Heat Source Estimation with the Conjugate Gradient Method in Inverse Linear Diffusive Problems

In this work, we present the solution of a class of linear inverse heat conduction problems for the estimation of unknown heat source terms, with no prior information of the functional forms of timewise and spatial dependence of the source strength, using the conjugate gradient method with an adjoint problem. After describing the mathematical formulation of a general direct problem and the procedure for the solution of the inverse problem, we show applications to three transient heat transfer problems: a one-dimensional cylindrical problem; a two-dimensional cylindrical problem; and a one-dimensional problem with two plates.

A study of the effect of heat source location in a ventilated room using multiple regression analysis

Multiple regression analysis is a statistical technique which allows to predict a dependent variable from m ore than one independent variable and also to determine influential independent variables. Using experimental data, in this study the multiple regression analysis is applied to predict the room mean velocity and determine the most influencing parameters on the velocity. More than 120 experiments for four different heat source locations were carried out in a test chamber with a high level wall mounted air supply terminal at air change rates 3-6 ach. The influence of the environmental parameters such as supply air momentum, room heat load, Archimedes number and local temperature ratio, were examined by two methods: a simple regression analysis incorporated into scatter matrix plots and multiple stepwise regression analysis. It is concluded that, when a heat source is located along the jet centre line, the supply momentum mainly influences the room mean velocity regardless of the plume strength. However, when the heat source is located outside the jet region, the local temperature ratio (the inverse of the local heat removal effectiveness) is a major influencing parameter.

Effect of damper and heat source on wind catcher natural ventilation performance

Experimental wind tunnel and smoke visualisation testing and CFD modelling were conducted to investigate the effect of air flow control mechanism and heat source inside rooms on wind catchers/towers performance. For this purpose, a full-scale wind catcher was connected to a test room and positioned centrally in an open boundary wind tunnel. Pressure coefficients (C-p's) around the wind catcher and air flow into the test room were established. The performance of the wind catcher depends greatly on the wind speed and direction. The incorporation of dampers and egg crate grille at ceiling level reduces and regulates the air flow rate with an average pressure loss coefficient of 0.01. The operation of the wind catcher in the presence of heat sources will potentially lower the internal temperatures in line with the external temperatures.

Resonant Wave Interactions in the Presence of a Diurnally Varying Heat Source

Resonant interactions among equatorial waves in the presence of a diurnally varying heat source are studied in the context of the diabatic version of the equatorial beta-plane primitive equations for a motionless, hydrostatic, horizontally homogeneous and stably stratified background atmosphere. The heat source is assumed to be periodic in time and of small amplitude [i.e., O(epsilon)] and is prescribed to roughly represent the typical heating associated with deep convection in the tropical atmosphere. In this context, using the asymptotic method of multiple time scales, the free linear Rossby, Kelvin, mixed Rossby-gravity, and inertio-gravity waves, as well as their vertical structures, are obtained as leading-order solutions. These waves are shown to interact resonantly in a triad configuration at the O(e) approximation, and the dynamics of these interactions have been studied in the presence of the forcing. It is shown that for the planetary-scale wave resonant triads composed of two first baroclinic equatorially trapped waves and one barotropic Rossby mode, the spectrum of the thermal forcing is such that only one of the triad components is resonant with the heat source. As a result, to illustrate the role of the diurnal forcing in these interactions in a simplified fashion, two kinds of triads have been analyzed. The first one refers to triads composed of a k = 0 first baroclinic geostrophic mode, which is resonant with the stationary component of the diurnal heat source, and two dispersive modes, namely, a mixed Rossby-gravity wave and a barotropic Rossby mode. The other class corresponds to triads composed of two first baroclinic inertio-gravity waves in which the highest-frequency wave resonates with a transient harmonic of the forcing. The integration of the asymptotic reduced equations for these selected resonant triads shows that the stationary component of the diurnal heat source acts as an ""accelerator"" for the energy exchanges between the two dispersive waves through the excitation of the catalyst geostrophic mode. On the other hand, since in the second class of triads the mode that resonates with the forcing is the most energetically active member because of the energy constraints imposed by the triad dynamics, the results show that the convective forcing in this case is responsible for a longer time scale modulation in the resonant interactions, generating a period doubling in the energy exchanges. The results suggest that the diurnal variation of tropical convection might play an important role in generating low-frequency fluctuations in the atmospheric circulation through resonant nonlinear interactions.

Investigation of the Effect of Sealer Use on the Heat Generated at the External Root Surface during Root Canal Obturation Using Warm Vertical Compaction Technique with System B Heat Source

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

An inverse method to estimate the moving heat source in machining process

The present work propounds an inverse method to estimate the heat sources in the transient two-dimensional heat conduction problem in a rectangular domain with convective bounders. The non homogeneous partial differential equation (PDE) is solved using the Integral Transform Method. The test function for the heat generation term is obtained by the chip geometry and thermomechanical cutting. Then the heat generation term is estimated by the conjugated gradient method (CGM) with adjoint problem for parameter estimation. The experimental trials were organized to perform six different conditions to provide heat sources of different intensities. This method was compared with others in the literature and advantages are discussed. (C) 2012 Elsevier Ltd. All rights reserved.

