Water Cooling a Personal Computer

Suppose that any one component has a power demand $P$ with a constant fraction $f_q$ going to heat output. The component hot temperature $T_h$ in air cooling $T_a$ will be approximated from the equation

$$f_q P = h_a A(T_h - T_a) $$

where $h_a$ is the convection coefficient and $A$ is the component area. For a given power load, to bring the temperature from $T_h$ to a desired temperature $T_d$, you will need to pull out a heat load $dot{q}_d$ to satisfy the revised equation

$$f_q P = h_a A(T_d - T_a) + dot{q}_d $$

This leads to $dot{q}_d = h_a A (T_h - T_d)$.

When you water cool, that extra heat load is taken by heat exchanger equations

$$dot{q}_d = U A (T_d - T_{wi}) = dot{m}_w tilde{C}_{pw}(T_{wo} - T_{wi}) $$

where $U$ is an exchanger coefficient, $dot{m}$ is the mass flow of water, $tilde{C}_{pw}$ is the specific heat of water, and $T_{wj}$ are the in and out temperatures of the water over the component.

The maximum efficiency of the water cooling is when $T_{wo} = T_d$. Substituting back gives this general governing formula for a perfect system

$$h_a A (T_h - T^star_d) = dot{m}_w tilde{C}_{pw}(T^star_d - T_{wi}) $$

You know the values of $A$, $T_h$, $T^star_d$ (the desired temperature for a perfect system), $tilde{C}_{pw}$, and $T_{wi}$. Estimate the value of $h_a$ and you can find the water mass flow you need in a perfect case.

Because the heat exchange cannot be perfect, $T_{wo} < T^star_d$ and the actual $T_d$ will be higher than the calculated $T^star_d$. The device will not cool as effectively. The trade-off that you might consider to increase $dot{m}_w$ is not as effective as to decrease $T_{wi}$.

This is for one component. When you work multiple components in parallel, each component behaves as above. When you work multiple components in series, the $T_{wi}$ temperature of an upstream component is the $T_{wo}$ temperature of its downstream component.

If you ran the entire system in series, then every heat source would get the same flow, so you would have to design the flow for the heaviest use component.

Running the system in parallel is no different from a central AC system. These are usually balanced via dampers (valves for water) to restrict flow to the lower heat rooms. You would need a way to measure the outlet temp of the water from each heat source. An industrial system might have control valves to control the flow to different loops; basically a cooling tower system.