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enigma October 29, 2009 02:53

Convective / Conductive Heat Transfer in Hypersonic flows
Hello there,

I've got a question concerning convective and conductive heat transfer. Let's imagine a cube in a hypersonic flow field, there will be a bow shock in front of the cube and there will be convective heat transfer to the surface of the cube.

The bit I'm struggling with is that people say, that there is ONLY convective (and radiative) heat transfer from the flow to the model and conductive heat transfer inside the model. Convective heat transfer depends on the heat transfer coefficient, this coefficient increases with velocity and temperature.

In our example, the edges of the cube will heat up most, more than the front surface does. Gas near the stagnation streamline is at zero velocity at the surface of the body, and hence, the convective heat transfer here is zero (zero velocity, zero heat transfer coefficient). Still, this region will heat up due to conductive heat transfer from the gas (at rest) to the surface of the model.

CFD only solves for convective heat transfer and I'm wondering where this conductive heat transfer (from the fluid to the surface) is? Is it somewhat implemented in the "conductive heat transfer coefficient"?

Any enlightment on the topic would be highly appreciated!
I hope that anyone in here can follow my thoughts!

Ananda Himansu October 29, 2009 08:45

When those people say, ONLY convection and radiation between flow and body, and conduction inside body, they are referring to a modeling approximation that lumps phenomena together.

More fundamentally, at the continuum level, there are simultaneously (a) flow of the fluid (with radiative heat transport within it, but this is neglected unless significant), (b) heat conduction between fluid and solid, (c) heat radiation between fluid and solid, and (d) heat conduction within the opaque solid. CFD codes based on detailed continuum physics will solve the conjugate heat transfer problem while accounting for all these effects in a direct way. The "solid conduction heat transfer coefficient" relates heat transfer within the solid to temperature gradients (within the solid), and the "fluid conduction H T coeff" does the same within the fluid.

The enhancement of phenomenon (b) by phenomenon (a), i.e., the enhancement of conduction by fluid flow, is termed convection. There are CFD codes that perform the modeling approximations of (1) neglecting unenhanced conduction between fluid and solid, and (2) using a Newton's convection law for the enhancement of conduction by fluid flow, be it forced or natural convection. The convection equation involves the heat transfer coefficient. The latter is usually modeled such that it is zero at zero flow velocity in forced or natural convection, thus neglecting the unenhanced conductive heat transfer. This is the model that the people you heard are referring to. The convection coefficient is a sort of an "enhanced conduction heat transfer coeff" for the conduction between fluid and solid, though using temperature differences rather than gradients.

So, to answer your question, CFD codes of the first (and more common) variety that account only for flow, conduction and radiation, will in principle correctly compute the temperature rise in the part of the solid next to the stagnation point due to heat conduction between stagnant fluid and solid. CFD codes of the second (and rarer) variety that account only for convection and radiation, will incorrectly compute this temperature rise (it will show a rise due to conduction from the rest of the solid, but not accounting for conduction from stagnant fluid to solid).

enigma November 1, 2009 23:53

This reply just hit the spot, precisely what I was looking for.

Thank you very much Sir,

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