If I need energy and my reactor emits heat while creating something
like electricity, why can't I simply surround my reactor with
something like a mantle of solar sails, so I could harness the heat
and transform it into power
It is all about Power Density
Military ship needs high power density (HUGE!!!). It needs it for:
- manuevering as thrust $F = P/I_{SP}$ ($P$ is power, $I_{SP}$ is specific impuls). You want to have very high specific impulse, because that's the only way how to achieve high velocity using limited storage of propelent (see Rocket Equation for details). So yur power requrement is $P = F I_{SP}$ where both $I_{SP}$ and $F$ you want to have as high as possible. But if the ship should be maneuverable it should be also very light, because maneuvering is about acceleration $a = F/m = P/(mI_{SP}) $. So $P/m = aI_{SP}$ ... and $P/m$ is your power density.
- weapons obviously you want to have as much power for weapons as possible, not only because you want to deposite as much energy to the target with your laser (and ablate its armor), but also you want to reach the far distance target fast with your railgun, which means your projectile must have high muzzle velocity. And muzzle velocity scales $v_{muzzle} \approx P^3$ (I don't want to derive it here, but believe me). Yet, you still want to keep the weapon light for the same reason as the whole ship should be light - it must be manueverable!
You can use waste heat as power source for next-process, but ...
Clearly you can e.g. use waste heat irradiated from engine of Daedalus Project to heat some watter, produce steam, than use turbine to make electricity. It is Molybedenum sphere of 1000m radius 1600K hot, that is a lot of waste heat! (According to Stefan-Boltzman law it is 2*pi*1000^2 [m^2] * 1600[K]^4 * 5.6e-8 ~ 2.3 TW of power (i.e. like 2000 decent nuclear powerplants ) or half of current humanity electricity consumption). =>
I guess you would need some sort of heat engine (biler, turbine etc.) of size of these 2000 nuclear power plants. Perhaps you can miniaturize it a bit (using better materials, like steel instead of concrete), but still it would be HEAVY.
Run, It is a Pyramide scheme ! :-)
all this only illustrates general picture which is a cascade (Djoser pyramide)
- every step of this cascade (pyramide) is at lower temperature (using waste heat from cooler of previous step)
- Therefore it needs more heavy machinery and space (e.g. area), because heat engines operating at lower temperature needs to be bigger for the same power
Why it is so?
One problem is Carnot efficiency $\eta = 1-T_C/T_H$, so in order to have high efficiency you need high difference between Heater temperature $T_H$ and cooler temperature $T_C$. If you have low efficiency you need to both produce and cool lot of heat, but you gain just little work.
More importaint problem is density of Heat flux. Heat flow differently in different environment/setting. But everywhere heat flows faster at high temperature. This makes sense, because Heat is transfered by some particles (e.g. moleculers of gas, electrons of metal, or photons from radiator). The higher temperature the more energy there is per particle, and the faster the particles are (=> higher flux or current of particles). It is loosly connected to 3rd law of thermodynamics but not very clearly, so I guess my explanation whit speed of particles is more clear.
The difference is sometimes HUGE, just consider how much area of radiators you would need to cool your steam powerplant (using waste heat from Daedalus main engine). So you have 40% Carnot efficieny, threfore you gain 0.92 TW of useful work and 1.38 TW of waste heat in form of hot watter (Assume T~100C=400K), so using Stefan-Boltzman law from above you need ~1e+9 m^2 of radiators ( that is square with side 33 km ) ! => You can do that, but your space-ship will be significantly heavier.
in effect circumventing ANY heat issues in the process?
You cannot. you always need cooling, because every usefull device on the ship need to do work and work can be only created at the expense of dissipating some heat (=cooling). This is absolutely general and essential 2nd law of thermodynamics. It has something to do with information (you don't have full information about position and velocity of every particle of photon, so you cannot employ them exactly as you want), seem Maxwell Daemon (but I don't want to go to much into theoretical physics). The best what you can do is expressed by Carnot Cycle and Carnot efficiency mentioned above. You may think this is something specific for steam engine (as I was thinking when I was young), but It is not, Carnot efficiency is absolutely general law for any device which turns heat into work.