Page 476 - Modelling in Transport Phenomena A Conceptual Approach

456 CHAPTER 10. UNSTEADY MICROSCOPIC BAL. WITHOUT GEN.

Example 10.63 A hen’s egg of mass 50 grams requires 5 minutes to hard boil.
How long will it tuke to hard boil an ostrich’s egg of mass 3kg7

Solution
For an unsteady-state conduction problem, the mtio of the mte of accumulation
to the rate of conduction is qual to the Fourier number. Let subscripts h and o
represent hen and ostrich, respectively. Then, it is possible to equate the Fourier
numbers as we did in Example 10.1:

If both eggs are chemically similar, then ah = ao. Since volume and hence mass,
My proportional to Lzh, Eq. (1) redues to
is

Substitution of the numerical values into Eq. (2) gives the time required to hard
boil ostrich’s egg as

= 76.6min (3)

10.2.2.2 Solution for BiH < 0.1

When BiH < 0.1, internal resistance to heat transfer is negligible. Considering the
sphere as a system, the inventory rate equation for thermal energy can be written
as
Rate of energy in = Rate of energy accumulation (10.2-118)

or,
& 4
4xR2(h)(T&, - T) = - [- VR3PCP(T - T 4 (10.2119)
dt
3
&arrangement of Eq. (10.2119) gives

(10.2-120)

Evaluation of the integrations leads to

Tm-T=(T,-To)exp (10.2-121)
PCPR
3This problem is taken from Konak (1994).