Page 451 - Bird R.B. Transport phenomena

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Table 14.2-2 Asymptotic Results for Local Nusselt Numbers (Thin-Slit Flow)"'' ; Nu loc = 4/* loc
Constant wall temperature Constant wall heat flux

/ T
I
All values are 2 = 0 M t M
local Nu numbers <> 2B

\l/2
Thermal entrance Plug flow (A) Plug flow (G)
region^

(v )B 2 1/3
z » 1 Laminar non- (B) Laminar non- (H)
az 9 1/3 Гф L a z V da
Newtonian flow Newtonian flow

(v )B 2 1/3 4Гф l/3
Laminar Nu = 1/3 z az (C) Laminar Nu = 31/3 az (I)
Newtonian flow 3 Г(|) Newtonian flow

2
Plug flow Nu - тг = 9.870 (D) Plug flow (J)

Thermally fully Laminar non- Nu = 4/3?, where fi } is the lowest Laminar non- (K)
developed flow Newtonian flow eigenvalue of Newtonian flow

2
(v )B 2 d X 2
z
az « 1 + р ф(о)Х„ = 0; X (±l) = 0 (E)
п
If
Laminar Nu = 7.541 (F) Laminar Nu = Щ = 8.235 (L)
Newtonian flow Newtonian flow

2
" Note: ф(о) = v /(v ), where a = y/B; for Newtonian fluids {v )D /az = 4 RePr(B/z) with Re = 4B<i;>p/|UL. Here a = k/pC .
z z z z p
h
J. M. Valstar and W. J. Beek, De Ingenieur, 75, No. 1, Ch. 1-7 (1963).
c 2 2
The grouping (v )B /az is sometimes written as Gz • (L/z) where Gz = (v )B /aL is called the Graetz number; here L is the length of the slit past 2 = 0. Thus the
z
z
thermal entry region corresponds to large Graetz number.