Page 314 - Academic Press Encyclopedia of Physical Science and Technology 3rd Chemical Engineering

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Encyclopedia of Physical Science and Technology En007c-310 June 30, 2001 17:30

260 Heat Exchangers

for resistance to chemical attack and high thermal
conductivity.

IV. BASIC HEAT EXCHANGER
EQUATIONS

A. Heat Balance
The heat required to heat a fluid that does not change phase
from t i is t o is
˙
Q = ˙ mc p (t o − t i ), (1)
T
where Q ˙ T is the sensible transfer rate (watts or joules
per second); ˙ m is the mass flow rate of the fluid (in kilo-
grams per second), c p is the mean specific heat of the fluid
over the temperature range (in joules per kilogram per FIGURE 11 Cross section of a heat exchanger tube, with convec-
kelvin), and t i and t o are the inlet and outlet temperatures tive heat transfer in the fluids and fouling deposits on the surfaces.
(in kelvins) of the fluid, respectively. The corresponding
heat given up by the hot fluid, assuming it does not change
phase and that there are no heat leaks, is where ˙ q is the local heat flux (in watts per square meter or
i
˙
˙
˙
Q = MC P (T i − T o ), (2) joules per square meter per second), dQ is the differential
T
amount of heat transferred through the differential heat
where the terms have similar meanings, applied to the hot transfer area (inside surface area) dA i (in square meters),
fluid.
U i is the overall heat transfer coefficient based on the
If, rather, the hot fluid is an isothermally condensing
inside heat transfer area (in watts per square meter per
vapor (such as steam), the latent heat duty is
kelvin or joules per second per square meter per kelvin),
˙
˙
Q = Mλ, (3) and T and t are the local hot and cold fluid temperatures
T
(in kelvins).
˙
where M is the mass rate of condensing (in kilograms per The overall heat transfer coefficient is related to the
second) and λ is the latent heat of condensation (in joules individual heat-transfer processes by the equation
per kilogram) at the condensing temperature.
If a fluid composed of more than one component (e.g., 1
U i = ,
a solution of ethanol and water, or a crude oil) partially or (1/h i ) + R f i +(r i /k w ) ln(r o /r i ) + 1/h o + R f o A i
A o
totallychangesphase,therequiredheatisacombinationof
(5)
sensible and latent heat and must be calculated using more
complex thermodynamic relationships, including vapor– where h i and h o are the convective heat transfer coeffi-
liquid equilibrium calculations that reflect the changing cients (in watts per square meter per kelvin or joules per
compositions as well as mass fractions of the two phases. second per square meter per kelvin) for the inside and out-
side fluids, respectively, each based on the corresponding
B. Rate Equation area. A i and A o ; R f i and R f o are the inside and outside
fouling resistances (in square meters-kelvins per watt or
Consider the typical case of heat transfer between one fluid second-square meters-kelvins per joule), each based on
inside a tube and another fluid outside the tube, shown in the corresponding area; r o and r i are the inside and out-
cross section in Fig. 11. Heat is transferred by convection side radii of the tube, k w is the thermal conductivity of the
fromthehotfluid(takenarbitrarilytobethe fluidinside the tube wall (watts per meter per kelvin or joules per sec-
tube) to the fouling deposit (if any) on the inside surface, ond per meter per kelvin), and A i and A o are the inside
through the fouling deposits and tube wall by conduction, and outside surface areas of the tube (in square meters).
and then by convection to the fluid outside the tube. At
Strictly speaking, the above equation applies only to plain
the point where the inside fluid temperature is T and the
cylindrical tubes for which
outside is t. the local heat flux inside the tube is
dQ ˙ A i = 2πr i L, (6a)
˙ q = = U i (T − t), (4)
i
dA i A o = 2πr o L, (6b)