| Ballpark calculation: 400km/h ~ 100m/s air intake cross section ~ 1m^2 ==> ~ 100m^3/s of air going through radiator density of air ~ 1kg/m^3 ==> ~ 100kg/s of air going through radiator specific heat of air ~ 1kJ/(kg * degC) ==> 100kJ/(s * degC) == 100kW/degC temperature difference between air entering and leaving the radiator ~ 10degC ==> 1MW So handling 2.5MW waste heat doesn't seem out of the question from this analysis. As another ballpark "upper bound" analysis, consider that copper is one of the most thermally conductive materials, with thermal conductivity ~ 400 Wm/(m^2 degC), let's round that up to 1kWm/(m^2degC). Let's assume that there is a thermal conducting surface of 1m^2 (i.e. the surfaces of the pipes that interface with the radiators). Let's assume that the copper is 1mm thick (= 1m/1000). Let's see what temperature difference would be needed to transfer 1MW of heat across: 1MW == 1kWm/(m^2degC) * 1m^2 * (1000/1m) * deltaT degC ==> deltaT ~ 1 degC which again doesn't seem out of the question. As another ballpark "upper bound", the convective heat transfer coefficient for forced air is ~ 100W/(m^2degC), which means that assuming that the radiator fins are 100 degC above the air temperature, in order for the fins to transfer 1MW of power to the air, you would need an area of 1MW == 100W/(m^2degC) * 100 degC * area m^2 ==> area ~ 100m^2 of surface area in the radiator, which doesn't seem unreasonable (a radiator 1m^2 area * 10cm deep, made up of thin plates spaced 1mm apart has this total surface area). So they Veyron dissipating ~ 1MW in waste heat at 400km/h doesn't fail any of these basic sanity tests. More complicated though is the interaction between the stages considered here. For example, how do we interface our 1m^2 of copper with our 100m^2 of radiator? Making the radiator fins thin lets us pack more surface area into the same volume, but also makes it difficult to keep the "edges" of the fins at a sufficiently high temperature so that they pull their weight transferring heat to the air: since the "copper tubing" has significantly less surface area, it only contacts (and thus transfers heat to) the radiator fins "sparsely". |