lect - 2 laws of heat transfer.pptx

8/17/2019 Lect - 2 Laws of Heat transfer.pptx

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Laws of Heat Transfer Dr. Senthilmurugan S. Department of Chemical Engineering IIT Guwahati - Part 2

Conduction, Convection andRadiation



5/12/16 | Slide 2

The First Law of Therod!naics

The first law of therod!naics

"conservation of ener#! $rinci$le% states

that energy can neither be created nor

destroyed during a process; it can only

change forms.

The ener#! &alance for an! s!ste

under#oin# an! $rocess in the rate for

At steady state



5/12/16 | Slide '

(ner#! &alance for closed s!stes "Fi)ed *ass%

+ closed s!ste consists of a fixed

mass.

The total ener#! E for ost s!stes

encountered in $ractice consists of the

internal ener#! U.

This is es$eciall! the case for stationar!

s!stes since the! dont involve an!

chan#es in their velocit! or elevationdurin# a $rocess-where . is the net aount of heat transfer

to or fro the s!ste- This is the for of

the ener#! &alance relation we will use

ost often when dealin# with a fi)ed ass

n the a&sence of an! wor0 interactions,

the chan#e in the ener#! content of a

closed s!ste is eual to the net heat

transfer



5/12/16 | Slide

(ner#! &alance for stead!3flow s!stes

+ lar#e nu&er of en#ineerin# devices

such as water heaters and car radiators

involve ass flow in and out of a

s!ste, and are odeled as control

volumes.

*ost control volues are anal!4edunder stead! o$eratin# conditions-

The ter steady eans no change with

time at a s$ecified location- *ass flow rate The aount of ass

flowin# throu#h a cross section of a flow

device $er unit tie- olue flow rate The volue of a fluid

flowin# throu#h a $i$e or duct $er unit

tie-

7nder stead! conditions, the net rate of

ener#! transfer to a fluid in a control

volue is eual to the rate of increase

in the ener#! of the fluid strea flowin#throu#h the control volue



5/12/16 | Slide 5

Surface ener#! &alance

+ surface contains no volue or ass,

and thus no ener#!- Therefore, a

surface can &e viewed as a fictitious

s!ste whose ener#! content reains

constant durin# a $rocess-

This relation is valid for &oth stead! and

transient conditions, and the surface

ener#! &alance does not involve heat

#eneration since a surface does not

have a volue-

1

2

'



5/12/16 | Slide 6

How to 8efine (ner#! Transfer .uantitativel!

(ner#! can &e transferred to or fro a

#iven ass &! two echaniss Heat transfer and wor0-

Heat transfer rate The aount of heat

transferred $er unit tie- ", watt%-

Heat flu) The rate of heat transfer $erunit area noral to the direction of heat

transfer "/area, watt / suare eter% -

9ower The wor0 done per unit time. (P

watt)



5/12/16 | Slide :

Theral Conduction

Conduction The transfer of ener#! fro the

ore ener#etic $articles of a su&stance to

the ad;acent less ener#etic ones as a result

of interactions &etween the $articles- n #ases and liuids, conduction is due to

the collisions and diffusion of the olecules

durin# their rando otion- n solids, it is due to the co&ination of

vibrations of the olecules in a lattice and

the ener#! trans$ort &! free electrons. Fouriers law of heat conduction The rate of

heat conduction throu#h a $lane la!er is

$ro$ortional to the te$erature differenceacross the la!er and the heat transfer area,

&ut is inversel! $ro$ortional to the thic0ness

of the la!er- 9ro$ortionalit! constant theral conductivit!

0

Heat conduction

throu#h a lar#e $lane

wall of thic0ness ∆ xand area A.

<hen x = >

?ne diensional heat flow



5/12/16 | Slide @

Fouriers law of heat conduction

Theral conductivit!, + easure of

the a&ilit! of a aterial to conduct heat- Te$erature #radient d!"dx The slo$e

of the te$erature curve on a !#xdia#ra-

Heat is conducted in the direction of

decreasin# te$erature, and the

te$erature #radient &ecoes ne#ative

when te$erature decreases with

increasin# x. The negative sign in theeuation ensures that heat transfer in

the $ositive x direction is a $ositive

uantit!-

n heat conduction anal!sis, A

re$resents the area normal to

the direction of heat transfer-



5/12/16 | Slide A

9ro$erties of Theral conductivit!

