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 D_{12}, 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/βρ_{a}s 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 T_{s} 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 T_{s}.

Heat & Mass Transfer, and Fluids Engineering