Governance by those who do the work.

Sunday, June 12, 2011

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 LHLW, 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 LH by LW rectangular isothermal plate inclined θ around the level edge which is LW long.


L* =LHLW / (2 (LH+LW))
R =min(LHLW)/2
Pr =cp⋅μ/k
Ra(L) =T|⋅g⋅ρ2cpL3 / (T⋅μ⋅k)
HHT*(Ra*) ={0.65 + 0.36 Ra*1/6}21≤Ra*≤1.5×109θ=−90°
T9.3(Ra) ={.825 +.387 Ra1/6

[1+(.492/Pr)9/16]8/27
}21≤Ra≤1012θ=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



No comments: