heat transfer

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Heat Transfer Su Yongkang

School of Mechanical Engineering

HEAT TRANSFER

CHAPTER 8

Internal flow

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Internal Flow Heat Transfer

Where we’ve been ……• Introduction to internal flow, basic concepts,

energy balance.

Where we’re going:• Developing heat transfer coefficient

relationships and correlations for internal flow

ro

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Internal Flow Heat Transfer

KEY POINTS THIS LECTURE

• Convection correlations– Laminar flow– Turbulent flow

• Other topics– Non-circular flow channels– Concentric tube annulus

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Convection correlations: laminar flow in circular tubes

• 1. The fully developed regionfrom the energy equation,we can obtain the exact solution.

for constant surface heat flux

for constant surface temperature

Note: the thermal conductivity k should be evaluated at .

36.4k

hDNuD Cqs

66.3k

hDNuD CTs

mT

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• 2. The entry region for the constant surface temperature condition

thermal entry length

3/2

PrReL

D04.01

PrReL

D0.0668

3.66

D

D

DNu

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• 2. The entry region(cont’d)for the combined entry length

• For values of

14.03/1

/

PrRe86.1

s

DD DL

Nu

2/)/Pr/(Re 14.03/1 sD DL

All fluid properties evaluated at the mean T 2/,, omimm TTT

CTs 700,16Pr48.0

75.9/0044.0 s

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Convection correlations: turbulent flow in circular tubes

• A lot of empirical correlations are available.

• For smooth tubes, the fully developed flow

Heating: Cooling:

• For rough tubes, coefficient increases with wall roughness. For fully developed flows

• Consider the entry length

• For liquid metals, see textbook p461.

4.05/4 PrRe023.0 DDNu 3.05/4 PrRe023.0 DDNu

)1(Pr)8/(7.121

Pr)1000)(Re8/(3/22/1

f

fNu D

d

fdDD NuNu , orm

fdD

D

Dx

C

Nu

Nu

)/(1

,

Short tubes

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Internal convection heat transfer coefficient(summary)

1. For laminar and fully developed flow (§8.4.1):i. q” constant:

ii. Ts constant:

2. For laminar flow in entry region (before fully developed flow, §8.4.2:i. Ts constant :

ii. Combined entry length with full tube:

3. For turbulent and fully developed (§8.5)

i. Heating

ii. Cooling

3/2

PrReL

D04.01

PrReL

D0.0668

3.66

D

D

DNu

14.03/1

/

PrRe86.1

s

DD DL

Nu

All fluid properties evaluated at the mean T 2/,, omimm TTT

Eq. 8.53

Eq. 8.55

Eq. 8.56

Eq. 8.57

Eq. 8.60

4.05/4 PrRe023.0 DDNu 3.05/4 PrRe023.0 DDNu

36.4DNu

36.3DNu

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Example: Oil at 150 flows slowly through a long, thin-℃walled pipe of 30-mm inner diameter. The pipe is suspended in a room for which the air temperature is 20 and the ℃convection coefficient at the outer tube surface is 11W/m2.K. Estimate the heat loss per unit length of tube.

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Internal Flow Heat Transfer(summary)

• If constant heat flux, mean fluid temperature can be computed directly from the pipe area and inlet temperature

• For constant wall temperature (such as if phase change occurs on outer pipe surface), mean fluid temperature will asymptotically approach the wall surface temperature, Ts

• Log mean temperature difference

• Use appropriate correlation equations for convection heat transfer based on flow conditions (laminar vs. turbulent, fully developed?). Evaluate fluid properties at mean fluid temperature

inp

convxm T

cm

PqT x

,

hcm

xP

TT

xTT

pims

ms

-exp

)(

,

ln

io

ioLM TT

TTTLMTD

LMTDAUTAUq sLMsconv

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Example: Air at 1atm and 285 K enters a 2-m long rectangular duct with cross section 75 mm by 150 mm. The duct is maintained at a constant surface temperature of 400 K, and the air mass flow is 0.10 kg/s. Determine the heat transfer rate from the duct to the air and the air outlet temperature.

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Additional Topic: Noncircular Tubes

• Use hydraulic diameter, Dh

• For turbulent flow, reasonably good analysis using same equations as for circular tubes.

• For laminar flow, Nusselt number have been determined for various shapes (Table 8.1)

channel flow theoflength perimeter theis Pchannel flow theof area sectional-cross theis

4

c

ch

AP

AD

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Additional Topic: Concentric Tube Annulus• Heat transfer analysis for both tube surfaces

• Flow in the inner tube computed using methods already presented

• Heat transfer for fluid in the tube annulus can involve heat transfer coefficient calculation on both inner and outer surface. Calculate using the hydraulic diameter

• Separate Nusselt # for inner and outer surface, for example

• Coefficients Nuii, etc. from Tables 8-2, 8-3.

ir

orim

i

Tmh

, ,

omTm , ,Tho ,

ioh DDD

iio

iii qq

NuNu

1

)( , misii TThq

)( , mosoo TThq

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Additional Topic: heat transfer enhancement

• Enhancement• Increase the convection coefficientIntroduce surface roughness to enhance turbulence. Induce swirl.• Increase the convection surface areaLongitudinal fins, spiral fins or ribs.

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Additional Topic: heat transfer enhancement

• Helically coiled tube• Without inducing turbulence or additional heat

transfer surface area.• Secondary flow

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Keep up the good work!

heat transfer

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