Heat Convection : Cylinder in Cross Flow

P M V Subbarao

Associate Professor

Mechanical Engineering Department

IIT Delhi

A Common Industrial Application ……

Tube Consumption in Power Plant Heat Exchangers in US (1000 of Feet)

Shell And Tube Heat Exchanger

A Shell and tube heat exchanger is a class of heat exchanger designs. It is the most common type of heat exchanger in power plants, oil refineries and other large chemical processes. As its name implies, this type of heat exchanger consists of a shell (a large vessel) with a bundle of tubes inside it.

Shell & Tube Heat Exchanger

Convection heat transfer with banks of tubes : Shell Side

• Typically, one fluid moves over the tubes, while a second fluid at a different temperature passes through the tubes. (cross flow)

• The tube rows of a bank are staggered or aligned. The configuration is characterized by the tube diameter D, the transverse pitch ST and longitudinal pitch SL.

Internal or External Flow !?!?!

Square Pitch Triangular Pitch

Inline Arrangement Zig-Zag Arrangement

Array of Cylinders in Cross Flow : Hydraulic Diameter

• The equivalent diameter is calculated as four times the net flow area as layout on the tube bank (for any pitch layout) divided by the wetted perimeter.

Perimeter Wetted

Area Flow Free4hD

Hydraulic Diameter : Square Pitch

do

PT

PT

o

oT

flowh d

dP

AD

4

4

P

4

22

wet

For square pitch:

For triangular pitch:

the tube clearance C is expressed as:

Then the shell-side mass velocity is found with

s

shellshell A

mG

Shell side Reynolds Number:

•For tube bundles composed of 10 or more rows

3/11 PrRe13.1 max,

mD DCNu

10

0.7r

104Re2000

:for valid

4max,

L

D

N

P

All properties are evaluated at the film temperature.

•For Reynolds number

DV

Dmax

max,Re

VDS

SV

T

T

max V

DS

SV

D

T

)(2max

If staggered and 2

DSS T

D

or

If number of tubes are less than 10, a correction factor is applied as:

)10(2

)10(

LL ND

ND NuCNu

And values for C2 are from table

•More recent results have been obtained by Zhukauskas.

4/1

36.0

Pr

PrPrRe max,

s

mD DCNu

20

500r7.0

102Re1000

:for valid

6max,

L

D

N

P

All properties except Prs are evaluated at the arithmetic mean of the fluid inlet and outlet temperatures.Values for C and m.

)20(2

)20(

LL ND

ND NuCNu

Thermal Resistance of infinitesimal Heat Exchanger

commcommth

comm

effcold

gain

effhot

loss UdTR

dT

A

Q

A

Q

,,,

• Thermal resistance of an Infinitesimal adiabatic Heat Exchanger

CONVECTION IN INTERNAL FLOWS

P M V Subbarao

Associate Professor

Mechanical Engineering Department

IIT Delhi

An Essential Part of Exchanging Heat……..

Development of Flow

Hydrodynamic Vs Thermal Development of FLow

• There are several fundamental problems in laminar internal flow that can be considered.

• The following problems arise as a result of considering the thermal entrance length in proportion to the hydrodynamic entrance length:

• L >> Lh, L >> Lt, i.e. thermally and hydrodynamically fully developed flow. • This rarely occurs in practice, but it affords many theoretical solutions.• L >> Lh, L << Lt, i.e. hydrodynamically fully developed, but thermally

developing flow, sometimes called the thermal entrance problem. • This type of flow is characteristic of high Prandtl number fluids Pr >> 1, e.g.

oils.• L << Lh, L << Lt, i.e. hydrodynamically and thermally developing flow,

sometimes called the combined entrance problem• L << Lh, L >> Lt, i.e. hydrodynamically developing flow and thermally fully

developed.• This type of flow occurs with low Prandtl number fluids Pr << 1, e.g. liquid

metals.

Nature of Convection

• In general, heat transfer is always higher in developing flows, since the thermal resistance of the boundary layer is lower.

• In the thermal entrance region, heat is being transferred from a warmer wall temperature (in the case of heating) to the lowest temperature which is the inlet fluid temperature.

• However, when the thermal boundary layers merge, there ceases to be a constant sink temperature and the bulk fluid temperature rises quickly.

• The local heat transfer rate is:

xTTAhq mwallxx