Free Convection from Rectangular Plate

Have completed a milestone in theory of convection  (corrected 2012-01-08) http://people.csail.mit.edu/jaffer/SimRoof/Convection/:



Free convection correlations for inclined rectangular plates involve characteristic-lengths L_H, L_W, and L* (area divided by perimeter). Each correlation is computed using its own characteristic-length. Flows are then compared and selected as convective surface-conductances (h).

Proposed is the complete free convective surface conductance for one side of a flat L_H by L_W rectangular isothermal plate inclined θ around the level edge which is L_W long.

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L* =	LH⋅LW / (2 (LH+LW))
R =	min(LH, LW)/2
Pr =	cp⋅μ/k
Ra(L) =	|ΔT|⋅g⋅ρ2⋅cp⋅L3 / (T⋅μ⋅k)
HHT*(Ra*) =		{0.65 + 0.36 Ra*1/6}2			1≤Ra*≤1.5×109		θ=−90°
T9.3(Ra) =	{.825 +	.387 Ra1/6 [1+(.492/Pr)9/16]8/27	}2		1≤Ra≤1012		θ=0°
Nu45(Ra) =		0.544 Ra1/5 [1+(0.785/Pr)3/5]1/3					θ=+90°

h = k⋅max(	Nu45(Ra(R)) R	,	T9.3(Ra(LH) cos θ) LH	)		0°≤θ≤90°		UCT3
h = k⋅max(	HHT*(Ra(L*) sin(−θ)) L*	,	T9.3(Ra(LH) cos θ) LH	)		−90°≤θ≤0°		UHT3

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