Page 30 - Modelling in Transport Phenomena A Conceptual Approach

1.4. SIMPLIFICATION OF THE RATE EQUATION 11

Solution
At steady-state, there is no accumulation of energy and the use of Eq. (1.4-5) gives
(Heat transfer rate),=L = (Heat transfer rate),,, + $2 ( Volume)
= 280 + (1 x lo6) (40 x 10-4)(20 x = 1080 W
The values of the heat fluxes at x = 0 and x = L are
280
(Heat flux),=, = = 70 x lo3 W/ m2
40 x 10-4
(Heat flux),=L = 40 lo8O 10-4 = 270 x lo3 W/ m2

Comment: Even though the steady-state conditions prevail, both the heat transfer
rate and the heat flux are not constant. This is due to the generation of energy
within the slab.

Bird, R.B., W.C. Stewart and E.N. Lightfoot, 1960, Transport Phenomena, Wiley,
New York.

SUGGESTED REFERENCES FOR FURTHER

STUDY

Brodkey, R.S. and H.C. Hershey, 1988, Transport Phenomena: A Unified
Approach, McGraw-Hill, New York.
Fahien, R.W., 1983, Fundamentals of Transport Phenomena, McGraw-Hill, New
York.

Felder, R.M. and R.W. Rousseau, 2000, Elementary Principles of Chemical
Processes, 3'" Ed., Wiley, New York.

Incropera, F.P. and D.P. DeWitt, 1996, Fundamentals of Heat and Mass Transfer,
4th Ed., Wiley, New York.