Page 439 - Modelling in Transport Phenomena A Conceptual Approach

PROBLEMS 419

where UA is the overall heat transfer coefficient based on the inside radius of the
inner pipe given by Eq. (8.2-42), i.e.,
Ri ] -1
Riln(R2IRi) I
kW (hB>R2
in which 16, represents the thermal conductivity of the inner pipe.
c) Subtract Eq. (2) from Eq. (3) to obtain

d) Combine Eqs. (1) and (5) to get

e) Integrate Eq. (6) and show that the rate of heat transferred is given as

Q = (?TD~L)UAATLM
where the logarithmic mean temperature difference is given by

f) Consider the double-pipe heat exchanger given in Problem 9.8 in which oil is used
as the heating medium instead of steam. Oil flows in a countercurrent direction
to water and its temperature decreases from 130°C to 80°C. If the average heat
transfer coefficient for the oil in the annular region is 1100 W/ m2. K, calculate the
length of the heat exchanger.
(Answer: f) 5.2m)

9.10 You are a design engineer in a petroleum refinery. Oil is cooled from 60 "C
to 40°C in the inner pipe of a doublepipe heat exchanger. Cooling water flows
countercurrently to the oil, entering at 15°C and leaving at 35°C. The oil tube
has an inside diameter of 22 mm and an outside diameter of 25 mm with the inside
and outside heat transfer coefficients of 600 and 1400 W/ m2. K, respectively. It is
required to increase the oil flow rate by 40%. Estimate the exit temperatures of
both oil and water at the increased flow rate.
(Answer: Toil = 43 "C, Twater = 39 "C)

9.11 Repeat the analysis given in Section 9.3.2 for laminar flow of a Newtonian
fluid between two fixed parallel plates under the action of a pressure gradient. The
temperatures of the surfaces at z = 0 and z = B are kept constant at To.