Heat transfer by conduction and convection, Lab report

8/18/2019 Heat transfer by conduction and convection, Lab report

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Lab Partners:

Corey Page

Isabella Pinos

Michael PerryRon

Florida Atlantic University, Boca Raton, Florida

October 13th and 15 th o !"15

AU#$OR% &O'( B(#A)COUR#

OC(A) ()*I)((RI)* +AB R(POR#$(A# #RA)'F(R


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Abstract

In this re ort, three di erent heat trans er e- eri.ents are er or.ed/ #he irst e- eri.ent consists o 0 barso di erent .etals !- brass, 1- al2.in2. and 1- stainless steel 4hich are heated by a co..on so2rce, thereare t4o te. erat2re sensors e.bedded in the bars 4hich allo4 to ta e te. erat2re readings at t4o di erent

oints along the bar se arated by a distance d, the rate o heat trans er by cond2ction in the o2r bars 4asco. 2ted and co. ared to deter.ine 4hich .aterial it6s a better cond2ctor/ #he t4o brass bars di er in crosssection area and this allo4ed to identi y the relation e-isting bet4een the rate o heat trans er by cond2ctionand the area, 4e concl2ded that the val2es obtained or the rate o heat trans er s2 ort the acce ted val2es o ther.al cond2ctivity o the .aterials, that the rate o heat trans er is directly ro ortional to the cross sectionarea and that ins2lation .aterial sho2ld be laced on to o the bars in order to revent the heat ro. beinglost to the environ.ent/ #he second e- eri.ent deals 4ith the .echanis. o convection, si- c2 s illed 4ithhot 4ater are being cooled do4n in di erent 4ays and te. erat2res are ta en at reg2lar intervals by .eans o a digital ther.o.eter, 2sing this in or.ation it 4as ossible to co. are the e ectiveness o every .ethod incooling do4n the 4ater inside the c2 s, 4e concl2ded that the e ectiveness o the rate o heat trans er byconvection increases 4hen a convective c2rrent is orced into the syste. either so by blo4ing air 2nto thes2r ace o the l2id, or by stirring the l2id or both , 4e also concl2ded that this e- eri.ent can be 2sed toesti.ate the val2e o the convection coe icient h as long as there is not any ins2lating .aterial on the c2

reventing the s2rro2nding air to be in contact 4ith the c2 or the l2id/ In the third e- eri.ent 4e so2ght to b2ild a device 4hich allo4s 2s to .eas2re the te. erat2re 2sing a ther.oco2 le and ad72sting its val2e by.eans o a otentio.eter, a c2rrent 4hich val2e de ends on the osition o the otentio.eter 4as orcedthro2gh a resistor to ta e advantage o the &o2le6s e ect to heat 2 the ther.oco2 le, 4e concl2ded that it is

ossible to satis actory control the increase o te. erat2re by this .ethod b2t 4hen the te. erat2re needs to be decreased 4e do not have any control on the rate o decay o the te. erat2re/

Introduction

$eat has al4ays been erceived to be so.ething that rod2ces in 2s a sensation o 4ar.th,

and one 4o2ld thin that the nat2re o heat is one o the irst things 2nderstood by .an ind/B2t it 4as only in the .iddle o the nineteenth cent2ry that 4e had a tr2e hysical

2nderstanding o the nat2re o heat, than s to the develo .ent at that ti.e o the kinetic

theory, 4hich treats .olec2les as tiny balls that are in .otion and th2s ossess inetic

energy/ $eat is then de ined as the energy associated 4ith the rando. .otion o ato.s and

.olec2les

In 18"1, )e4ton 2blished in +atin and anony.o2sly in the Phil/ #rans/ o the Royal

'ociety a short article 'cala grad22. Caloris , in 4hich he established a relationshi bet4een the te. erat2res # and the ti.e t in cooling rocesses/ $e did not 4rite any

or.2la b2t e- ressed verbally his cooling la4%

“The excess of the degrees of the heat were in geometrical progression

when the times are in an arithmetical progression (by ‘‘degree of heat’’


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Newton meant what we now call ‘‘temperature’’, so that ‘‘excess of the

degrees of the heat’’ means ‘‘temperature difference’’). !"

In the or.2lation o his la4, )e4ton sho4s his con 2sion, 4hich 4as nor.al in his days,

bet4een heat and te. erat2re/ $e s o e o heat loss and degree o heat and this .eans thator hi. a loss o heat 4as al4ays ro ortionally acco. anied by a decrease o 99degree o

heat66/

$e 4rote%

“The heat which hot iron, in a determinate time, communicates to cold

bodies near it, that is, the heat which the iron loses in a certain time is as

the whole heat of the iron# and therefore (ideo$ue in %atin), if e$ual time

of cooling be ta&en, the degrees of heat will be in geometrical

proportion.' !"

