A comparative study on applying the method of fundamental solutions to the backward heat conduction problem

We investigate an application of the method of fundamental solutions (MFS) to the backward heat conduction problem (BHCP). We extend the MFS in Johansson and Lesnic (2008) [5] and Johansson et al. (in press) [6] proposed for one and two-dimensional direct heat conduction problems, respectively, with the sources placed outside the space domain of interest. Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate and stable results can be obtained efficiently with small computational cost.

A method of fundamental solutions for transient heat conduction in layered materials

In this paper we investigate an application of the method of fundamental solutions (MFS) to transient heat conduction in layered materials, where the thermal diffusivity is piecewise constant. Recently, in Johansson and Lesnic [A method of fundamental solutions for transient heat conduction. Eng Anal Boundary Elem 2008;32:697–703], a MFS was proposed with the sources placed outside the space domain of interest, and we extend that technique to numerically approximate the heat flow in layered materials. Theoretical properties of the method, as well as numerical investigations are included.

Recovering boundary data in planar heat conduction using boundary integral equation method

We consider a Cauchy problem for the heat equation, where the temperature field is to be reconstructed from the temperature and heat flux given on a part of the boundary of the solution domain. We employ a Landweber type method proposed in [2], where a sequence of mixed well-posed problems are solved at each iteration step to obtain a stable approximation to the original Cauchy problem. We develop an efficient boundary integral equation method for the numerical solution of these mixed problems, based on the method of Rothe. Numerical examples are presented both with exact and noisy data, showing the efficiency and stability of the proposed procedure and approximations.

Computer methods for the heat conduction equation

The merits of various numerical methods for the solution of the one and two dimensional heat conduction equation with a radiation boundary condition have been examined from a practical standpoint in order to determine accuracies and efficiencies. It is found that the use of five increments to approximate the space derivatives gives sufficiently accurate results provided the time step is not too large; further, the implicit backward difference method of Liebmann (27) is found to be the most accurate method. On this basis, a new implicit method is proposed for the solution of the three-dimensional heat conduction equation with radiation boundary conditions. The accuracies of the integral and analogue computer methods are also investigated.

The preparation of a common technique for selecting counter flow and crossflow cooling towers

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Effect of cooling rate on intercritically reheated microstructure and toughness in high strength low alloy steel

High strength low alloy steels have been shown to be adversely affected by the existence of regions of poor impact toughness within the heat affected zone (HAZ) produced during multipass welding. One of these regions is the intercritically reheated coarse grained HAZ or intercritical zone. Since this region is generally narrow and discontinuous, of the order of 0.5 mm in width, weld simulators are often employed to produce a larger volume of uniform microstructure suitable for toughness assessment. The steel usedfor this study was a commercial quenched and tempered steel of 450 MN m -2 yield strength. Specimen blanks were subjected to a simulated welding cycle to produce a coarse grained structure of upper bainite during the first thermal cycle, followed by a second thermal cycle where the peak temperature T p2 was controlled. Charpy tests carried out for T p2 values in the range 650-850°C showed low toughness for T p2 values between 760 and 790°C, in the intercritical regime. Microstructural investigation of the development of grain boundary martensite-retained austenite (MA) phase has been coupled with image analysis to measure the volume fraction of MAformed. Most of the MA constituent appears at the prior austenite grain boundaries during intercritical heating, resulting in a 'necklace' appearance. For values of T p2 greater than 790°C the necklace appearance is lost and the second phase areas are observed throughout the structure. Concurrent with this is the development of the fine grained, predominantly ferritic structure that is associated with the improvement in toughness. At this stage the microstructure is transforming from the intercritical regime structure to the supercritically reheated coarse grained HAZ structure. The toughness improvement occurs even though the MA phase is still present, suggesting that the embrittlement is associated with the presence of a connected grain boundary network of the MA phase. The nature of the second phase particles can be controlled by the cooling rate during the second cycle and variesfrom MA phase at high cooling rates to a pearlitic structure at low cooling rates. The lowest toughness of the intercritical zone is observed only when MA phase is present. The reason suggested for this is that only the MA particles debond readily, a number of debonded particles in close proximity providing sufficient stress concentration to initiate local cleavage. © 1993 The Institute of Materials.

Experiments for CFD-modelling of cooling water and Insulation debris two-phase flow phenomena during loss of coolant accidents

The knowledge of insulation debris generation and transport gains in importance regarding reactor safety research for PWR and BWR. The insulation debris released near the break consists of a mixture of very different fibres and particles concerning size, shape, consistence and other properties. Some fraction of the released insulation debris will be transported into the reactor sump where it may affect emergency core cooling. Experiments are performed to blast original samples of mineral wool insulation material by steam under original thermal-hydraulic break conditions of BWR. The gained fragments are used as initial specimen for further experiments at acrylic glass test facilities. The quasi ID-sinking behaviour of the insulation fragments are investigated in a water column by optical high speed video techniques and methods of image processing. Drag properties are derived from the measured sinking velocities of the fibres and observed geometric parameters for an adequate CFD modelling. In the test rig "Ring line-II" the influence of the insulation material on the head loss is investigated for debris loaded strainers. Correlations from the filter bed theory are adapted with experimental results and are used to model the flow resistance depending on particle load, filter bed porosity and parameters of the coolant flow. This concept also enables the simulation of a particular blocked strainer with CFDcodes. During the ongoing work further results of separate effect and integral experiments and the application and validation of the CFD-models for integral test facilities and original containment sump conditions are expected.