The rate of heat conduction throu#h a

solid is directl! $ro$ortional to its

theral conductivit!- Theral conductivit! The rate of heat

transfer throu#h a unit thic0ness of the

aterial $er unit area $er unitte$erature difference-

The theral conductivit! of a aterial is

a easure of the a&ilit! of the aterial

to conduct heat- + hi#h value for theral conductivit!

indicates that the aterial is a #ood heatconductor, and a low value indicates that

the aterial is a $oor heat conductor or

insulator .



5/12/16 | Slide 1>

The ran#e of theral conductivit! of various aterialsat roo te$erature-

The theral

conductivities of#ases such as air

var! &! a factor of

1> fro those of

$ure etals

The theral

conductivities

of liuidsusuall! lie

&etween

those of solid

and liuids

Bood heat conductors &ut $oor

electrical conductors and used in

the electronics industr! H



5/12/16 | Slide 11

Theral conductivit! vs Te$erature

Kinetic theory "Bases%

Therefore, for a $articular #as "fi)ed *w%, the

theral conductivit! increases with increasin#

te$erature and at a fi)ed te$erature the theral

conductivit! decreases with increasin# *w-

The theral conductivit! of #ases is nde$endent of

$ressure in a wide ran#e of $ressures encountered

in $ractice

The theral conductivit! of liuids is #enerall!

insensitive to $ressure e)ce$t near the

therod!naic critical $oint

The theral conductivities of ost liuids decrease

with increasin# te$erature, with water &ein# a

nota&le e)ce$tion-

Theral conductivit! of liuids decreases with

increasin# olar ass *w

Theral conductivit! of $ure etal #enerall!

increases with te$erature "+luiniu, 9latinu

are an e)ce$tion% -

0 D f"T% D 0o"1EβT%



5/12/16 | Slide 12

<iedeann3Fran4 law

The <iedeann3Fran4 law states that the ratio of

theral conductivit! to the electrical conductivit!

of a etal is $ro$ortional to its te$erature-

<here $ the $ro$ortionalit! constant "also 0nown

as the Loren4 nu&er%, isD2-51>G@ <IG2

The law can &e e)$lained &! the fact that free

electrons in the etal are involved in the

echaniss in &oth heat and electrical trans$ort-

The theral conductivit! increases with the

avera#e electron velocit! since this increases the

forward trans$ort of ener#!- However, the

electrical conductivit! decreases with an increasein $article velocit! &ecause the collisions divert

the electrons fro forward trans$ort of char#e

Theral conductivit! s (lectrical conductivit!

k LT

σ =



5/12/16 | Slide 1'

Theral Conductivit! and S$ecific heat

Specific heat cp is a easure of a aterials a&ilit! to store

theral ener#!- For e)a$le, C$ D -1@ 0J/0#KC for water and

C$ D >-5 0J/0#KC for iron at roo te$erature, which

indicates that water can store alost 1> ties the ener#! that

iron can $er unit ass-

Thermal conductiity 0 is a easure of a aterials a&ilit! to

conduct heat- For e)a$le, 0 D >-6>: </KI for water and 0 D @>-2 </KI

for iron at roo te$erature, which indicates that iron conducts

heat ore than 1>> ties faster than water can-

Thus we sa! that water is a $oor heat conductor relative to iron,

althou#h water is an e)cellent ediu to store theral ener#!

Superconductor!" The theral conductivities of certain solids

e)hi&it draatic increases at te$eratures near a&solute 4ero

The conductivit! of co$$er reaches a a)iu value of a&out

2>,>>> </KI at 2> I, which is a&out 5> ties the conductivit!

at roo te$erature



5/12/16 | Slide 1

Theral 8iffusivit!

c p S$ecific heat, J/0# K C Heat ca$acit! $er

unit ass

ρ c p Heat ca$acit!, J/'KC Heat ca$acit! $er

unit volue

α Theral diffusivit!, 2/s Re$resents how

fast heat diffuses throu#h a aterial

+ aterial that has a hi#h theral

conductivit! or a low heat ca$acit! will

o&viousl! have a lar#e theral diffusivit!-

The lar#er the theral diffusivit!, the fasterthe $ro$a#ation of heat into the ediu-

+ sall value of theral diffusivit! eans that

heat is ostl! a&sor&ed &! the aterial and a

sall aount of heat is conducted further-



5/12/16 | Slide 15

+ si$le e)$eriental setu$ to deterine the theralconductivit! of a aterial-

+ la!er of sa$le aterial of 0nown

thic0ness and area can &e heated fro

one side &! an electric heater of 0nown

heat transfer rate "w%-

f the outer surfaces of the heater are

well insulated, all the heat #enerated &!the resistance heater will &e transferred

throu#h the aterial whose conductivit!

is to &e deterined-

Then easurin# the two surface

te$eratures "T1 MT2% of the sa$le

aterial when stead! heat transfer isreached and su&stitutin# the into

FourierNs heat conduction euation

to#ether with other 0nown uantities

#ive the theral conductivit!