C2rrently, )e4ton6s cooling la4 is 2s2ally given in ter.s o heat l2- :, i/e/, the rate o

heat loss ro. a body : ; d18?0 in 18@?/ ! #he caloric

theory asserts that heat is a l2id li e s2bstance called the caloric that is a .assless,

colorless, odorless, and tasteless s2bstance that can be o2red ro. one body into another/

Dhen caloric 4as added to a body, its te. erat2re increasedE and 4hen caloric 4as

re.oved ro. a body, its te. erat2re decreased/ Dhen a body co2ld not contain any .ore

caloric, .2ch the sa.e 4ay as 4hen a glass o 4ater co2ld not dissolve any .ore salt or

s2gar, the body 4as said to be sat2rated 4ith caloric/ #his inter retation gave rise to theter.s saturated liquid and saturated vapor that are still in 2se today/ #he caloric

theory ca.e 2nder attac soon a ter its introd2ction/ It .aintained that heat is a s2bstance

that co2ld not be created or destroyed/ et it 4as no4n that heat can be generated

inde initely by r2bbing one6s hands together or r2bbing t4o ieces o 4ood together/ In

18?@, the A.erican Ben7a.in #ho. son Co2nt R2. ord 1853>1@10 sho4ed in his


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a ers that heat can be generated contin2o2sly thro2gh riction/ #he validity o the caloric

theory 4as also challenged by several others/ B2t it 4as the care 2l e- eri.ents o the

(nglish.an &a.es P/ &o2le 1@1@>1@@? 2blished in 1@03 that inally convinced the

s e tics that heat 4as not a s2bstance a ter all, and th2s 2t the caloric theory to rest/

Altho2gh the caloric theory 4as totally abandoned in the .iddle o the nineteenth cent2ry,

it contrib2ted greatly to the develo .ent o ther.odyna.ics and heat trans er/ !

Background

Heat Transfer

$eat can be trans erred in three di erent .odes% cond2ction, convection, and radiation/ All

.odes o heat trans er re:2ire the e-istence o a te. erat2re di erence, and all .odes are

ro. the high te. erat2re .edi2. to a lo4er te. erat2re one ! /

Cond2ction is the trans er o energy ro. the .ore energetic articles o a s2bstance to the

ad7acent less energetic ones as a res2lt o interactions bet4een the articles/ Cond2ction can

ta e lace in solids, li:2ids, or gases/ In gases and li:2ids, cond2ction is d2e to the

collisions and di 2sion o the .olec2les d2ring their rando. .otion/ In solids, it is d2e to

the co.bination o vibrations o the .olec2les in a lattice and the energy trans ort by ree

electrons/

#he rate o heat cond2ction thro2gh a .edi2. de ends on the geo.etry o the .edi2., its

thic ness, and the .aterial o the .edi2., as 4ell as the te. erat2re di erence across the

.edi2./

Consider steady heat cond2ction thro2gh a large lane 4all o thic ness D-; + and area A/

#he te. erat2re di erence across the 4all is D#; #! #1/ (- eri.ents have sho4n that the

rate o heat trans er < thro2gh the 4all is do2bled 4hen the te. erat2re di erence D#

across the 4all or the area A nor.al to the direction o heat trans er is do2bled, b2t is

halved 4hen the 4all thic ness + is do2bled/ #h2s 4e concl2de that the rate o heat

cond2ction thro2gh a lane layer is ro ortional to the te. erat2re di erence across the

layer and the heat trans er area, b2t is inversely ro ortional to the thic ness o the layer/


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Fig2re 1% $eat trans er by cond2ction thro2gh a 4all

´Q cond = kAT 1 − T 2

∆ x

Dhere the constant o ro ortionality is the ther.al cond2ctivity o the .aterial, 4hich is

a .eas2re o the ability o a .aterial to cond2ct heat, a high val2e or ther.al cond2ctivity

indicates that the .aterial is a good heat cond2ctor, and a lo4 val2e indicates that the

.aterial is a oor heat cond2ctor or ins2lator

In the li.iting case o D- G ", the e:2ation above red2ces to the di erential or./

