Page 466 - Modelling in Transport Phenomena A Conceptual Approach

446 CHAPTER 10. UNSTEADY MICROSCOPIC BAL,. WITHOUT GEN.

The time required is
1 2
(')
t = -
4a 0.19
2
-
- (E) =43,283s-l2h (3)
4(4 x 10-7) 0.19
Comment: Note that when SI& = 2, Eq. (10.2-59) becomes
TI -T
-- - erf(2) = 0.995
Tl -To
indicating that T 21 To. Therefore, the penetration distance for heat, &, is given by
6t = 4 6

In this particular example, the penetration distance after 12 hours is

& = 4d(4 x 10-7)(12)(3600) = 0.53m

10.2.2 Heating of a Rectangular Slab: Revisited
In Section 10.2.1, the temperatures of the surfaces at z = f L are assumed constant
at TI. This boundary condition is only applicable when the external resistance to
heat transfer is negligible, Le., BiH > 40. In practice, however, it is not the surface
temperature but the temperature of the medium surrounding the slab, T,, that is
generally constant and the external resistance to heat transfer should be taken into
consideration. The governing equation for temperature is given by Eq. (10.2-7).
The initial and the boundary conditions are given by
at t=O T=T, for all z (10.2-62)
aT
at z=O -- t>O (10.263)
-0
az
t>O (10.2-64)

Introduction of the dimensionless quantities

(10.265)

(10.266)

(10.267)

(10.268)