Cooling of greenhouses using seawater:a solar driven liquid-desiccant cycle for greenhouse cooling in hot climates

Evaporative pads are frequently used for the cooling of greenhouses. However, a drawback of this method is the consumption of freshwater. In this paper it is shown, both theoretically and through a practical example, that effective evaporative cooling can be achieved using seawater in place of fresh water. The advantages and drawbacks of using seawater are discussed more generally. In climates that are both hot and humid, evaporative systems cannot always provide sufficient cooling, with the result that cultivation often has to be halted during the hottest months of the year. To overcome this, we propose a concept in which a desiccant pad is used to dehumidify the air before it enters the evaporative pad. The desiccant pad is supplied with a hygroscopic liquid that is regenerated by the energy of the sun. The performance of this concept has been modelled and the properties of various liquids have been compared. An attractive option is to obtain the liquid from seawater itself, given that seawater contains hygroscopic salts such as magnesium chloride. Preliminary experiments are reported in which magnesium chloride solution has been regenerated beneath a solar simulator.

Solar pond powered liquid desiccant evaporative cooling

Liquid desiccant cooling systems (LDCS) are energy efficient means of providing cooling, especially when powered by low-grade thermal sources. In this paper, the underlying principles of operation of desiccant cooling systems are examined, and the main components (dehumidifier, evaporative cooler and regenerator) of the LDCS are reviewed. The evaporative cooler can take the form of direct, indirect or semi-indirect. Relative to the direct type, the indirect type is generally less effective. Nonetheless, a certain variant of the indirect type - namely dew-point evaporative cooler - is found to be the most effective amongst all. The dehumidifier and the regenerator can be of the same type of equipment: packed tower and falling film are popular choices, especially when fitted with an internal heat exchanger. The energy requirement of the regenerator can be supplied from solar thermal collectors, of which a solar pond is an interesting option especially when a large scale or storage capability is desired.

Liquid desiccant dehumidification and regeneration process to meet cooling and freshwater needs of desert greenhouses

Agriculture accounts for ~70% of freshwater usage worldwide. Seawater desalination alone cannot meet the growing needs for irrigation and food production, particularly in hot, desert environments. Greenhouse cultivation of high-value crops uses just a fraction of freshwater per unit of food produced when compared with open field cultivation. However, desert greenhouse producers face three main challenges: freshwater supply, plant nutrient supply, and cooling of the greenhouse. The common practice of evaporative cooling for greenhouses consumes large amounts of fresh water. In Saudi Arabia, the most common greenhouse cooling schemes are fresh water-based evaporative cooling, often using fossil groundwater or energy-intensive desalinated water, and traditional refrigeration-based direct expansion cooling, largely powered by the burning of fossil fuels. The coastal deserts have ambient conditions that are seasonally too humid to support adequate evaporative cooling, necessitating additional energy consumption in the dehumidification process of refrigeration-based cooling. This project evaluates the use of a combined-system liquid desiccant dehumidifier and membrane distillation unit that can meet the dual needs of cooling and freshwater supply for a greenhouse in a hot and humid environment.

A method of fundamental solutions for radially symmetric and axisymmetric backward heat conduction problems

We propose and investigate an application of the method of fundamental solutions (MFS) to the radially symmetric and axisymmetric backward heat conduction problem (BHCP) in a solid or hollow cylinder. In the BHCP, the initial temperature is to be determined from the temperature measurements at a later time. This is an inverse and ill-posed problem, and we employ and generalize the MFS regularization approach [B.T. Johansson and D. Lesnic, A method of fundamental solutions for transient heat conduction, Eng. Anal. Boundary Elements 32 (2008), pp. 697–703] for the time-dependent heat equation to obtain a stable and accurate numerical approximation with small computational cost.

Effects of engine cooling water temperature on performance and emission characteristics of a CI engine operated with biofuel blend

The temperature of the coolant is known to have significant influence on engine performance and emissions. Whereas existing literature describes the effects of coolant temperature in engines using fossil derived fuels, very few studies have investigated these effects when biofuel is used. In this study, Jatropha oil was blended separately with ethanol and butanol. It was found that the 80% jatropha oil + 20% butanol blend was the most suitable alternative, as its properties were closest to that of fossil diesel. The coolant temperature was varied between 50°C and 95°C. The combustion process enhanced for both diesel and biofuel blend, when the coolant temperature was increased. The carbon dioxide emissions for both diesel and biofuel blend were observed to increase with temperature. The carbon monoxide, oxygen and lambda values were observed to decrease with temperature. When the engine was operated using diesel, nitrogen oxides emissions correlated in an opposite manner to smoke opacity; however, nitrogen oxides emissions and smoke opacity correlated in an identical manner for biofuel blend. Brake specific fuel consumption was observed to decrease as the temperature was increased and was higher on average when the biofuel was used. The study concludes that both biofuel blend and fossil diesel produced identical correlations between coolant temperature and engine performance. The trends of nitrogen oxides and smoke emissions with cooling temperatures were not identical to fossil diesel when biofuel blend was used in the engine.