9 "w%D

9 D



5/12/16 | Slide 16

Te$erature 8e$endenc! of I s OuericalCo$le)it!

The te$erature de$endence of theral conductivit! causes considera&le

co$le)it! in conduction anal!sis- Therefore, it is coon $ractice to evaluate the

theral conductivit! 0 at the avera#e te$erature and treat it as a constant in

calculations-

n heat transfer anal!sis, a aterial is norall! assued to &e isotro$icP that is, to

have unifor $ro$erties in all directions- This assu$tion is realistic for ostaterials, e)ce$t those that e)hi&it different structural characteristics in different

directions, such as lainated co$osite aterials and wood- The theral

conductivit! of wood across the #rain, for e)a$le, is different than that $arallel to

the #rain



5/12/16 | Slide 1:

Convection Heat Transfer

Convection The ode of ener#!

transfer &etween a solid surface

and the ad;acent liuid or #as that is

in otion, and it involves the

co&ined effects of conduction and

fluid motion. The faster the fluid otion, the

#reater the convection heat transfer-

n the a&sence of an! &ul0 fluid

otion, heat transfer &etween a

solid surface and the ad;acent fluidis &! $ure conduction-

Heat transfer fro a hot surface to air &!convection-



5/12/16 | Slide 1@

Oature of Theral Convection

Forced convection f the fluid is forced

to flow over the surface &! e)ternal

eans such as a fan, $u$, or the

wind-

Oatural "or free% convection f the fluid

otion is caused &! &uo!anc! forcesthat are induced &! densit! differences

due to the variation of te$erature in

the fluid-

Heat transfer $rocesses that involve

change of phase of a fluid are also

considered to &e convection &ecause ofthe fluid otion induced durin# the

$rocess, such as the rise of the va$or

&u&&les durin# &oilin# or the fall of the

liuid dro$lets durin# condensation-

The coolin# of a &oiled e## &! forced andnatural convection-



5/12/16 | Slide 1A

Oewtons Law of Coolin# for Convective HeatTransfer

Oewtons Law of Coolin#

Heat transfer rate

h # convection heat transfer coefficient,

</2 K C

As # the surface area throu#h which

convection heat transfer ta0es $lace

! s # the surface te$erature

! ∞ 3 the te$erature of the fluid

sufficientl! far fro the surface

Heat transfer fro a hot surface to air &!

convection-



5/12/16 | Slide 2>

Convection Heat Transfer Coefficient

The convection heat transfer coefficient

h is not a $ro$ert! of the fluid- t is an e)$erientall! deterined

$araeter whose value de$ends on all

the varia&les influencin# convection

such as the surface #eoetr! the nature of fluid otion the $ro$erties of the fluid the &ul0 fluid velocit!



5/12/16 | Slide 21

Oewtons Law of Coolin#



5/12/16 | Slide 22

Theral Radiation

Radiation The ener#! eitted &! atter in the for of electromagnetic waves "or

photons% as a result of the chan#es in the electronic confi#urations of the atos or

olecules-

7nli0e conduction and convection, the transfer of heat &! radiation does not reuire

the $resence of an intervening medium.

n fact, heat transfer &! radiation is fastest "at the s$eed of li#ht% and it suffers noattenuation in a vacuu- This is how the ener#! of the sun reaches the earth-

n heat transfer studies we are interested in thermal radiation% which is the for of

radiation eitted &! &odies &ecause of their te$erature-

+ll &odies at a te$erature a&ove a&solute 4ero eit theral radiation-

Radiation is a volumetric phenomenon% and all solids, liuids, and #ases eit,

a&sor&, or transit radiation to var!in# de#rees-

However, radiation is usuall! considered to &e a surface phenomenon for solids-



5/12/16 | Slide 2'

StefanQolt4ann Law of Theral Radiation

*a)iu theral radiation fro surface

&! Stefan#$olt%mann &aw " loc0

od!%

where is Stefan3olt4ann constant

with the value of 5-66A1>G@

</2

KI

- This Law is a$$lies onl! to &lac0&odies-

8erived fro Plan'(! &aw

t is i$ortant to note that this euation

is valid onl! for theral radiationP other

t!$es of electroa#netic radiation a!

