Energy generation flat plate

Generation of internal energy finds many important applications in engineering. Examples are electric heaters, nuclear reactors, exothermic chemical reactions, etc. In this section we shall consider variable as well as uniform energy generation in flat plates, cylinders, and spheres. Also, the conductivity will be assumed variable in some of these considerations. 

Let the rate of energy per unit volume u " x) be generated in a flat plate and let the thickness and the thermal conductivity of the plate be 2i and k(T), respectively. Under steady conditions, the total energy generated in the plate is transferred, with a heat transfer coefficient h, to an ambient at temperature Too This plate could be one of the fuel plates of a nuclear reactor core or one of the elements of an electric heater.4... 

Figure 2.12 (a) Flat plate with energy generation, (b) first law for the system of flat plate. 

The second corresponds to our key problem for the flat plate (of thickness l). Because of the symmetry with respect to the middle plane, each surface of the plate transfers one-half of the energy generated within the plate, that is,... 

Having learned the effect of energy generation on flat plates, we proceed now to the effect of energy generation on cylinders and spheres. ... 

The temperature distribution in a flat plate, solid cylinder, and solid sphere with internal energy generation given respectively by Eqs. (2.55), (2.98), and (2.100) are sketched in Fig. 2.22 for l = R. For the same v ", the temperature levels in the cylinder and sphere respectively are 1/2 and 1/3 of those in the flat plate. Increasing the effect of curvature increases the heat loss, as expected. 

The shield of a nuclear reactor can be idealized by a large flat plate 25 cm thick having a thermal conductivity of 4 W/m-K. Radiation from the interior of the reactor penetrates the shield and generates energy in the shield which decreases exponentially from a value of 200 kW/m3 at the inner surface to a value of 20 kW/m3 at a distance of 12.5 cm from the interior surface. For the case where the exterior surface is kept at 40 °C by forced convection, determine the temperature at the inner surface of the shield. 

For an application of the foregoing general considerations, reconsider the flat plate (key problem) of Section 2.3, Let the uniform internal energy u " be suddenly generated and thereafter held constant in the plate which has a uniform initial temperature Foe-The governing equation for a variable conductivity, obtained. from the one-dimensional form of Eq. (3.73), is... 

Three types of measurements were performed in this study. First, photodissociation cross sections were measured, in which the total photofragment yield was measured as a function of dissociation photon energy. In these experiments, the electron signal generated by the microchannel plates is collected with a flat metal anode, so that only the total charge per laser pulse is measured. The beam block is 3 mm wide for these measurements. 

The core of a pool reactor is composed of flat fuel plates of thickness 71. Both sides of each plate are covered with fiat clads, each of thickness L. Assume that the gap between the fuel plates and the clads is negligible. Nuclear energy is generated only in the fuel plates (Fig. 2.20). Under steady conditions, this energy is transferred, with a heat transfer coefficient h, from the clads to an ambient at temperature %0. We wish to know the maximum temperature in the fuel plates. 

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