     

Coupled heat equation in thermoelasticity with temperature dependent moduli

Abstract

New and consistent expressions for the coupled heat equation are developed within the framework of small-strain thermoelasticity for both Fourier and Cattaneo–Vernotte conduction models. These expressions place no restrictions on the changes in temperature, allow for the temperature dependence of the thermoelastic moduli, and include all the coupling terms as functions of the thermoelastic moduli and their derivatives. As applications, (i) an extended Lord–Shulman-type model is derived that takes into account the temperature dependence of the thermoelastic moduli, and (ii) the equations underpinning the experimental technique of thermoelastic stress analysis are revisited.     

Augmentation of heat transfer through passive techniques

The thermal performance of energy preservation systems is greatly improved by increasing miniaturization and boosting. These are imaginative (or Promethean) techniques to enhance heat transfer. Enhancement methods of heat transfer draw great attention in front of the industrial sector because of their ability to provide energy savings and raise the economic efficiency of thermal systems. Three techniques these methods are categorized; those are active, passive, and compound. Different types of components are used in passive methods because of the transfer/working fluid flow path to the enhancement of the heat transfer rate. In this article, the subject of the review was the passive heat transfer enhancement methods including inserts (conical strips, winglets, twisted tapes, baffles), porous materials, coil/helical/spiral tubes, rough surfaces (corrugated/ribbed surfaces), extended surfaces (fins) and nanofluids (mono and hybrid nanofluid). Recent passive heat transfer enhancement techniques are studied in this article as they are cost-effective and reliable, and also comparably passive methods do not need any extra power to promote the energy conversion systems' thermal efficiency than active methods. In the passive approaches, various components are applied to the heat transfer/working fluid flow path to improve the heat transfer rate. The passive heat transfer enhancement methods studied in this article include inserts (twisted tapes, conical strips, baffles, winglets), extended surfaces (fins), porous materials, coil/helical/spiral tubes, rough surfaces (corrugated/ribbed surfaces), and nanofluids (mono and hybrid nanofluid). From the pioneers' research work, it is clear that a lower twist ratio and lower pitch, lesser winglet angles can provide more heat transfer rate and a little bit more friction factor. In the case of nanofluids, a little bit of pumping power is enhanced. Finally, heat transfer enhancement is compared with the thermal performance factor, which is more than unity.     

Electro-osmotic flow of fractional second-grade fluid with fractional Cattaneo heat flux through a vertical microchannel

This study investigates the unsteady electro-osmotic flow (EOF) of a fractional second-grade fluid through a vertical microchannel with convection heat transfer. The fractional Cattaneo heat flux model will be used to modify the heat equation. The solutions for the velocity and the temperature have been derived by employing the Laplace and finite Fourier sine transforms and their numerical inverses. The results show that at the beginning of the time period, the fractional parameter postpones the movement of the fluid. Furthermore, the results show that at the high values of retardation time (non-Newtonian case), the required time for the velocity and the flow rate to reach the steady state increases. Moreover, the heat relaxation time reduces the heat transfer until a critical time, and then the effect reverses.     

Development of wavelet image compression technique to particle image velocimetry

IntroductionParticle Image Velocimetry (PIV) is a non-intrusiveflow visualization technique and is now firmly established as a powerful fluid dynandcs tool to measure flowvelocity in the area of fluid mechanics. Even moreimportant than this remarkably improved performance ofthe PIV technique, is its unique ability to captureinstantaneous full-field flow and thus to allow thequantitative detection of spahal stfuctllres in unsteadyflows, which is not possible with other experimentaltechniques…