thermal fluids

8/13/2019 Thermal Fluids

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Thermal luids I

Dr. Primal Fernando

Chapter 16 – Mechanisms of heat transfer

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Mechanisms of heat transfer

• Heat can flow spontaneously from an object with a high temperature to

an object with a lower temperature.

• Heat can only be transferred between objects, or areas within an object,

with different temperatures (as given by the zeroth law of

thermodynamics), and then, in the absence of work, only in the direction

of the colder body (as per the second law of thermodynamics).

• There are 3 mechanisms of heat transfer– Conduction– Convection– Radiation

2

Conduction

• Conduction is the transfer of energy from the more energetic particle

interactions between the particles.

• , .

• In liquids and gasses conduction heat transfer is due to the collisions

an us on o t e mo ecu es ur ng t e r ran om mot on.

• In solids: it is due to the combination of vibrations of molecules in a

lattice and energy transported by free electrons.

3

Rate of heat conduction

Consider steady heat conduction through a

,

• Area= A • c ness= x

• Temperature difference= T=T 1‐T 2

the heat transfer rate

AQcond

T T T Q21cond

4

xQcond x

AQcond x

kAQcond



Fourier ʹs law of heat conduction

T

xcond

k ‐ Thermal conductivit Wm ‐ 1K‐ 1 , measure of material ʹs abilit to

conduct heat

T ‐ Tem erature radient which has a ne ative slo e x

T

(con

mW xq A

5

‐ a e o ea con uc on per un area

T )mW

xq

A

2

o

o mC

C mW

12030

401q )(

2

o

o

m1480

mC

C mW

12030148q

/

)(

6

Thermal conductors and thermal insulators

)(W T

kAQcond

To obtain high heat transfer, use materials with high thermal conductivity

(thermal conductors; high k) and to reduce heat transfer use materials with

low thermal conductivity (thermal insulators; low k)

7

Thermal conductivity of some materialsDiamond 2300 W/m.K Cu 401 W/m.K Al 237 W/m.K Iron 80.2 W/m.KGlass 0.78 W/m.K Brick 0.71 W/m.K Water 0.613 W/m.K Air 0.026 W/m.K

8



decreased with

increasing temperature

water is exce tional

• In gases and liquids k

increasing molar mass

(in kinetic theory,

M T

k

• n

gases

increases

with increasing

temperature

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Some definitions in short

• C p (J/kg) = Specific heat; material’s ability to store thermal energy (per

unit mass).

• C (J/m3) = Heat capacity; material’s ability to store thermal energy (per

unit volume).

• k (W/m°C) = Thermal conductivit ; material’s abilit to conducts heat.

• (m2 /s) = Thermal diffusivity; how fast heat diffuses through a material

k conducted heat

10

ps oreea

Measuring thermal conductivity of a material

Experiment: In a certain experiment, cylindrical samples of diameter 5 cm

and length 10 cm are used. The two thermocouples in each sample are

placed 3 cm apart. After initial transient, the electrical heater is observed to

draw 0.4 A at 110 V, and both differential thermometers read a temperature

difference of 15°C. Determine the thermal conductivity of the material.

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Assumptions

• Steady state: temperature

do

not change.

• Insulated very well: heat

loss through lateral

surfaces are negligible.

• n re ea genera e y

resistance heater is

conducted through

sam les.

• The apparatus posses

thermal s mmetr .

12



T xcond

x

T Ak con

ply power electrical sup

40110VI .22cond

222 m00196 0m0501

D1

A .. 44

13

C mW 422C 15m00196 0

k 2 /.

))(.(.

Conversion between SI and En lish units

, .

• Length, 1m=3.2808 ft

• Temperature, 1°C= 1.8°F

• Thermal conductivity, 1 W/m°C=0.5778 Btu/h.ft.°F

F ft h Btu

57780F 81 ft 28083h Btu412143

C mW

1 ..

.).)(.(

/.

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Convection• Convection is the mode of energy transfer between a solid surface and the

adjacent liquid or gas that is in motion, and it involves the combined effects

.

