# Does aerodynamic heatings at the wall depend on the material of the wall itself?

I am reading "Fundamentals of Aerodynamics" 5th edition, J.D.Anderson. He said:

"The slope of the temperature profile at the wall is very important; it dictates the aerodynamic heating to or from the wall. Let $(dT/dy)_{y=0}$be definedas the temperature gradient at the wall. Then the aerodynamic heating rate (energy per second per unit area) at the wall is given by: $$q_{w} = -k\left(\frac{dT}{dy} \right)_{y = 0}$$ where k is the thermal conductivity of the gas, and the minus sign connotes that heat is conducted from a warm region to a cooler region, in the opposite direction as the temperature gradient. We note that k is a physical property of the fluid, and is a function of temperature"

It seems like the aerodynamic heating does not depend on the material of the wall, which in normal sense, it should depend. Why was that ?

• I'm more confused as to why the temperature profile increases through the boundary layer and then decreases again. Surely temperature doesn't normally 'bunch up' like that? – Time4Tea Aug 15 '18 at 0:54
• @Time4Tea I strongly believe that curve was arbitrary. The important point here is the author want to express the term dT/dy at the wall. – Dat Aug 15 '18 at 15:19
• You are probably right that it is arbitrary. I think it's very confusing though, to use such a non-physical diagram as an example in a text book. It implies that heat is being generated within the boundary layer and flowing in both directions to the free stream and the wall. – Time4Tea Aug 15 '18 at 15:55

• Do you mean: $q_w = k_{property of the air}(dT/dy)_{air side} = k'_{property of the material of the wall}(dT/dy)_{wall side}$ ? Because k $\neg$ k' so dT/dy is discontinuous at the wall ?? Am I right? – Dat Aug 16 '18 at 2:38