´Q cond =− kA dT dx

$ere d#=d- is the te. erat2re gradient, 4hich is the slo e o the te. erat2re c2rve on a # -

diagra. the rate o change o # 4ith - , at location -/ #he heat trans er area A is al4ays

nor.al to the direction o heat trans er/

#he inetic theory o gases redicts and the e- eri.ents con ir. that the ther.al

cond2ctivity o gases is ro ortional to the s:2are root o the absol2te te. erat2re #, and

inversely ro ortional to the s:2are root o the .olar .ass M/ #here ore, the ther.al

cond2ctivity o a gas increases 4ith increasing te. erat2re and decreasing .olar .ass/

Convection is the .ode o energy trans er bet4een a solid s2r ace and the ad7acent li:2id

or gas that is in .otion, and it involves the co.bined e ects o cond2ction and l2id

.otion . #he aster the l2id .otion, the greater the convection heat trans er/ In the absence


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o any b2l l2id .otion, heat trans er bet4een a solid s2r ace and the ad7acent l2id is by

2re cond2ction/ #he resence o b2l .otion o the l2id enhances the heat trans er

bet4een the solid s2r ace and the l2id, b2t it also co. licates the deter.ination o heat

trans er rates/

Consider the cooling o a hot bloc by blo4ing cool air over its to s2r ace as sho4n in

Fig2re ! / (nergy is irst trans erred to the air layer ad7acent to the bloc by cond2ction/

#his energy is then carried a4ay ro. the s2r ace by convection, that is, by the co.bined

e ects o cond2ction 4ithin the air that is d2e to rando. .otion o air .olec2les and the

b2l or .acrosco ic .otion o the air that re.oves the heated air near the s2r ace and

re laces it by the cooler air/ Convection is called orced convection i the l2id is orced to

lo4 over the s2r ace by e-ternal .eans s2ch as a an, 2. , or the 4ind/ In contrast,

convection is called nat2ral or ree convection i the l2id .otion is ca2sed by b2oyancy

orces that are ind2ced by density di erences d2e to the variation o te. erat2re in the

l2id

Fig2re !% Cooling o a hot bloc

Hes ite the co. le-ity o convection, the rate o convection heat transfer isobserved to be ro ortional to the te. erat2re di erence, and is conveniently e- ressed by

Newton’s law of cooling as

Q́= h As(T s− T ∞ )


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Dhere h is the convection heat transfer coe cient in D=. ! C or Bt2=h t! F, As

is the s2r ace area thro2gh 4hich convection heat trans er ta es lace, T s is the s2r ace

te. erat2re, and T _ is the te. erat2re o the l2id s2 iciently ar ro. the s2r ace/ )ote

that at the s2r ace, the l2id te. erat2re e:2als the '2r ace te. erat2re o the solid/

#he convection heat trans er coe icient h is not a ro erty o the l2id/ It is an

e- eri.entally deter.ined ara.eter 4hose val2e de ends on all the variables in l2encing

convection s2ch as the s2r ace geo.etry, the nat2re o l2id .otion, the ro erties o the

l2id, and the b2l l2id velocity/

Radiation is the energy e.itted by .atter in the or. o electro agnetic waves or

photons as a res2lt o the changes in the electronic con ig2rations o the ato.s or

.olec2les/ Unli e cond2ction and convection, the trans er o energy by radiation does notre:2ire the resence o an intervening ediu ! In act, energy trans er by radiation is

astest at the s eed o light and it s2 ers no atten2ation in a vac22./ #his is ho4 the

energy o the s2n reaches the earth/ Fort the 2r oses o this e- eri.ent, heat trans er

thro2gh radiation 4ill not be considered/

PID Controller

#he PIH controller is the .ost co..on or. o eedbac / It 4as an essential ele.ent o

early governors and it beca.e the standard tool 4hen rocess control e.erged in the 1?0"s/

In rocess control today, .ore than ?5J o the control loo s are o PIH ty e, .ost loo s

are act2ally PI control/ PIH controllers are today o2nd in all areas 4here control is 2sed/

#he controllers co.e in .any di erent or.s/ #here are stand alone syste.s in bo-es or

one or a e4 loo s, 4hich are .an2 act2red by the h2ndred tho2sands yearly/ PIH control

is an i. ortant ingredient o a distrib2ted control syste./ #he controllers are also

e.bedded in .any s ecial 2r ose control syste.s/ PIH control is o ten co.bined 4ith

logic, se:2ential 2nctions, selectors, and si. le 2nction bloc s to b2ild the co. licateda2to.ation syste.s 2sed or energy rod2ction, trans ortation, and .an2 act2ring/ Many

so histicated control strategies, s2ch as .odel redictive control, are also organiKed

hierarchically/ PIH control is 2sed at the lo4est levelE the .2ltivariable controller gives the

set oints to the controllers at the lo4er level/ #he PIH controller can th2s be said to be the

