Page 362 - Modelling in Transport Phenomena A Conceptual Approach

342 CHAPTER 9. STEADY MICROSCOPIC BALANCES WITH GEN.

term
On the other hand, the use of ~(P(V~)~) instead of pressure is not apprG
priate since this term comes from the Bernoulli equation, which is developed for
no-friction (or, reversible) flows.
Therefore, in the case of a fully developed laminar flow, attributing a physical
significance to the Reynolds number is not correct. For a more thorough discussion
on the subject, see Bejan (1984).

9.2 ENERGY TRANSPORT WITHOUT
CONVECTION

For steady transport of energy, the inventory rate equation takes the form
( Rate of ) - ( Rate of ) + ( Rate of

energy in energy out energy generation ) =o (9.21)

As stated in Section 5.2, generation of energy may occur as a result of chemical and
nuclear reactions, absorption radiation, presence of magnetic fields, and viscous
dissipation. It is of industrial importance to know the temperature distribution
resulting from the internal generation of energy because exceeding of the maximum
allowable temperature may lead to deterioration of the material of construction.

9.2.1 Conduction in Rectangular Coordinates

Consider one-dimensional transfer of energy in the z-direction through a plane
wall of thickness L and surface area A as shown in Figure 9.5. Let ZR be the rate
of energy generation per unit volume within the wall. In general, R may depend
on z.

Fluid B
ttt

TB . <hg>

Figure 9.5 Conduction through a plane wall with generation.