• The faster the fluid motion, greater the heat transfer

• It can be divided in to two parts, natural convection and force convection

• Natural convection (free convection)– Fluid motion is caused by buoyancy forces that are induced by density

differences due to the variation of temperature in the fluid.

• Force

convection– Fluid is forced flow over the surface by external mean such as fan, pump

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Natural convection

Natural convection

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Newton’s law of coolin

ssconv

17

– convect on eat trans er coe c e

Measurin convection heat transfer coefficient

Experiment: A 2m ‐ long, 0.3cm ‐ diameter electrical wire extends across a

room at 15°C, as shown in fi ure. Heat is enerated in the wire as a results

of

resistance

heating,

and

the

surface

temperature

of

the

wire

is

measured

to

be 152°C. Also, the voltage drop and electric current through the wire are

measured to be 60V and 1.5A, respectively. Disregarding any heat transfer

by radiation, determine the convection heat transfer coefficient for heat

transfer between the outer surface of the wire and the air in the room.

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• Assumptions–

condition; no

temperature

chan e– Radiation heat

transfer

negligible.

)()()(

T T AQ

hW T T hAQss

convssconv

2s m018850m2m0030 DL A .))(.(

W 90 A51V 60VI PQ ply power electricalconv ).)((sup

W 90

19

C mW 934C 15152m018850T T A 2

ss

.))(.()(

Radiation• Radiation is the energy emitted by matter in the form of electromagnetic

waves (or photons).

• It does not require a medium to transfer energy (this is how energy of the

sun reaches the earth.

• It suffers no attenuation (weakening) in a vacuum. Radiation from the sun is

attenuated by the Earth ʹs atmosphere.

• Radiation is volumetric phenomenon: all solids, liquids gasses, absorb, emits

or transmit radiation to varying degrees.

• However, radiation is usually considered to be a surface phenomenon for

solids

that

are

opaque

to

thermal

radiation

such

as

metals,

wood

and

rocks

since the radiation emitted b the interior re ions of such material can never

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reach the surface, and radiation incident on such bodies is usually absorbed

within a few microns from the surface



e max mum ra e o ra a on a can e em e

from a surface at an absolute temperature of T s is

‐

4ssrad T AQ max,

428 unitsSI K mW 1067 5t Cons BoltsmanStefan )(/.,tan

428 R ft h Btu1017140or ../.

21

Blackbod radiation

,

radiation that falls onto it. No radiation passes through it and none is

reflected. It is this lack of both transmission and reflection to which

.

thermal radiation.

ʺ .

ssblackbodyrad T AQ ,

22

e ra a on em s y rea o es are ess an

black bodies

4a at on rom a rea o y ssrealrad ,

is called emissivity of the surface: it is different to surface tosurface, olish surfaces have low emissivities and rou h and ainted surfaces have high emissivities.

23 24



s

enclosed by a much larger surface at absolute temperature of T surr separated by a gas (such as air) that does not intervene with radiation, the

,

( 44 T T A

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Combine heat transfer coefficient

as air occurs parallel to conduction (or convection, if there is bulk gas

motion) between the surface and the gas. Thus, the total heat transfer

mechanisms. By simplicity and convenience, this is often done by

defining combined heat transfer coefficient h combined that includes the

effects of both convection and radiation. The total heat transfer rate to

or from a surface is by convection and radiation is expressed as,

sscombined total

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Example: The total heat transfer rate (by convection and radiation) of a

surface is iven b followin ex ression. Derive and ex ression for the

combined heat transfer coefficient (hcombined )

)( T T AhQ sscombined total

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Where; )( T T AhQ sscombined totalrad contotal

)( 44ssrad T T AQ

)( T T AhQ ssconconv

)()( 44sssconstotal T T AT T h AQ

))(()( 22s

22sssconstotal T T T T AT T h AQ

22 sssssconstotal

)())(( T T T T T T Ah AQ ss22

ssconstotal

)())(( T T AT T T T AhQ sss22

sscontotal

)( T T AhQ sscombined total

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))(( T T T T Ahh s22

ssconcombined

thermal fluids

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