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Going by the definition of convective heat transfer coefficient from Wikipedia (which I have started to doubt; reason follows): $h=\frac{q}{\Delta T}$, where the $\Delta T$ is taken as the difference between fluid and solid surface. Generally the temperature of the fluid is taken as the free stream far field temperature, $T_{\infty}$.

But in Chapter 4 of Modern Engineering for Design of Liquid-Propellant Rocket Engines by Huzel and Huang, for calculating the convective heat transfer to the engine walls, the adiabatic wall temperature, $T_{aw}$, is used instead of $T_{\infty}$.

Also Prof.Manuel Martinez-Sanchez's MIT OCW notes describe along the same line:

The $T_{aw}$ temperature is shown dashed because, as we know it is not the actual gas temperature outside the gas boundary layer, but is the one driving heat. (page 3 of 12).

The definition of $T_{aw}$ is:

Adiabatic wall temperature is the temperature acquired by a wall in liquid or gas flow if the condition of thermal insulation is observed on it.

It is not the actual temperature of the fluid and also it is the temperature of the fluid considering adiabatic conditions.

Given this: Why is such a temperature used for calculating the convective heat transfer?

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    $\begingroup$ As with a lot of things in engineering, it’s a good estimate of reality, even if it isn’t perfect or exact. Often times, it’s convenient to assume that gas slows down adiabatically because we can derive expression for thermodynamic quantities analytically rather than computationally. $\endgroup$ – Paul Nov 10 '18 at 16:46
  • $\begingroup$ @Paul what does not make sense is the necessity to use the temperature of the gas so close to the wall for convective heat transfer. For conduction, adjacency makes sense as the transfer of material is not possible. But convection is a bulk phenomenon with considerable fluid movement. Why is Taw preferred? Is it just a overkill/conservative estimate for heat flux? $\endgroup$ – karthikeyan Nov 11 '18 at 10:48
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I don't know how to make this any more concise than the authors did, so here is the relevant page from Hill & Peterson, "Mechanics and Thermodynamics of Propulsion", 3rd printing, November 1970.

Note that they say the gas stagnation temperature can be used instead at the max heat transfer point.

enter image description here

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  • $\begingroup$ A very nice and apt explanation for why Twa is not T_stag. But still, the reason to use the Twa for heat transfer is not clear! Thanks for the reference! $\endgroup$ – karthikeyan Nov 11 '18 at 10:46

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