Page 221 - Modelling in Transport Phenomena A Conceptual Approach

7.5. CONSERVATION OF ENERGY 201

The we of the Whitaker correlation, Eq. (4.3-30), gives
(
Nu = 2 + 0.4ReT +0.06R~$!~) (pm/p,,,)'14
= 2 i- b.4 (4826)'/2 + 0.06(4826)2/3] (0.712)0.4 ( 19.11 18.41 x 10-6)1'4

= 40.9
The average heat transfer coeficient is

= (40.9) ( 25*96 = 71 W/ m2.
K
0.015
Therefore, the time required for cooling is
(0.015)(8924)(387) In
t=
(6)(71)
The amount of energy transferred from the sphere to the air can be calculated from
t t
Qint = 1 &t dt = ~@(h) (T - T,) dt (3)
0
Substitution of Eq. (2) into Eq. (3) and integration yields

Note that from Eq. (2)

Substitution of Eq. (5) into Eq. (4) gives

Qint = (T) (Ti - T)
(&'p)cu

[(8924)(387)] (50 - 30) = 122 J

Verification of assumptions
Assumption # 1