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3-D heat transfer - Essay Example

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Glass is one of the major construction materials, and it is necessary to understand its behaviour under different conditions that it might have to face in service. One of the most common hazards faced in buildings is fire. …
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3-D heat transfer
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Download file to see previous pages Glass is one of the major construction materials, and it is necessary to understand its behaviour under different conditions that it might have to face in service. One of the most common hazards faced in buildings is fire. It is vital to know the behaviour of glass in case of a fire, so that we can understand what should be done to improve its performance It also helps us learn the length of time that glass can sustain before softening. This gives important information about rescue and emergency time frame for a building on fire. To understand the behaviour of glass in case of a fire, we need to model the heat transfer from the fire to the glass and the temperature distribution over the surface of the glass, as temperature is the main determinant of the properties of glass. Models can be simulated in 3 dimensions or in one dimension. Both will vary in complexity as well as in the accuracy of the results that they produce. The discussion ahead focuses on the difference between the two types of models, the complexities involved, the requirements for solution and the viability of using each of the two models, starting first with the 3-d model and then the 1-d model. The 3 dimensional heat transfer model is easy to imagine physically. The same, though, cannot be said about its modelling. The ease of the physical imagination is only because we can see it happen and sense all the variables. There are tens of variables, all of which cannot be understood mathematically, and thus have to be inculcated into the system as constants with inherent limitations. Before discussing the limitations, however, we shall start right at the basics of what makes a heat transfer model in such a situation and what variables are involved. The identification of the variables can be made easier by breaking the model down into different physical zones, such as the fire, the glass itself, and the medium in between the two. These will be discussed separately to identify determinants of heat transfer model. Fire is not a point source of light and heat; rather it is a big varying volume which can be thought of as multiple point sources. In terms of heat transfer, we are interested in the intensity of the radiation being emitted from the fire. Due to the variation of the intensity from point to point in the fire, we can express radiation as a function of position in space. This function though, changes from time to time as well, because the fire radiation intensity at one point does not remain the same at that point as time changes. Thus, we have to take fire radiation intensity as a function of time and spatial position. The previous discussion complicates mathematical interpretation in terms of modelling as the dependent parameters seem too independent and unpredictable. To resolve that issue, we have to understand that the fire radiation intensity at one point in space at a certain instant has a bearing on adjacent points in space at adjacent instants in time. Similarities to this property of fire can be found in fluid behaviour, suggesting that fire can be modelled as a fluid radiating heat. The continuity equation is the basis of modelling such a situation involving fluid flow. The problem of radiation and heat transfer is addressed by the heat equation, of course. Three dimensional dependency of fluid flow has to be taken into account in the form of partial differentials. As has already been discussed, the variable of time is involved as well. There are different methods of modelling fire as a point source, a group of point sources, block models and their variations. All these models have their limitations and advantages and these should be kept in mind. The heat that flows from the fire to the glass has to pass through a medium. Common sense suggests that the medium is, in most cases, air. But, due to the fire, smoke collects in the enclosed space as well. This changes the viscosity, absorptivity, conductivity and density of the medium drastically. Also, the heat flow is not only through the conductivity based heat equation, but ...Download file to see next pagesRead More
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