The Eckert number (Ec), first named in the early 1950s, is a dimensionless quantity useful in determining the relative importance in a heat transfer situation of the kinetic energy of a flow. It is the ratio of the kinetic energy to the enthalpy (or the dynamic temperature to the temperature) driving force for heat transfer
where U is an appropriate fluid velocity (e.g., outside the boundary layer or along the centerline of a duct), cp is the specific heat at constant pressure and ΔT is the driving force for heat transfer (e.g., wall temperature minus free stream temperature). For small Eckert number (Ec << 1) the terms in the energy equation describing the effects of pressure changes, viscous dissipation, and body forces on the energy balance can be neglected and the equation reduces to a balance between conduction and convection.
The Eckert number when multiplied by the Prandtl number (Pr) is also a key parameter in determining the viscous dissipation of energy in a low speed flow.
where η and λ are the dynamic viscosity and the conductivity, respectively, of the fluid. The parameter Ec · Pr (sometimes called the Brinkman number) is essentially the ratio of the kinetic energy dissipated in the flow to the thermal energy conducted into or away from the fluid.
When (Ec · Pr) << 1, the energy dissipation can be neglected relative to heat conduction in the fluid. For large (Ec · Pr) the energy dissipated is an important parameter in the heat transfer process and the kinetic energy can play a significant role in determining the temperature distribution in the flow and the overall heat transfer.