Learning Forum

[prajput]

Hello, I'm trying to understand the viscous fluid flow. The energy equation has a term called viscous dissipation. Why is this part of the energy equation and how do I understand this better?

[Karthik Remella]

Viscous dissipation is generally talked about in high speed turbulent flows, especially in cases where heat transfer is extremely important. At these speeds, the kinetic energy due to the motion of the fluid (in this case, the turbulent kinetic energy) causes a change in the internal energy of the fluid (thermal energy). This process is irreversible and leads to localized heating of the fluid. The viscous dissipation term shows up in the energy equation of the fluid. Usually, the viscous dissipation term is negligible compared to the diffusive and convective terms. However, in case of aerodynamic heating in high speed transonic and supersonic flows, this term is extremely important.

[prajput]

How do I understand whether I should include this in my analysis?

[Karthik Remella]

You should take a look a non-dimensional number called the Brinkmann Number. It gives an indication of how important is the heat produced by viscous dissipation compared to the heat that gets transferred via molecular conduction. You can calculate the Brinkmann Number as

Br = mu * U_e^2 / (k * delta_T)

Here, delta_T represents the temperature difference in the system.

If Br > 1, viscous dissipation effects must be included in the fluid flow analysis.