Page 474 - Modelling in Transport Phenomena A Conceptual Approach
P. 474
454 CHAPTER 10. UNSTEADY MICROSCOPIC BAL. WITHOUT GEN.
Analysis
It is first necessary to calculate the average heat tmnsfer coeficient. The Reynolds
number is
The use of the RantMarshall correlation, Eq. (4.3-29)) gives
Nu = 2 + 0.6Reg2 Pfi3
= 2 + 0.6 (22, 043)1/2(0.716)1/3
= 81.7
The average heat transfer coeficient is
= 19.9 W/ m2. K (3)
The Biot number is
- (19.9) (5 x
-
0.51 = 1.95 (4)
From Eq. (10.2-log), the first root is XI = 2.012. Considering only the first tern
of the series in Eq. (10.2-112) gives
The time required for the surface of the orange, i.e., E = 1, to reach 0°C is
-3- 0 sin 115.3 - 2.012~0s 115.3 e- (2,012)2T sin 115.3
2.012 - sin 115.3 cos 115.3 (6)
in which 2.012rad = 115.3'. Solving for r yields
T = 0.26 (7)
Therefore, the time is
rR2
t=-
a
- (0.26)(5 x 10-2)2 = 5200s N 1 h 27min
-
1.25 x 10-7