Lbread and b2tter o control engineering 3 /


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Pro ortional control is ill2strated in Fig2re 3 / #he ig2re sho4s that there is al4ays a steady

state error in ro ortional control/ #he error 4ill decrease 4ith increasing gain, b2t the

tendency to4ards oscillation 4ill also increase/ Fig2re 0 ill2strates the e ects o adding

integral/ #he ig2re sho4s that the steady state error disa ears 4hen integral action is

2sed/

Fig2re 3% ( ect o ro ortional control

Fig2re 0% ( ects o the addition o integral

Objective of the e !eri"ents

In this re ort, 3 di erent heat trans er e- eri.ents 4ill be addressed, one de.onstrating the

behavior o the cond2ction .echanis. o heat trans er, one on convection, and a ractical

sit2ation 4here reading the te. erat2re and ad72sting a variable to control the te. erat2re

4ill be re:2ired/ #he 4ay this re ort is str2ct2red addresses irst the .aterials and .ethods

2tiliKed d2ring the realiKation o the e- eri.ents, the res2lts obtained, a brie disc2ssion o


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the res2lts and concl2sions and it6s organiKed in se:2ence so that all the sections o one

e- eri.ent are sho4n be ore .oving on to the ne-t e- eri.ent/

#he ob7ective o this lab it6s to st2dy the behavior o t4o o the .echanis.s o heat trans er

cond2ction and convection , ho4 the cross section area is related to the rate o heattrans er in cond2ction and ho4 a convective c2rrent on a l2id can i. rove the rate o heat

trans er/


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Heat Bar # !eri"ent $Conduction%

&aterials and "ethods

#'ui!"ent List

In order to er or. this e- eri.ent the allo4ing e:2i .ent has been rovided%

Pasco N lorer *+N P' !""!

Pasco N lorer 1!v HC Po4er #rans or.er

Pasco $eat Cond2ction A arat2s #H @513

Pasco PasPort P' !158

Po4er '2 ly Cable

15 HC !A Po4er '2 ly

Higital Ca.era

Higital Chrono.eter

Higital Cali er

#'ui!"ent Descri!tion

#he $eat Cond2ction A arat2s has 0 bars 4ith @ te. erat2re sensors e.bedded in the

bars and designated by the n2.bers ro. #1 to #@, t4o sensors in every bar/ #he .aterial

ro erties o the bars 4ere obtained ro. the .an2 act2rer6s 4ebsite and are sho4n belo4

in #able 1 /

#able 1Material ro erties o the bars 1

Bars 4ere .eas2red 2sing a digital cali er once the e- eri.ent concl2ded/ #he di.ensions

are sho4n in #able ! /


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#able !Hi.ensions o the bars o the $eat Cond2ction A arat2s

Bar (idth $""% Length $""%Alu"inu" 11/@ = "/1 @8/0 = "/1(ide Brass 11/8 = "/1 @8/0 = "/1)arro* Brass 8/? = "/1 @@/@ = "/1+tainless +teel 11/? = "/1 @@/@ = "/1

#he location o the sensors is listed belo4 in re erence to the bar 4here they are e.bedded

and the osition res ect to the heat sin located at the center o the board/

#1; 4ide brass ar

#!; 4ide brass close

#3; narro4 brass close

#0; narro4 brass ar

#5; 4ide Al2.in2. ar

#Q;4ide Al2.in2. close

#8;4ide 'tainless 'teel close

#@; 4ide 'tainless 'teel ar

# !eri"ent +etu!All connections 4ere done rior to the beginning o the e- eri.ent as sho4n in Fig2re 5 /

Pasco N lorer 4as connected to the o4er so2rce 4hich 4as set to Q and to the $eat

Cond2ction A arat2s,


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Fig2re 5% N lorer *+N and Po4er 'o2rce

Fig2re Q% $eat Cond2ction A arat2s

#he .achine 4as set to the Cool osition d2ring 5 .in2tes and the te. erat2res o every

sensor 4ere recorded 'ee #able 3

#able 3'table #e. erat2re o 'ensors

+ensor T, T- T. T/ T0 T1 T2 T3Te"!$4C% !Q/50 !Q/35 !5/?Q !Q/3@ !5/8" !Q/@" !Q/Q@ !5/@1

