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9. EXTERNAL FORCED CONVECTION

FLOW ACROSS CYLINDERS AND

SPHERES

For flow over flat plate assumption zero pressure

gradient along the plate 0x

p=

ux

y

For flow across a cylinder 0xp

At stagnation point the fluid strikes the

cylinder, pressure raises, then fluid acceleratesand pressure decreases

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Similarly like for flat plate region ofboundary layer close

to the surface and free stream outside

Relation between velocity and

pressure given by Bernoulli equation

dxdp

1

dxduu =

u

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Different flow regimes depending onRe number

duRe =

Laminar flow less resistant to

separation.

Separation at about = 80

Red

> 2.105

Red< 2.105

Turbulent flow more resistant to

separation.

Transition to turbulence at about

= 80.

Separation at about = 145

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Flow separation visualization

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Turbulent flow -Transition to turbulence

Separation of turbulentboundary layer

Laminar flow

separation of laminar

boudary layer

Heat transfer depends

on flow regime

Local heat transfer coefficient

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Average heat transfer coefficient

41

w

nm

dd

Pr

PrPrCReNu

=

dNud

0.7

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Tube bundle

41

w

0.36m

maxd,d Pr

PrPrCReNu

=

dVRe max

maxd,

Vmax- velocity in the

narrowest cross section

A1 or A2