Convection Heat Transfer 3qsy2012-13

8/10/2019 Convection Heat Transfer 3qsy2012-13

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CONVECTIONHEAT TRANSFER


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CONVECTION

Heat transfer by CONVECTIONoccurs as a result of themovement of fluid on a macroscopic scale in the form ofeddies or circulating currents.

If currents arise from the heat transfer itself, NATURALCONVECTIONoccurs.

In FORCED CONVECTIONthe circulating currents are producedby an external agency (e.g. an agitator in a reaction vessel oras a result of turbulent flow in pipe).


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Newtons Law of Cooling:

Q = h A (Ts-T)

CONVECTION: heat transfer between a solid

and a fluid


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CONVECTION BOUNDARY

LAYERS

u

u

(x)

The Velocity Boundary Layer

- velocity boundary layer thickness

- the value of y for which u = 0.99u

y

x

free stream

velocity BL


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Velocity Boundary Layer

Develops whenever there is fluid flow over a

surface

Of fundamental importance to problems

involving convection transport

In fluid mechanics

For external flow, it provides the basis for

determining the local friction coefficient2

2

u

C sf


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T

t

T

t(x)

The Thermal Boundary Layer

t- thermal boundary layer thickness

- the value of y for which (TsT) = 0.99 (Ts- T)

y

xTs

free stream

thermal BL


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Thermal Boundary Layer

Must develop if the fluid free stream and surface

temperatures differ

At the surface, there is no fluid motion and energy

transfer occurs only by conduction

Conduction

Convection

TThA

Qs

s

0y

fs

y

TkA

Q

TT

y

Tk

hs

0y

f


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Significance of Boundary Layers

For the engineer, the principalmanifestation of the boundary layers areas follows:

SURFACE FRICTION

Key BL parameter: friction coefficient, Cf

CONVECTIVE HEAT TRANSFER Key BL parameter: convective heat transfer

coefficient, h


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Boundary Layer Parameters

Key BL parameters are evaluated from BL

equations BL approximations

Velocity BL

Thermal BL

x

u,

y

u,

x

u

y

u

uu

yyxx

yx

x

T

y

T


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Boundary Layer Parameters

BL similarity parameters

Parameter Definition Significance

Reynoldsnumber

Ratio of inertia and viscous forces

Prandtl

number

Ratio of momentum and thermal

diffusivities

Nusselt

number

Dimensionless temperature

gradient at the surface

k

C

Pr

p

k

hLNu

LuRe


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PRANDTL NUMBER (Pr):a measure of the relative

effectiveness of momentum and energy transport by

diffusion in the velocity and thermal boundary layers,respectively.

For laminar flow

n is a positive number

For gas: t (n =1) For liquid metal: t >> (n < 1)

For oil: t 1)

n

t

Pr


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Momentum and Heat TransferREYNOLDS ANALOGY

NuCf

2

Re

RePrNuuCh2CSt pf StantonNumber

for Pr = 1

Relates key parameters of thevelocity and thermal BL


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Momentum and Heat Transfer

CHILTON-COLBURN ANALOGY

If Pr 1 (0.60 < Pr < 60)

H

2/3f

jPrSt2

C


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FORCED CONVECTION


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Dimensional Analysis in Heat Transfer(Buckingham Method)

),,,,,( ukCLhh p

hukL

CukL

ukL

lkji

phgfe

dcba

3

2

1

For FORCED CONVECTION


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Final form of the correlation for convective heat

transfer coefficient (forced convection):

k

C,

Luf

k

hL p

PrRe,fNu


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FORCED COVECTION INSIDE PIPES

1. LAMINAR FLOW INSIDE A PIPE / TUBE (Re < 2100)

SIEDER-TATE EQUATION [(Re Pr D/L) > 100]

14.03/1

PrRe86.1

w

b

L

D

k

DhNu

Equation 4.5-4 Geankoplis 4ed


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2. TURBULENT FLOW INSIDE A PIPE / TUBE

2.1 FULLY-DEVELOPED (hydrodynamically and thermally)turbulent flow in a smooth circular tube

2/3

D

D2/3f Pr

PrRe

NuStPr

8

f

2

C

1/34/5

DD Pr0.023ReNu

COLBURN EQUATION


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n4/5DD Pr0.023ReNu

DITTUS-BOELTER EQUATION

n = 0.40 for heating (Ts> Tm)

n = 0.30 for cooling (Ts< Tm)

