11. Macroscopic Energy Balance

Not to be confused with the heat transfer coefficient!!

Although this is rigorously true only for incompressible fluids, it is generally true that even for gases the dependence of enthalpy on pressure can be neglected.

Note the Nusselt number has an identical expression as the Biot number, Bi, defined in Eq. (9.​2.​3), as both dimensionless quantities represent the ratio between the total heat flux at the wall, J _U , and a conductive heat flux, J _Ud . However, in the definition of Bi, k and J _Ud denote the thermal conductivity and the heat flux inside the solid medium, which means that the two heat fluxes J _U , and J _Ud appearing in the definition of Bi take place in two different locations, i.e. one in the fluid (h) and the other in the solid medium (k). On the other hand, in the definition of Nu, J _Ud represents the heat flux at the wall that one would have if the heat exchange were exclusively conductive. Therefore, in this case, k denotes the thermal conductivity of the fluid, and the two heat fluxes J _U , and J _Ud appearing in the definition of Nu take place at the same location, i.e., within the fluid.

There a third flow arrangement, namely cross-flow, where the fluids travel roughly perpendicular to one another through the heat exchanger (see Sect. 11.3.2).

Generally, by exchange surface we denote the outer tube surface, as tubes are measured by their outside diameter.

We can also determine a lower bound, corresponding to the case where there is no fin at all, so that the heat exchanged across a surface area 2BW with heat flux hΔT is 2WBhΔT.

See Perry’s Chemical Engineers’ Handbook.