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Although ordinary heat exchangers may be extremely

different in design and construction and may be of the single-

or two-phase type, their modes of operation and effectiveness

are largely determined by the direction of the fluid flowwithin the exchanger.

The most common arrangements for flow paths within a heat

exchanger are counter-flow and parallel flow. A counter-flow

heat exchanger is one in which the direction of the flow of one

of the working fluids is opposite to the direction to the flow of 

the other fluid. In a parallel flow exchanger, both fluids in the

heat exchanger flow in the same direction.

Figure represents the directions of fluid flow in the parallel

and counter-flow exchangers. !nder comparable conditions,

more heat is transferred in a counter-flow arrangement than in

a parallel flow heat exchanger.

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The temperature profiles of the two heat exchangers indicatetwo ma"or disadvantages in the parallel-flow design. First, the

large temperature difference at the ends #Figure $%& causes

large thermal stresses. The opposing expansion and

contraction of the construction materials due to diverse fluid

temperatures can lead to eventual material failure. 'econd, the

temperature of the cold fluid exiting the heat exchanger never

exceeds the lowest temperature of the hot fluid. This

relationship is a distinct disadvantage if the design purpose isto raise the temperature of the cold fluid.

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The design of a parallel flow heat exchanger is advantageous

when two fluids are re(uired to be brought to nearly the same

temperature.

The counter-flow heat exchanger has three significant

advantages over the parallel flow design. First, the more

uniform temperature difference between the two fluids

minimi)es the thermal stresses throughout the exchanger.

'econd, the outlet temperature of the cold fluid can approach

the highest temperature of the hot fluid #the inlet temperature&.

. 'econd, the outlet temperature of the cold fluid can approach

the highest temperature of the hot fluid #the inlet temperature&.

*hether parallel or counter-flow, heat transfer within the heat

exchanger involves both conduction and convection. +nefluid #hot& convectively transfers heat to the tube wall where

conduction takes place across the tube to the opposite wall.

The heat is then convectively transferred to the second fluid.

ecause this process takes place over the entire length of the

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exchanger, the temperature of the fluids as they flow through

the exchanger is not generally constant, but varies over the

entire length, as indicated in Figure $%. The rate of heat

transfer varies along the length of the exchanger tubes

 because its value depends upon the temperature difference

 between the hot and the cold fluid at the point being viewed.

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The heat transfer coefficient or film coefficient, in

thermodynamics and in mechanics is the proportionality 

coefficient between the heat flux and the thermodynamic driving

force for the flow of heat #i.e., the temperature difference, T &

where

q" : heat fux, W/m2 i.e., thermal power per unit

area, q = dQ/dA

h : heat transer coecient, W/(m2•!

T  : #i$erence in temperature %etween thesoli# surace an# surroun#in& fui# area,  

It is used in calculating the heat transfer , typically by convection

or phase transition between a fluid and a solid.

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The heat transfer coefficient has 'I units in watts per s(uared

meter kelvin */#m01&.

2eat transfer coefficient is the inverse of thermal insulance. Thisis used for building materials #3-value& and for clothing

insulation.

The log mean temperature difference #also known by its

initialism LMTD& is used to determine the temperature driving

force for heat transfer  in flow systems, most notably in heat

exchangers. The 45T6 is a logarithmic average of the

temperature difference between the hot and cold streams at each

end of the exchanger. The larger the 45T6, the more heat is

transferred. The use of the 45T6 arises straightforwardly from

the analysis of a heat exchanger with constant flow rate and

fluid thermal properties.

'ontents

e)nition

*e assume that a generic heat exchanger has two ends #which

we call 7A7 and 77& at which the hot and cold streams enter or

exit on either side8 then, the 45T6 is defined by the logarithmic

mean as follows

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where  ΔT  A is the temperature difference between the two streams

at end  A, and  ΔT  B is the temperature difference between the two

streams at end  B. *ith this definition, the 45T6 can be used to

find the exchanged heat in a heat exchanger

*here Q is the exchanged heat duty #in watts&, U  is the heat

transfer coefficient #in watts per kelvin per s(uare meter& and  Ar 

is the exchange area. 9ote that estimating the heat transfer

coefficient may be (uite complicated.

This holds both for cocurrent flow, where the streams enter from

the same end, and for counter-current flow, where they enter

from different ends.

In a cross-flow, in which one system, usually the heat sink, has

the same nominal temperature at all points on the heat transfer

surface, a similar relation between exchanged heat and 45T6

holds, but with a correction factor. A correction factor is also

re(uired for other more complex geometries, such as a shell and

tube exchanger with baffles.