0.70 Pr 160

ReD10,000

L/D 10


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0.14

w

b1/34/5D

L

Pr0.027Re

k

DhNu

SIEDER-TATE EQUATION

0.70 Pr 16000

Re > 6,000

L/D 60

Equation 4.5-8 Geankoplis 4ed


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3. TRANSITION FLOW INSIDE A PIPE / TUBE

2100 < Re < 6000

Use Figure 4.5-2 Geankoplis 4ed

4. ENTRANCE-REGION EFFECT ON h

0.7

L L

D1

h

h

L

D61

h

h

L

2 < L/D < 20 4.5-12

20 < L/D < 60 4.5-13


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5. LIQUID-METALS HEAT-TRANSFER COEFFICIENT

0.40L 0.625Pek

DhNu

Fully developed turbulent flow in

tubes with uniform heat flux

L/D > 60

100 < Pe < 104

0.8L

0.025Pe5.0k

DhNu

Fully developed turbulent flow in

tubes with constant wall

temperaturesL/D > 60

Pe > 100

Eq. 4.5-14

Eq. 4.5-15


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Correlations from Perrys ChE handbook


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FORCED COVECTION OUTSIDE

VARIOUS GEOMETRIES

Heat-transfer coefficient on immersed

bodies is given by

1/3mPrcReNu

NOTE: FLUID PROPERTIES ARE EVALUATED AT THE

FILM TEMPERATURE:

bwf TT2

1T

Eq. 4.6-1


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FLOW PARALLEL TO FLAT PLATE

Re < 3 x 105(laminar)

Nu = 0.664 Re0.50Pr1/3 Eq. 4.6-2

Re < 3 x 105(turbulent)

Nu = 0.0366 Re0.80Pr1/3 Eq. 4.6-3


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CYLINDER WITH AXIS PERPENDICULAR TO FLOW

1/3m

PrcReNu Eq. 4.6-1

Re m c

1 - 4 0.330 0.989

4 - 40 0.385 0.911

40 to 4 x 103 0.466 0.683

4 x 103to

4 x 104

0.618 0.193

4 x 104 to

2.5 x 105

0.805 0.0266

TABLE 4.6-1


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FLOW PAST SINGLE SPHERE

1/30.50Pr0.60Re2.0Nu

1 < Re < 70,000 Eq. 4.6-4

0.60 < Pr < 400


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Correlations from Perrys ChE handbook


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FREE CONVECTION

or NATURAL CONVECTION


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Free or Natural Convection

Very common

Either external or internal flows

Main source of momentum: hydrostatic

force (buoyancy)

Tends to result in low Nusselt number


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No imposed flow = No Reynolds number

Since there is no free-stream velocity to quantify

the forces of momentum in free convection flows,

a new dimensionless group for inertial and

viscous forces is needed.

Since buoyancy is the source of movement:

TgL~vg gravitational acceleration

coefficient of thermal expansion


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Natural Convection from Vertical Planesand Cylinder

mm aRaGrPraNu

a and m are constants (see Table 4.7-1

Geankoplis)

Properties are evaluated at film temperatureTable 4.7-2 (Geankoplis) gives simplified

correlations for natural convection from

various surfaces


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Natural Convection from HorizontalCylinder

Same as the case of vertical planes and

cylinders

Replace L with D

mm

aRaGrPraNu


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Natural Convection from HorizontalPlates

Same as the case of vertical planes and

cylinder

L

Side of a square

Linear mean of 2 dimensions of a rectangle

0.90 times the diameter of circular disc

In general: L = area / perimeter


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Natural convection in enclosed surfaces

Refer to equations 4.7-5to 4.7-15


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TUBE BUNDLES /BANK OF TUBES

Typical industrial application as in heatexchangers

Bundles of tube improve heat transfer byincreasing the surface area

Bundles of tube are generally eitherarranged in ALIGNED or STAGGEREDconfiguration.


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In general, the STAGGERED configuration is best

for heat transfer.

Sn

Note: ST= SN(in lecture notes) SD= SP

SL = SP(in lecture notes)


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For more than 10 transverse rows and 2000 < Re

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Convection Heat Transfer 3qsy2012-13