Heat Exchange and Recovery in Process and Facilities - Energy Conversion and Management - page 255

A general expression of the heat transferred from one fluid to the other
through the heat exchanger's separating surfaces can be formulated as
follows (see also Sect. 8.3 for heat transfer modes):

Q ¼ U A AT (W) (Btu/h)

where
U 1/R th (W/m 2 K; Btu/h ft 2 F). ¼ overall heat-transfer coefficient ¼

A ¼ surface area of the exchanger, generally taken as the surface in

contact with one fluid or stream (m 2 ;ft 2 ).

Δ T ¼ effective temperature difference between the streams, assumed

constant in any point of the exchanger surface, generally expressed
as the log-mean difference between the temperatures of the fluids at
the two sides of the exchanger. Notice that these differences are not
the same for parallel and counterflow arrangements (K; C; F).

With a pure parallel flow exchanger, which is the simplest heat exchanger, and
on the assumption of constant specific heats and constant overall coefficient
U along the exchanger,

T must be introduced as follows (see Fig. 15.1 for fluid
temperatures at both sides of the exchanger):

Δ

ð T 1i T 2i Þ ð T 1o T 2o Þ

T ¼ Δ T LM ¼

Δ

ln T 1i ð ð T 2i Þ= ð T 1o T 2o Þ Þ

With a pure countercurrent flow exchanger, which is the most efficient heat
exchanger, and on the assumption of constant specific heats and constant overall
coefficient U along the exchanger, T must be introduced as follows (see Fig. 15.1

for fluid temperatures at both sides of the exchanger):

Δ

ð T 1i T 2o Þ ð T 1o T 2i Þ

Δ T ¼ Δ T LM ¼

ln T 1i ð ð T 2o Þ= ð T 1o T 2i Þ Þ

In practice, many exchangers can be derived from a counterflow device, so that
the effective temperature difference is defined as follows:

T ¼ FT Δ T LM pure counterflow ð Þ

Δ

where
FT is a correction factor of the log-mean difference of temperature, generally
obtainable from curves (see Fig. 15.3 ) where FT value is expressed as functions of
R or P parameters:

R ¼ ð T 1i T 1o Þ= ð T 2o T 2i Þ ¼ C 2 = C 1