Thermatronic Stagnation (nothing to do with male deers)

Stagnation, not the land of male deer, more the tendency for something not to flow. Still brown dirty pools spring to mind (a spring being what they need most). Normally applied to air flow, a stagnation point is a point at which there is no flow whereas there is flow around it. Not knowing what your experiences are I don’t know whether to make an analogy to the middle of the eye of a hurricane or to the middle of the wake area behind a cars wing mirror. From a heat flow perspective there is a concept of thermal stagnation, or taking up from the previous ‘thermatron’ post, a thermatronic stagnation point.

(I like reading SF a lot. The use of Lagrange points to position or locate vessels has a small similarity here, enough to mention it).

Take a block sitting in free air that has a certain number of Watts being dissipated throughout its volume. (I build this model all the time in FloTHERM, my directories are littered with spent examples). At each point in that block thermatrons (the word used with the usual caveat of it not being bound by reality, sitting comfortably instead on the comfy sofa of analogy) are being introduced. First thing they try to do is to race towards the cold, wherever that might be. In this case the air surrounding the block. The air gets hot, starts to move, and thus continues to carry the thermatrons away. You end up with a nice thermal plume:

With the hot air moving upwards, pulling cold air in from the sides and underneath (arrows are air movement):

Now let’s look at the arrows that indicate the route the thermatrons take as they go from the cradle to their cold ambient nirvana:

Note that in the middle, towards the top, of the cuboid there is a point at which the thermatrons do not budge. Although not clear from the first temperature plot, it is this point that is the hottest within the block as those there thermatrons are getting mighty frustrated at their inability to get out.

Now instead of the block sitting in free space with a natural convection plume rising off it due to buoyancy, let’s blow lots of air over it from beneath (arrows are air movement):

Now look at how the thermatrons leave:

In the air, the thermatrons spread faster sideways, this is due to turbulent mixing (they’re not hitching a ride on a bus, more hitching a ride on those big spinning tea cups that your kids make you go on in ‘amusement’ parks).

The stagnation point has moved down into the middle of the cuboid.  Why? (had to write that, I am indeed making this up as I go along, helps if I talk to myself through my blog). I first thought this was due to the effect the air was having on the lower and upper faces of the cuboid. On closer inspection I think it is actually due to the fact that with air blasting from the underside, the sides of the cuboid, from bottom to top, are good at extracting the thermatrons via convection. From a fluid dynamics perspective the forced convection boundary layer (the air that moves close to the solid surfaces) develops very quickly along the vertical sides. Compared to the natural convection situation where  the air speed is faster towards the top of the vertical sides thus the heat would rather go towards that top section of the cuboid.

The ability for air to extract thermatrons from a solid surface can in fact be quantified as a surface ‘heat transfer coefficient’ HTC (W/m^2 degC). In this case it is the non-uniformity of the laminar natural convection boundary layer HTC distribution over the vertical sides that moves the point of maximum temperature from the middle. Once the flow is turbulent the HTC variation is both more uniform and that uniformity does not change with an increasing air speed, i.e. if you blow air over at 10x the air speed the location of maximum temperature (thermatronic stagnation point) would NOT budge.

(I think).

28th August 2009 Ross-on-Wye