Page 270 - Modelling in Transport Phenomena A Conceptual Approach

250 CHAPTER 8. STEADY MICROSCOPIC BALANCES WITHOUT GEN.

The temperature dist7dbution in the ice block under steady conditions can be deter-
mined from Eq. (H) in Table 8.1 as
Tm-T
z
-- --
T, -Ts L
Therefore, the steady heat flm through the ice block is given by

For the ice block, the macroscopic inventory rate equation for energy is

-Rate of energy out = Rate of energy accumulation (3)
- (4)
If the enthalpy of liquid water at Tm is taken as zero, then the enthalpy of solid ice
is

Negligible
Therefore, Eq. (3) is expressed as

For the unsteady-state problem at hand, pseudo-steady-state assumption implies
that Eq. (2) holds at any given instant, i.e.,

Substitution of Eq. (6) into Eq. (5) and rearrangement gives

lLLdL= - f(T, - Ts)dt
pi 0
Integration yields the thickness of the ice block in the fonn

8.2.1.1 Electrical circuit analogy
Using the analogy with Ohm’s law, i.e., current = voltage/resistance, it is custom-
ary in the literature to express the rate equations in the form
Driving force
Rate = (8.2 10)
Resistance