Expert: Paul Soderman - 8/10/2009

Question
I would like to know how air friction heating is calculated.
Is there any equation or it is obtained by numerical methods from test results?
Does a shotgun bullet (at 80 m/s) experience that heating?

Thank you.

Answer
Rolando
This is a very good question.  All fluid flow past a surface generates heat, even shotgun bullets.  At low Mach number the heat is small, but as Mach number increases the heat generation becomes large.  The heat comes from the work done via shear stress in the flow.  As the flow is sheared a velocity gradient is created in the boundary layer near the surface.  Because of the variation in possible boundary layers and surface friction, no single solution is found.  Consider a simple Couette flow established by a sliding plate separated by fluid over a fixed plate, which creates a linear velocity gradient.  In that case the surface temperature, also called the recovery temperature is  related to the temperature at infinity.  It is also related to and less than the stagnation temperature of the flow.  The result is that the recovery temperature depends on the external flow temperature, Mach number squared, and Prandtl number.  The Pandtl number contains information on gas properties and viscosity.  I suggest a google search on Couette flow.  I found the thermal equation in Elements of Gas Dynamics by Liepmann and Roshko.
Paul