# Can I neglect kinetic energy when modeling convective heat transfer for viscous, low mach airflow? Why or why not?

I'm looking at convective heat transfer for air flow over a solid at Ma=0.2. At this speed, it is plausible to model the flow as incompressible because of small density variations in the air. Normally, when modeling compressible flow, we include the kinetic energy term in the energy equation. But for viscous incompressible flow at this speed, is it necessary? Can I neglect kinetic energy as a component of the energy equation due to the incompressibility assumption?

The kinetic energy per unit volume will be $1/2 \rho u^2$, which is about 2800 $J/m^3$ for your conditions. Given that the volumetric heat capacity is ~ 1200 $J/m^3.K$ The most you'd get out of your KE is a few degrees K (if you're lucky), due to viscosity, rather than compression. Unless you're dealing with such a small $\Delta T$ between your gas and solid, that effect is probably unimportant.