Effect on scaling of heat removal requirements in three-dimensional systems

A first-order discussion of convective heat removal from a hypothetical 3-dimensional computing system is presented. A textbook treatment indicates that our heat removal capability can be characterized by a quantity Q, the amount of power we can remove per unit cross-section. Thus the minimum length of the system is proportional to the square root of the total power dissipated. We predict Q ∼ 10⁴Wcm⁻² assuming an applied pressure difference of 1 atm, a maximum temperature rise of 100K and the use of water as the coolant fluid.