Heat Transfer · interactive
Blow fluid across a hot plate and a thin, sluggish layer clings to the surface — the boundary layer, where all the action is. Its thickness sets how hard heat has to fight its way out. Speed up the flow, change the fluid, and watch the layer thin, trip into turbulence, and carry heat away faster.
Flow over a heated plate · boundary layers growing left → right
Local heat-transfer coefficient h(x) along the plate
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Right at the wall the fluid is stuck (the no-slip condition), and far away it moves at full speed. In between sits the boundary layer — a thin sheared region that grows downstream like δ ≈ 5x/√Re_x. Heat leaving the plate has to cross this layer by conduction before the bulk flow can sweep it away, so a thinner layer means a steeper temperature gradient at the wall and a higher heat-transfer coefficient. That's why blowing harder cools faster: it pins the layer thin.
The Prandtl number Pr = ν/α compares how fast momentum diffuses versus heat. For air (Pr ≈ 0.7) the thermal layer is slightly thicker than the velocity layer. For water (Pr ≈ 6) heat diffuses sluggishly and the thermal layer is much thinner, nested inside. For engine oil (Pr ≈ 10⁴) it's a sliver. Switch fluids and watch the red thermal layer slide relative to the blue velocity layer: δ/δₜ ≈ Pr^(1/3).
Once Re_x passes about 5×10⁵, the orderly laminar layer trips into turbulence. It suddenly thickens — but the violent mixing scrubs heat off the wall far more effectively, so h jumps up (note the kink in the h(x) plot). Long plate, fast flow, or thin fluid all push the transition point upstream. Crank the velocity and watch the yellow transition marker march toward the leading edge.
EngineeringCandy · Blasius & turbulent flat-plate correlations, computed live · blow on it, break it, learn