Page 465 - Modelling in Transport Phenomena A Conceptual Approach

10.2. ENERGY TRANSPORT 445

Further simplification of Eq. (10.2-57) gives

(10.259)

The rate of heat transfer into the semi-infinite slab of cross-sectional area A is

(10.2-60)

The amount of heat transferred is

t
&= J Qdt
0
- 2Ak (Ti - To)&
- (10.2-61)
6

Example 10.2 One of the surfaces of a thick wall is exposed to gases at 350°C.
If the initial wall temperature is uniform at 20"C, determine the time requid for
a point 5 cm below the surface to reach 280 "C. The thermal diffwivity of the wall
is 4 x 10-~ m2/ s.

Solution

Assumption
1. The Biot number is large enough to neglect the external resistance to heat
transfer so that the surface temperature of the wall is almost equal to the gas
temperature.

2. Since the wall thickness is large, it may be considered as a semi-infinite
medium.
Analysis

The left-side of Eq. (10.2-59) is

TI - T
-- - 350 - 280 = 0.212
TI -To 350-20
Therefore,