On Tue, Nov 22, 2011 at 10:33 PM, Berke Durak <[email protected]> wrote:
> > > You would need to cover 7 times the area in a matter of minutes, also not > > plausible, and it would still require 7 times the heat transport rate > from > > the core, which doesn't depend as simply on the area of contact. > > As the diagram shows, heat flow into water depends extremely > non-linearly on the temperature differential. It is non-linear with the temperature difference between the surface and the water, because of the complication of the phase change. But the heat flow in the solid metal of the ecat is proportional to the temperature gradient. And whatever heat is removed from the surface has to be replaced by conduction through the ecat heating elements. It also depends > more or less linearly on area of contact. We don't know what the > inner geometry of the devices, No, but we don't need to know that to know that the heat flow is proportional to temperature differentials (absent phase changes in the metal). > and we don't know how the water level > changes. > But we can put limits on the *increase* in the water level based on the input flow rate. And on the scale of minutes, you can ignore this. So you cannot say that an increase in power transfer of x times > requires an increase in core temperature of x times, because that can > be achieved by a small increase in temperature, or a proportional > increase in area of contact. > I think you can say it. You only need a small increase in the surface temperature, but if you remove heat from the surface 7 times faster, then you need to supply heat *to* the surface 7 times faster. That means you need a temperature gradient 7 times steeper, and since the surface temperature doesn't change much, the core temp (less 100C) would have to increase by 7 times. > Also, do you know what the thermal mass of the reactor is? I don't. > What we know is how long it takes to heat it up to the point necessary for the onset of boiling. That time constant is *determined* by the thermal mass. So we can use the rate it heats up during pre-heating to estimate the rate it would heat up to reach full vaporization. This is not perfect, because we don't know the actual temperatures at the boiling onset. But the required rate is so much greater increasing the rate of heat transport by a factor of 7 in 1/60th of the time that detailed knowledge isn't needed to realize it is not plausible. > > Thus, in principle, the area of contact can be increased easily by > changing the water level as demonstrated in the following example. > No it can't. At the input flow rate of 675 kg/h, in two minutes, each ecat gets about .2 L added, which changes the depth by less than 1 %. You can't get 7 times the area coverage in a few minutes by changing the depth. And even if you could, it doesn't change the fact that when you remove the heat 7 times faster, it has to be replaced 7 times faster. You still need to transport the heat through the thermal mass of the ecat. Control the heating element using feedback from the thermocouple to > keep T constant above the boiling point of water. By matching the > flow rate to the evaporation rate using the water level sensor, you > keep the water level l constant. > The flow rate was fixed. The customer measured it with gauges he added at the last minute, and then a constant flow rate was used for the calculations. > > To the first approximation, the power transfer should be proportional > to the area of contact which is proportional to the water level. An > electric heating element can have quite a small thermal mass. The > current can be ramped up very quickly. > But then why does it take 2 hours before the water flowing through is at the boiling point? > So if you start pumping more, the water level rises, and so does the > evaporation rate and the power transfer. The pumps were run close to capacity, so there is no way you can account for 7 times the area in a few minutes by adding water. > In principle, you just have > to control the pumps and provide enough power to have a dQ/dt as high > as you wish (within limits, of course). > Right, and the limits of the flow rate and the heat transport through the ecat mean it would take hours to reach 470 kW from 70 W.
