Page 303 - Modelling in Transport Phenomena A Conceptual Approach

8.3. ENERGY TRANSPORT WITH CONVECTION 283

Since the fin efficiency is inversely proportional to A, it can be improved either
by increasing IC and B, or by decreasing (h) and L. If the average heat transfer
coefficient, (h), is increased due to an increase in the air velocity past the fin, the
fin efficiency decreases. This means that the length of the fin, L, can be smaller
for the larger (h) if the fin efficiency remains constant. In other words, fins are not
necessary at high speeds of fluid velocity.

8.2.4.3 Comment

In general, the governing differential equations represent the variation of the de-
pendent variables, such as temperature and concentration, as a function of position
and time. On the other hand, the transfer coefficients, which represent the inter-
action of the system with the surroundings, appear in the boundary conditions. If
the transfer coefficients appear in the governing equations rather than the bound-
ary conditions, this implies that these equations are obtained as a result of the
averaging process.

8.3 ENERGY TRANSPORT WITH
CONVECTION

Heat transfer by convection involves both the equation of motion and the equation
of energy. Since we restrict the analysis to cases in which neither momentum nor
energy is generated, this obviously limits the problems we might encounter.
Consider Couette flow of a Newtonian fluid between two large parallel plates
under steady conditions as shown in Figure 8.25. Note that this geometry not only
considers flow between parallel plates but also tangential flow between concentric
cylinders. The surfaces at x = 0 and x = B are maintained at To and TI, re-
It
spectively, with To > TI. is required to determine the temperature distribution
within the fluid.

E

-V
Figure 8.25 Couette flow between parallel plates.