not &e treated so si$l!-

Radiation eitted &! real surfaces

(issivit! + easure of how closel! a

surface a$$ro)iates a &lac0&od! for

which D 1 of the surface- >≤ ≤ 1-



5/12/16 | Slide 2

Radiation asic Conce$ts

+&sor$tivit! α The fraction of the

radiation ener#! incident on a surface

that is a&sor&ed &! the surface- >≤ α ≤ 1

+ &lac0&od! a&sor&s the entire radiation

incident on it "α D 1%-

Iirchhoffs law The eissivit! and thea&sor$tivit! of a surface at a #iven

te$erature and wavelen#th are eual-

Oet radiation heat transfer The

difference &etween the rates of radiation

eitted &! the surface and the radiation

a&sor&ed-

The deterination of the net rate of heat

transfer &! radiation &etween twosurfaces is a co$licated atter since it

de$ends on

the $ro$erties of the surfaces their orientation relative to each

other

the interaction of the ediu&etween the surfaces with radiation

Radiation is usuall! si#nificant relative to

conduction or natural convection, &ut

ne#li#i&le relative to forced convection-



5/12/16 | Slide 25

Radiation heat transfer &etween a surface and thesurfaces surroundin# it

<hen a surface is co$letel! enclosed

&! a uch lar#er "or &lac0% surface at

te$erature Tsurr se$arated &! a #as

"such as air% that does not intervene

with radiation, the net rate of radiation

heat transfer &etween these two

surfaces is #iven &!

f radiation and convection occur

siultaneousl! &etween a surface and a

+ir as $er Oewtons Law of Coolin#

E

D

E



5/12/16 | Slide 26

Siultaneous Heat Transfer *echaniss

Heat transfer is onl! &! conduction in opa&ue solids% &ut &!

conduction and radiation in semitransparent solids. + solid a! involve conduction and radiation &ut not

convection- + solid a! involve convection and/or radiation

on its surfaces e)$osed to a fluid or other surfaces-

Heat transfer is &! conduction and $ossi&l! &! radiation in astill fluid "no &ul0 fluid otion% and &! convection and

radiation in a flowing fluid. n the a&sence of radiation, heat transfer throu#h a fluid is

either &! conduction or convection, de$endin# on the

$resence of an! &ul0 fluid otion-

Convection D Conduction E Fluid otion Heat transfer throu#h a vacuum is &! radiation- *ost #ases &etween two solid surfaces do not interfere with

radiation- Liuids are usuall! stron# a&sor&ers of radiation-

Co&ination of conduction, convection M radiation



5/12/16 | Slide 2:

9R?L(*3S?LOB T(CHO.7(

Ste$ 1 9ro&le Stateent

Ste$ 2 Scheatic

Ste$ ' +ssu$tions and +$$ro)iations

Ste$ 9h!sical Laws

Ste$ 5 9ro$erties

Ste$ 6 CalculationsSte$ : Reasonin#, erification, and8iscussion

*atheatical odelin# of $h!sical $ro&les



5/12/16 | Slide 2@

Suar!

The First Law of Therod!naics

(ner#! &alance for closed s!stes

"Fi)ed *ass%

(ner#! &alance for stead!3flow

s!stes

Surface ener#! &alance Heat Transfer *echaniss

Conduction

Fouriers law of heat conduction

Theral Conductivit!

Theral 8iffusivit!

Convection

Oewtons law of coolin#

Radiation

StefanQolt4ann law

Siultaneous Heat Transfer

*echaniss 9ro&le Solvin# Techniue

*atheatical odelin# of $h!sical

$ro&les



5/12/16 | Slide 2A

Tutorial 9ro&les

?ne face of a co$$er $late ' c thic0 is aintained at >> °C,

and the other face is aintained at 1>> °C- How uch heat is

transferred throu#h the $late

Biven data The theral conductivit! for co$$er is ': < " K°C

at >> °C and 'A5 < " K°C at 1>> °C - +ssu$tion The theral conductivit! for co$$er varies linearl!

with te$erature fro 1>> to >> °C

9ro&le 1



5/12/16 | Slide '>

Solution 9ro&le 1

Biven Thic0ness D >->'

