Commonly-used relationships for heat and mass transfer in turbulent flow in channels take the form:
where Nu is the Nusselt Number; Sh, the Sherwood Number; α, the heat transfer coefficient; λ, the Thermal Conductivity; D, the tube diameter; β,the Mass Transfer Coefficient; and D12, the Diffusion Coefficient for a binary mixture (this is replaced by effective diffusivity in the case of a multicomponent mixture). From these two equations, it follows that:
where Le is the Lewis Number (= Sc/Pr). From Eq. (3), it follows that the ratio of mass transfer coefficient to heat transfer coefficient is given by:
which is known as the "Lewis Relationship". This relationship is particularly important in the air-water system, where the ratio α/βρas is known as the psychrometric ratio (b). Here, s is the humid heat, which is the amount of heat required to increase 1 kg of air plus its associated moisture by 1 Kelvin. For the air-water system, Le ≈ 1 and thus:
since, for the air-water system with low concentrations of water vapor (as in the atmosphere), C p ≈ s and b = 1. The implication of a unity value of b is that the adiabatic saturation temperature and the Wet-bulb Temperature are equal for the air-water system. Here, the adiabatic saturation temperature is defined as the temperature Ts reached by a gas stream containing a given amount of vapor, which is contacted adiabatically with a stream of liquid from where the vapor is derived, the temperature of the liquid at the entrance of the contactor also being at Ts.