(18) External Forced Convection Part2

8/11/2019 (18) External Forced Convection Part2

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EXTERNAL FORCED CONVECTION

Associate Professor

IIT Delhi

E-mail: [email protected]


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Flate plate with unheated

starting length

Using integral solution methods,

the local Nusselt numbers for both

laminar and turbulent flows aree erm ne o e

31

3

31

5.0

x

31

3

)0_for(x

x

PrRe332.0NuNu == =Laminar flow

x1x1

31

8.0

P.Talukdar/Mech-IITD 2

91

109

x

91

109

0_orx

x

x1

.

x1

Nu

=

= =


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The determination of the average Nusselt number for the heated section

of a plate requires the integration of the local Nusselt number

Lx

43

h.x

12

h =

=Laminar flow

L

1

109

x15

The late is sub ected to uniform Heat Flux condition

Lx.

L14

=

=

31

5.0

xx PrRe453.0Nu =Laminar flow

These relations give values that are 36 percent higher for laminar flow and

318.0

xx PrRe0308.0Nu =Turbulent flow


4 percent higher for turbulent flow relative to the isothermal plate case.


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Flow over a cylinder and

sphere



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Pressure distribution along a

cylinder Consistentwithboundar la ertheor the ressurethrou h

theboundary

layer

is

essentially

constant.

p=p(x)

only.

Thusthepressureintheboundarylayershouldfollowthatof

e rees ream orpo en a owaroun acy n er



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. Astheflow ro ressesalon thefrontsideofthec linder the

pressurewould

decrease

and

then

increase

along

the

back

sideofthecylinder,resultinginanincreaseinfreestream

thebackside



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Sincethe

ressure

is

assumed

constant

throu hout

the

boundarylayer,wenotethatreverseflowmaybegininthe

boundarylayernearthesurface;thatis,themomentumof

overcomethe

increase

in

pressure.



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coefficientdecreases

with

increasing

Reynolds

number.Forasphere,itisCD=24/Re.Thereisno

flowseparationinthisregime.

Atabout

Re

=10,

separation

starts

occurring

on

the

rearofthebodywithvortexsheddingstartingat

aboutRe= 90.

Theregion

of

separation

increases

with

increasing

ReynoldsnumberuptoaboutRe= 103.Atthispoint,

drag.P.Talukdar/Mech-IITD 12


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Thedragcoefficientcontinuestodecreasewithincreasing

3

.

Adecreaseinthedragcoefficientdoesnotnecessarily

indicateadecreaseindrag.Thedragforceisproportionalto

thesquareofthevelocity,andtheincreaseinvelocityat

higherReynolds

numbers

usually

more

than

offsets

the

decreaseinthedra coefficient



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Inthemoderateran eof103


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Thereisasuddendropinthedragcoefficientsomewherein

theran e

of

10

5

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(18) External Forced Convection Part2