A procedure for determining a spacewise dependent heat source and the initial temperature

The inverse problem of determining a spacewise dependent heat source, together with the initial temperature for the parabolic heat equation, using the usual conditions of the direct problem and information from two supplementary temperature measurements at different instants of time is studied. These spacewise dependent temperature measurements ensure that this inverse problem has a unique solution, despite the solution being unstable, hence the problem is ill-posed. We propose an iterative algorithm for the stable reconstruction of both the initial data and the source based on a sequence of well-posed direct problems for the parabolic heat equation, which are solved at each iteration step using the boundary element method. The instability is overcome by stopping the iterations at the first iteration for which the discrepancy principle is satisfied. Numerical results are presented for a typical benchmark test example, which has the input measured data perturbed by increasing amounts of random noise. The numerical results show that the proposed procedure gives accurate numerical approximations in relatively few iterations.

A variational method for identifying a spacewise-dependent heat source

The inverse problem of determining a spacewise-dependent heat source for the parabolic heat equation using the usual conditions of the direct problem and information from one supplementary temperature measurement at a given instant of time is studied. This spacewise-dependent temperature measurement ensures that this inverse problem has a unique solution, but the solution is unstable and hence the problem is ill-posed. We propose a variational conjugate gradient-type iterative algorithm for the stable reconstruction of the heat source based on a sequence of well-posed direct problems for the parabolic heat equation which are solved at each iteration step using the boundary element method. The instability is overcome by stopping the iterative procedure at the first iteration for which the discrepancy principle is satisfied. Numerical results are presented which have the input measured data perturbed by increasing amounts of random noise. The numerical results show that the proposed procedure yields stable and accurate numerical approximations after only a few iterations.

Determination of a spacewise dependent heat source

This paper investigates the inverse problem of determining a spacewise dependent heat source in the parabolic heat equation using the usual conditions of the direct problem and information from a supplementary temperature measurement at a given single instant of time. The spacewise dependent temperature measurement ensures that the inverse problem has a unique solution, but this solution is unstable, hence the problem is ill-posed. For this inverse problem, we propose an iterative algorithm based on a sequence of well-posed direct problems which are solved at each iteration step using the boundary element method (BEM). The instability is overcome by stopping the iterations at the first iteration for which the discrepancy principle is satisfied. Numerical results are presented for various typical benchmark test examples which have the input measured data perturbed by increasing amounts of random noise.

Photovoltaic and solar-assisted ground-source heat pump systems

This review investigates the performance of photovoltaic and solar-assisted ground-source heat pumps in which solar heat is transferred to the ground to improve the coefficient of performance. A number of studies indicate that, for systems with adequately sized ground heat exchangers, the effect on system efficiency is small: about 1% improvement if the heat source is photovoltaic, a 1–2% decline if the source is solar thermal. With possible exceptions for systems in which the ground heat exchanger is undersized, or natural recharge from ground water is insufficient, solar thermal energy is better used for domestic hot water than to recharge ground heat. This appears particularly true outside the heating season, as although much of the heat extracted from the ground can be replaced, it seems to have little effect on the coefficient of performance. Any savings in electrical consumption that do result from an improved coefficient can easily be outweighed by an inefficient control system for the circulation pumps.

Coupling short-term (B2G model) and long-term (g-function) models for ground source heat exchanger simulation in TRNSYS. Application in a real installation

Ground-source heat pump (GSHP) systems represent one of the most promising techniques for heating and cooling in buildings. These systems use the ground as a heat source/sink, allowing a better efficiency thanks to the low variations of the ground temperature along the seasons. The ground-source heat exchanger (GSHE) then becomes a key component for optimizing the overall performance of the system. Moreover, the short-term response related to the dynamic behaviour of the GSHE is a crucial aspect, especially from a regulation criteria perspective in on/off controlled GSHP systems. In this context, a novel numerical GSHE model has been developed at the Instituto de Ingeniería Energética, Universitat Politècnica de València. Based on the decoupling of the short-term and the long-term response of the GSHE, the novel model allows the use of faster and more precise models on both sides. In particular, the short-term model considered is the B2G model, developed and validated in previous research works conducted at the Instituto de Ingeniería Energética. For the long-term, the g-function model was selected, since it is a previously validated and widely used model, and presents some interesting features that are useful for its combination with the B2G model. The aim of the present paper is to describe the procedure of combining these two models in order to obtain a unique complete GSHE model for both short- and long-term simulation. The resulting model is then validated against experimental data from a real GSHP installation.

The effect of heat transfer mode on heart rate responses and hysteresis during heating and cooling in the estuarine crocodile Crocodylus porosus

The effect of heating and cooling on heart rate in the estuarine crocodile Crocodylus porosus was studied in response to different heat transfer mechanisms and heat loads. Three heating treatments were investigated. C. porosus were: (1) exposed to a radiant heat source under dry conditions; (2) heated via radiant energy while half-submerged in flowing water at 23degreesC and (3) heated via convective transfer by increasing water temperature from 23degreesC to 35degreesC. Cooling was achieved in all treatments by removing the heat source and with C. porosus half-submerged in flowing water at 23degreesC. In all treatments, the heart rate of C. porosus increased markedly in response to heating and decreased rapidly with the removal of the heat source. Heart rate during heating was significantly faster than during cooling at any given body temperature, i.e. there was a significant heart rate hysteresis. There were two identifiable responses to heating and cooling. During the initial stages of applying or removing the heat source, there was a dramatic increase or decrease in heart rate ('rapid response'), respectively, indicating a possible cardiac reflex. This rapid change in heart rate with only a small change or no change in body temperature (