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Heat Exchangers

ME 430

Heat Exchanger Performance

The performance of heat exchangers

operating under forced flow conditions is

defined by the amount of heat transferred

between the two fluid streams and is

characterized by the UA value or the

dimensionless factors: the effectiveness,e, or number of transfer units (NTU’s), and

the capacity ratio,Cr,

e

Energy Balance

the rate of heat transfer between

the two fluid streams in the heat

exchanger, Q, is,

where is the heat

capacity rate of one of the fluid

streams.

c

ci

m

T

Q0Q 0Q

Q

s

so

m

T

c

co

m

T

s

si

m

T

( ) ( ) ( ) ( )p s so si p c ci coQ mc T T mc T T

pmc

Simple Configurations

Q = qx A

and

Q = UA (DT)

U = (1/h1 + Rwall +1/h2)-1

Heat transfer through a wall

Simple Configurations

for Tube & Shell

Q = UA (DT)

Need to determine DT.

This is not straightforward

as for the parallel flow case.

UA –Value & LMTD

The unit’s overall conductance or UA value is defined as

the product of the overall heat transfer coefficient and the

heat transfer area. For counter-flow applications, the heat

transfer rate is defined as the product of overall

conductance and the log-mean temperature difference,

LMTD, i.e.,Q UA LMTD

where the log-mean temperature difference is equal to,

ln

out in

out

in

T TLMTD

T

T

D D

D D

Parallel Flow

Q UA LMTD

ln

out in

out

in

T TLMTD

T

T

D D

D D

Counter Flow

Q UA LMTD

ln

out in

out

in

T TLMTD

T

T

D D

D D

From “Heat Transfer”,

By Y. Cengel

Types (cont.)

• Cross-flow Heat Exchangers

Finned-Both Fluids

Unmixed

Unfinned-One Fluid Mixed

the Other Unmixed

For cross-flow over the tubes, fluid motion, and hence mixing, in the transverse

direction (y) is prevented for the finned tubes, but occurs for the unfinned condition.

Heat exchanger performance is influenced by mixing.

Types (cont.)

• Shell-and-Tube Heat Exchangers

One Shell Pass and One Tube Pass

Baffles are used to establish a cross-flow and to induce turbulent mixing of the

shell-side fluid, both of which enhance convection.

The number of tube and shell passes may be varied, e.g.:

One Shell Pass,

Two Tube Passes

Two Shell Passes,

Four Tube Passes

Types (cont.)

• Compact Heat Exchangers

Widely used to achieve large heat rates per unit volume, particularly when

one or both fluids is a gas.

Characterized by large heat transfer surface areas per unit volume, small

flow passages, and laminar flow.

(a) Fin-tube (flat tubes, continuous plate fins)

(b) Fin-tube (circular tubes, continuous plate fins)

(c) Fin-tube (circular tubes, circular fins)

(d) Plate-fin (single pass)

(e) Plate-fin (multipass)

Overall Coefficient

Overall Heat Transfer Coefficient

• An essential requirement for heat exchanger design or performance calculations.

• Contributing factors include convection and conduction associated with the

two fluids and the intermediate solid, as well as the potential use of fins on both

sides and the effects of time-dependent surface fouling.

• With subscripts c and h used to designate the hot and cold fluids, respectively,

the most general expression for the overall coefficient is:

, ,

1 1 1

1 1

c h

f c f h

w

o o o oc c h h

UA UA UA

R RR

hA A A hA

Overall Coefficient

o,

Overall surface efficiency of fin array (Section 3.6.5)

1 1

o

f

c or h f

c or h

A

A

total surface area (fins and exposed base) surface area of fins only

t

f

A AA

Assuming an adiabatic tip, the fin efficiency is

,

tanhf c or h

c or h

mL

mL

2 /c or h p w c or hm U k t

, partial overall coe1

fficientp c or h

f c or h

hUhR

2 for a unit surfFouling fact ace area (m W)or K/fR

Table 11.1

conduction resistan Wall (K/Wce )wR

Compact HX

Compact Heat Exchangers

• Analysis based on method NTUe

• Convection (and friction) coefficients have been determined for selected

HX cores by Kays and London . 5 Proprietary data have been obtained by

manufacturers of many other core configurations.

• Results for a circular tube-continuous fin HX core:

2 / 3

max

Pr

/

h

p

j St

St h Gc

G V

EffectivenessThe heat exchanger effectiveness, e, is defined as the ratio

of the rate of heat transfer in the exchanger, Q, to the

maximum theoretical rate of heat transfer, , i.e.,maxQ

max

Q

Qe

The maximum theoretical rate of heat transfer

is limited by the fluid stream with the smallest

heat capacity rate, i.e.

min

( ) ( )

( ) ( )

p s so si

p ci si

mc T T

mc T Te

where the is the smaller of or .min( )pmc ( )p smc ( )p cmc

c

ci

m

T

Q0Q 0Q

Q

s

so

m

T

c

co

m

T

s

si

m

T

NTUThe number of transfer units (NTU) is an indicator of the actual heat-transfer area or physical size of the heat exchanger. The larger the value of NTU, the closer the unit is to its thermodynamic limit. It is

defined as,

min( )p

UANTU

mc

Capacity RatioThe capacity ratio, Cr, is representative of the operational condition of a given heat exchanger and will vary depending on the geometry and flow configuration (parallel flow, counterflow, cross flow, etc.) of the exchanger. This value is defined as the minimum heat capacity rate divided by the maximum capacity rate, i.e.,

min

max

( )

( )

p

r

p

mcC

mc

It is important to note that the capacity ratio will be directly

proportional to the ratio of the mass flow rates if the specific

heats of the flows are fairly constant.

Effects of Capacity Ratio and NTU on Effectiveness

Effectiveness Relations

NTU Relations

Special Conditions

Special Operating Conditions

Case (a): Ch>>Cc or h is a condensing vapor .hC

– Negligible or no change in , , .h h o h iT T T

Case (b): Cc>>Ch or c is an evaporating liquid .cC

– Negligible or no change in , , .c c o c iT T T

Case (c): Ch=Cc.

1 2 1mT T TD D D –

Refrigeration

Examples

Other Types

Heat Pipe

Rotary

ILC Enthalpy Wheel

Heat Pipe

Enthalpy WheelThe heart of the Energy Recovery Ventilator is

the desiccant coated energy recovery wheel,

which slowly rotates between its two sections.

In one section, the stale, conditioned air is

passed through the wheel, and exhausted in

the atmosphere. During this process, the

wheel absorbs sensible and latent energy

from the conditioned air, which is used to

condition (cool / heat) the incoming Fresh Air

in the other section, during the second half of

its rotation cycle.