Share:
How It Works
The Eckert number tells you whether the kinetic energy of a flow is large enough to cause meaningful heating through viscous friction. It compares the flow's kinetic energy (v²) to the thermal energy stored across a temperature difference (cₚΔT).
When Ec is small, viscous dissipation is negligible and you can ignore frictional heating. When Ec is on the order of 1 or larger -- as in hypersonic flight or polymer extrusion -- the heat generated by friction significantly affects the temperature field.
Example Problem
Air flows at 300 m/s over a surface. The specific heat of air is 1,005 J/(kg·K) and the temperature difference across the boundary layer is 50 K. What is the Eckert number?
- Ec = v² / (2 × cₚ × ΔT) = 300² / (2 × 1,005 × 50)
- Ec = 90,000 / 100,500 = 0.896
An Ec near 1 means viscous dissipation is significant -- frictional heating must be included in the thermal analysis.
Frequently Asked Questions
What does the Eckert number tell you about a flow?
It quantifies how important viscous heating is relative to the overall temperature difference. When Ec << 1, frictional heat generation is negligible. When Ec approaches 1, the kinetic energy being converted to heat is comparable to the convective heat transfer driving the temperature difference.
When is the Eckert number important in engineering?
It matters most in high-speed aerodynamics (Mach 2+ flows), spacecraft re-entry, polymer and glass processing, and lubrication of high-speed bearings. In these cases, ignoring viscous dissipation leads to significant errors in predicted temperatures.
How is the Eckert number related to the Brinkman number?
The Brinkman number (Br) equals the Eckert number times the Prandtl number: Br = Ec × Pr. Both measure viscous dissipation effects, but Br also accounts for the fluid's thermal conductivity relative to its viscosity. For Pr ≈ 1 fluids like air, the two numbers are similar in magnitude.
Related Calculators
- Prandtl Number Calculator — ratio of momentum to thermal diffusivity, key to boundary-layer analysis.
- Nusselt Number Calculator — convective-to-conductive heat transfer ratio at a surface.
- Mach Number Calculator — velocity relative to the speed of sound, central to compressible-flow heating.
- Thermal Diffusivity Calculator — measure how quickly heat spreads through a material.
- Speed Converter — convert between m/s, ft/s, and other velocity units.