Jakob Number

Boiling and condensing move astonishing amounts of heat for very little temperature difference, and the Jakob number is the arithmetic behind why. It divides the sensible heat — the energy that changes the fluid's TEMPERATURE — by the latent heat, the energy that changes its PHASE: $\mathrm{Ja} = c_p\Delta T/h_{fg}$. Water at atmospheric pressure needs about 4.2 kJ to warm a kilogram by one degree and about 2257 kJ to boil that same kilogram. The ratio is roughly 540 to 1, so ten degrees of superheat on a boiling surface gives a Jakob number of about 0.019: under two percent of the energy crossing the surface goes into warming the liquid and the rest goes into making steam.

Because it is normally small, its usual role is as a licence to simplify. Condensation analyses assume the film is at the saturation temperature; boiling analyses assume the bubble leaves at saturation. Both are approximations that are excellent while Ja is small, and both acquire corrections when it is not. The best-known is Rohsenow's, which replaces $h_{fg}$ with $h_{fg}(1 + 0.68\,\mathrm{Ja})$ in film condensation to account for the film being genuinely subcooled below saturation on its way down the wall. At Ja = 0.02 that is a one percent adjustment nobody would bother with; at Ja = 0.3 it is a twenty percent adjustment that changes the design.

Where Ja becomes large is worth knowing, because it is usually a signal that the problem has left the regime the correlation was written for. It grows with the excess temperature, so a large Ja in boiling means a large wall superheat — and on water at atmospheric pressure, superheats beyond roughly 30 K carry the surface past the critical heat flux and into transition and then film boiling, where a vapour blanket insulates the wall and the coefficient COLLAPSES by an order of magnitude instead of improving. It also grows as pressure rises toward the critical point, because $h_{fg}$ falls to zero there while $c_p$ rises: near-critical boiling has Jakob numbers of order 1 and behaves nothing like the atmospheric case. And refrigerants have latent heats around a tenth of water's, so an ordinary evaporator superheat gives a Jakob number ten times larger than the same superheat on water would.

Two definitional cautions. The specific heat belongs to the LIQUID in most usages — it is the liquid film being subcooled or the liquid being superheated — though some vapour-side analyses use the vapour value, and the two differ by about a factor of two for water. And the $\Delta T$ is an EXCESS temperature: wall minus saturation in boiling, saturation minus wall in condensation. It is a difference in both cases, never an absolute reading, which is why this page types it as a temperature difference and would give a badly wrong answer if it did not.