Burn through locations

Fig. 1 - Hertzsprung-Russell diagram for stars of 15 and 20 M and composition appropriate to the LMC (Z /4) (solid lines) and to the sun (dashed lines) evolved through hydrogen, helium, and carbon burning. The location of the presupernova stars are indicated. The four-pointed star indicates the best estimated properties of SK-202-69. 

If, in an infinite plane flame, the flame is regarded as stationary and a particular flow tube of gas is considered, the area of the flame enclosed by the tube does not depend on how the term flame surface or wave surface in which the area is measured is defined. The areas of all parallel surfaces are the same, whatever property (particularly temperature) is chosen to define the surface and these areas are all equal to each other and to that of the inner surface of the luminous part of the flame. The definition is more difficult in any other geometric system. Consider, for example, an experiment in which gas is supplied at the center of a sphere and flows radially outward in a laminar manner to a stationary spherical flame. The inward movement of the flame is balanced by the outward flow of gas. The experiment takes place in an infinite volume at constant pressure. The area of the surface of the wave will depend on where the surface is located. The area of the sphere for which T = 500°C will be less than that of one for which T = 1500°C. So if the burning velocity is defined as the volume of unbumed gas consumed per second divided by the surface area of the flame, the result obtained will depend on the particular surface selected. The only quantity that does remain constant in this system is the product u,fj,An where ur is the velocity of flow at the radius r, where the surface area is An and the gas density is (>,. This product equals mr, the mass flowing through the layer at r per unit time, and must be constant for all values of r. Thus, u, varies with r the distance from the center in the manner shown in Fig. 4.14. 

The temperature in the condensed phase increases from the initial propellant temperature, Tq, to the burning surface temperature, Tj, through conductive heat feedback from the burning surface. Then, the temperature increases in the gas phase because of the exothermic reaction above the burning surface and reaches the final combustion temperature, Tg. Since the physical structure of AP composite propellants is highly heterogeneous, the temperature fluctuates from time to time and also from location to location. The temperature profile shown in Fig. 7.2 thus illustrates a time-averaged profile. This is in a clear contrast to the combustion wave... 

Figure 2.24 A human subject with a cut corpus callosum views a color Mondrian. Half of the color Mondrian is covered with black velvet. A purple test region is located at the center of the stimulus. The left half of the stimulus is processed by the right hemisphere of the brain and vice versa. The subject views the stimulus either directly or through a mirror. (Adapted by permission from Macmillan Publishers Ltd Nature, E. H. Land, D. H. Hubei, M. S. Livingstone, S. Hollis Perry, M. M. Burns, Nature, Vol. 303, No. 5918, pp. 616-618, Copyright 1983. Figure 2.24 shows the visual path (Figure 2.9) which is reproduced from Semir Zeki. A Vision of the Brain. Blackwell Science, Oxford, 1993, by permission from Blackwell Science Ltd.)...

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