Emergency Time Frame for a Building on Fire - Essay Example

?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 also dependent on convection and radiation. These combine to make the fluid flow within the medium very complex. Also, with the continuously changing composition, it is mathematically improbable to be able to simulate the medium behaviour accurately. This is an inherent limitation in any simulation model. To evaluate the impact of the medium, its variables are treated as constants, and behaviours at different values of the constant are simulated separately and graphed together. This, although a limitation, is still a representative simulation, which can help in predicting many important aspects of this science. The third aspect of the model deals with the glass. From the perspective of materials science, we know that glasses do not have a periodic structure with microscopically uniform properties. This means that the thermal properties of glass that we might be interested in, are not uniform throughout the structure. That, though, is just a theoretical science consideration. From the mathematical point of view, we average out a possible range and test our models on constant values of properties such as thermal conductivity, heat capacity, reflectivity of heat, absorptivity and transmittance. Averaging out these properties does not affect the accuracy of the model as much as averaging out medium properties and flow model. One important point that comes in this model is the angle at which the heat flows to the surface of the glass at a certain point. The simulation model required for modelling the glass surface temperature distribution is the boundary equation. This is combined with the heat transfer through the glass medium based on its capacity, conductivity and instantaneous temperature. From the discussion above, it is evident that the 3-d model involves many complexities. These sometimes becomes too much of a task, as modelling is not a job for everyone. Thus, 1-d models are developed instead, with inherent limitations increased, but kept in mind. 1-dimensional models are relatively simple to develop, though the word “simple” should not be taken misleadingly. The different factors involved and required to be known for this model are again classified in terms of the three regions defined earlier. Fire modelling in this case is very easy. The 3 variables of position are cut down to just one. The only factors to be known are the distance between the point source and the point on the glass surface in that dimension. Fire intensity can be simulated as required to produce different radiation based and heat transfer models. The medium involved between the fire and the glass has to be treated in the same way as in the 3-dimensional model. One ease in the simulation is that the dimension can be modelled for different kinds of turbulent and streamlined flows and combined to study the effects of different modes. The simulation again is in the form of a single positional variable, thus the modelling is easier. In terms of the glass, we have only a single angle for which the values of thermal variables as well as reflectivity and absorption are needed. These can be accurately calculated, so this increases the accuracy of the model in this regard. One thing that should be kept in mind is that never in any real problem does a glass get heated at a single point only from a single angle. This model predicts a grossly reduced temperature than reality, which has to be catered to by using multiplication factors. This, though, is a very inaccurate method. Still, temperature distribution is relatively more accurate than the values of the temperature predicted. The discussion above has focused more on the factors that have to be catered to in the models and less on how the factors are mathematically combined to form equations and the equations worked upon to find solutions. The following section will talk about the mathematical models, the laws involved and the mathematical tools used to evaluate the models. The need of this discussion arises because that also determines how simple or complex a model might be. Equation of continuity is used to study flow parameters. The boundary equation is used when we have to study properties of the boundary layer of a certain solid body. Reynolds number is used to characterize turbulence of flow. This is a very important factor in modelling the flow. Momentum equation or the equation of motion is used when motion is involved. The continuity equation and the momentum equation are present in every such modelling problem. Black body radiation, heat equation, Fourier equation for heat conduction, and convection flow equations are used for heat transfer. These are some of the points that have been repeated to combine and review all the different equations and models discussed in the write up earlier. What was not discussed earlier was how all these equations combine to make a solution that can be meaningful. As is evident, there are too many equations to be solved analytically. To evaluate these, we combine them as coupled equations or do similarity transformation, which combines all equations to a single differential equation of non-linear high order. These are numerically evaluated to get the results that we need. The discussion has discussed in great detail the different variables involved in heat transfer from a fire to a glass surface in an enclosed system. The write up has discussed both 3-d and 1-d aspects of the system, and it is hoped that it will serve as a guide to help engineers and mathematicians work on simulations in this field that will help civil engineers and materials engineers alike in understanding properties of glass and its behaviour in fire. Read More