T1 D >> CP T2 D 1>> CP I D ': </ C

To find Heat Transfer rate $er unit area

Solution

Fro Fourier law of Heat Conduction,

/+ D . D 3I "dT/d%

D 3 I "T2 Q T1% / "2 Q 1%

D 3 ': "1>> 3 >>% / ">->'%

D '-: ) 1>6 </2

C o $ $ e r $ l a t e

'c

>> C

1>> C



5/12/16 | Slide '1

Tutorial 9ro&les

+ir at 2> °C &lows over a hot $late 5> &! :5 c

aintained at 25> °C- The convection heat3transfer

coefficient is 25 </2K °C- Calculate the heat transfer-

+ssuin# that the $late is ade of car&on steel "1U%2 c thic0 and that '>> < is lost fro the $late

surface &! radiation, calculate the inside $late

te$erature-

Biven data 0car&on steel D 43 W/m °C

9ro&le 2



5/12/16 | Slide '2

Solution 9ro&le 2

B(O TV D 2> CP Ts D 25> º C; Area = (50 * 75 * 10-4) m2 ; h = 25 W/m2 C

Heat loss by a!"at"o# = 300 W$ %& '+ Heat %ra#s,er &.%&+

'rom eto#s la o, ool"# o# = h*A*(Ts 3 TV%

D 25 W 5> W :5 W 10-4 * (250 6 20 ) = 215$25 W$

o#! = o# 8 ra! = 215$25 8 300 = 245$25 W$

'rom ,o9r"er la o, heat o#!9t"o#

= -:*A*(!%/!)

!% = (*!)/(-:*A) = (245$25* 0$02)/(-43*50*75*10-4) = -3$04 º C %2 6 %1 = -3$04 º C; 250 6 %1 = -3$04 º C; %1 = 253$04 º C$

s t e e l

2 c

25> C

2> C



5/12/16 | Slide ''

Tutorial 9ro&les

+n electric current is $assed throu#h a wire 1 in

diaeter and 1> c lon#- The wire is su&er#ed in

liuid water at atos$heric $ressure, and the current

is increased until the water &oils- For this situationhD5>>> < " 2K°C, and the water te$erature will &e

1>>°C- How uch electric $ower ust &e su$$lied to

the wire to aintain the wire surface at 11°C

9ro&le '



5/12/16 | Slide '

Solution 9ro&le '

Biven d D >->>1 P L D >-1 P h D 5>>> </2 CP TV D

1>> CP Ts D 11 º C

%o ,"#!+

ol9t"o#+ 'rom eto#s la o, ool"#

= h * A * (Ts 3 TV% D 5>>> W " '-1 W >->>1 W >-1% W "11 Q 1>>%

D 21-A@ <-



5/12/16 | Slide '5

Tutorial 9ro&les

Two infinite &lac0 $lates at @>> °C and '>>

°C e)chan#e heat &! radiation- Calculate

the heat transfer $er unit area-

9ro&le



5/12/16 | Slide '6

Solution 9ro&le

Solution 3

T1 D @>>E2:' D 1>:'I , T2 D '>>E2:' D 5:' I ,

D 5-66A ) 1>3@ w/2I,

lac0 &od! , X D 1

D X + " T13 T2

%

. D /+ D "5-66A ) 1>3@ % "1% "1>:' Q 5:'%

D 6A>'-:' </2



5/12/16 | Slide ':

Tutorial 9ro&les

+ hori4ontal steel $i$e havin# a diaeter of 5 c is

aintained at a te$erature of 5> °C in a lar#e roo

where the air and wall te$erature are at 2> °C- The

surface eissivit! of the steel a! &e ta0en as >-@-Calculate the total heat lost &! the $i$e $er unit

len#th-

Biven 8ata heat3transfer coefficient for freeconvection with this #eoetr! and air is hD6-5</2 K

°C-

9ro&le 5



5/12/16 | Slide '@

Solution 9ro&le 5

Biven d D >->5 , Ts D 5> C , Tsurr D 2> C , XD >-@ ,

hD6-5</2 K°C-

Heat loss &! convection Q

conv D h + "Ts Q Tsurr%

"/L%conv D "6-5% "Y% ">->5% "5>32>%

D '>-6' </

9i$e is surrounded &! lar#e enclosure , So heat also transfer &!

radiation rad D X + "Ts3Tsurr %

"/L%rad D "5-66A ) 1>3@ % ">-@% "'2'32A'%

D 25-> w/

Total heat Loss "/L% T D "/L%conv E " /L%rad

D 55-6: </

lect - 2 laws of heat transfer.pptx

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