I have been researching the ECAT sized metal spheres in order to determine the expected behavior as their diameters are varied. This has lead to some interesting results which I share on occasion with the vortex in the hope that the insight will spark ideas within the group. Whether or not this information is helpful is left to the discretion of the readers.
My assumed system consists of 100 grams of nickel generating 10000 watts of heat power. Each reaction releases 5 MeV of energy. The actual physical source of the energy is not taken into consideration since that is not generally understood as of this time. My crude model consists of a very large quantity of nickel spheres of an assumed diameter such that the total mass is as listed above. One of my variables is obviously the diameter of each sphere which is modified in an attempt to understand what might be expected as this dimension is changed. For the following results I am attempting to estimate the temperature of a single sphere in open space that emits all of the energy generated within without having any incoming radiation to balance since it sees cold space as it looks outward. In normal operation each sphere will be surrounded by the thermal environment so that it must operate at a higher temperature than my calculation suggests and that is one of the paths that I am pursuing in further research. The calculations that I am posting would therefore represent a low extreme temperature value that could not be reduced if the power output constraints are to be met. I chose an emissivity of .8 for the nickel material, but this can be modified if anyone has a better estimate and wants me to take it into consideration. The radiation from the surface is assumed to be normal to the sphere surface. I calculate that the temperature of the 10 micrometer diameter test sphere is 425 K degrees (152 C) in open space. This is the minimum temperature that the surface of the sphere supports which will result in the expected radiation level. If the sphere is surrounded by other spheres or parts of the system at an operating temperature that is required to transfer energy to the load by radiation the temperature will have to increase in order to deposit its portion of the total energy. Conduction and convection are not taken into consideration for this calculation. The absolute surface temperature of each sphere must increase as the diameters increase. This is not too surprising since the total surface area of the large collection of spheres is reduced as the diameter of each sphere increases. Since the power is assumed constrained at 10000 watts the surface power density by necessity must rise. My model was tested with varying diameters of spheres and the relationship appears to follow an interesting function. It so happens that the absolute temperature is directly proportional to the forth root of the diameter ratio. To clarify the calculation, you take the desired sphere diameter and divide it by the original diameter first. Then take this ratio and raise it to the .25 power. The result will be the absolute temperature ratio expected for radiation of a constant total power. In the case that I use as reference you would obtain: initial 10 micrometer sphere collection, with absolute temperature of 425 K: desired 160 micrometer diameter spheres. Calculate 160 micrometers/10 micrometers = 16. Take the forth root of 16 and obtain 2. Since the 10 micrometer spheres reach 425 K, the 160 micrometer spheres should be at 850 K (578 C) as the calculated value. The numbers are rounded for clarity. Dave