#he .achine 4as s4itched ro. the cool osition to the heat osition and te. erat2re

reading or every sensor 4ere ta en a ro-i.ately every 3" seconds d2ring the ollo4ing

1" .in2tes by 2sing a digital ca.era to ca t2re the readings ro. the N lorer *+N, the

ti.e can be read on the screen o the N lorer as 4ell/ #he readings have been lotted vs

ti.e or every bar by 2sing Matlab and can be seen in Fig2re 8 /


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5esults

Fig2re 8% *ra h o 'ensor #e. erat2re vs #i.e or every bar

Discussion

As e- ected, the te. erat2re raises irst at the sensor that is closer to the heat sin , and

a ter so.e ti.e, the te. erat2re at the sensor arther a art ro. the heat sin reaches the

val2e attained by the irst sensor/ #his ill2strates ho4 the heat lo4s ro. the 4ar.er

section o the body to the coldest/

)otice the behavior o the te. erat2re in both sensors or every .aterialE in the gra h

corres onding to the Al2.in2. bar, the te. erat2re o the arther sensor gets very close to

the te. erat2re o the closer sensor, this .eans that the di erence in te. erat2re bet4een

these t4o oints o the bar is very s.all co. ared to the other .aterials, so the al2.in2.

4o2ld have val2es o te. erat2re very close to each other along the bar, co. ared to the

other bars/

Hoing the sa.e analysis or the steel bar, it can be observed that the te. erat2re in the

arther sensor it6s distant ro. the te. erat2re o the closer sensor, indeed, i 4e e-a.ined

the data ro. (rror% Re erence so2rce not o2nd it can be observed that the D# o sensors

#8 and #@ increases 4ith ti.e, .eaning that the te. erat2res at these oints get arther

a art ro. each other as ti.e asses/ As or the Brass bar, it e-hibits a behavior bet4een


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Al2.in2. and 'teel, both te. erat2res being close to each other at the beginning b2t then

start to se arate as ti.e asses/

T*o Brass bars of different cross sectional area6

$eat trans er by cond2ction bet4een t4o oints o a solid body can be deter.ined by thee:2ation%

Q́= kA(T 2 − T 1 )d

Dhere%

Q́ ;It6s the rate o heat trans er 4atts

; ther.al cond2ctivity o the .aterial 4=.

#! and #1; te. erat2re o t4o oints in the sa.e body

A; area o the section er endic2lar to the heat lo4 . !

d; distance bet4een oint 1 and oint !

#he te. erat2re data collected ro. the 4ide brass bar and the narro4 brass bar can be

2sed to e-a.ine the behavior o the heat trans er as a 2nction o the cross sectional area/

#he rate o heat trans er has been calc2lated and lotted vs ti.e or both bars in Fig2re @/


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Fig2re @% Co. arison o $eat #rans er in the 4ide and narro4 brass bars

Fro. Fig2re @, t4o re.ar able as ects can be ointed o2t/

1 #he greater the cross sectional area, the greater the rate o heat trans er by

cond2ction/! #he rate o heat trans er sho4s a si.ilar behavior in both bars/

Observing the behavior o both lots, the c2rve re resenting the rate o heat trans er o the

4ide bar


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Fig2re ?% t s


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Fig2re 11% Co. arison o the act2al and redicted


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Q́ wQ́ n

= Aw An

#his .eans that the actor revio2sly calc2lated -;1/5!!8 it6s act2ally the area ratio o the

t4o bars/ I 4e co. 2te the area ratio o2t o the no4n di.ensions o the bars 4e obtain%

Aw An

= (3.5 ± 0.1 )∗(11.7 ± 0.1 )(3.5 ± 0.1 )∗(7.9 ± 0.1 )

= 1.4 < Aw An


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V ice=−[1 gmL .500 mL. 4.186 kJ kgK .(60 − 80 ) K ]coffee

[0.9167 gmL . 2.108 kJ kgK .(60 − 0 ) K ]ice= 361 mL

! I yo2 have a !"".D heat so2rce inside a sealed container that is co. letely

ins2lated against any trans er o heat, 4hat is the .a-i.2. te. erat2re that 4ill be

reached in the bo- a ter a very long ti.eT

Conclusions

*iven the evidence ointed above, 4e can concl2de that the ratio o heat trans erred by

cond2ction o t4o bodies o the sa.e .aterial and constant cross section it6s e:2al to the

ratio o the cross section area o the t4o bodies as long as they share the sa.e heat so2rce

and the e ects o other .echanis.s o heat trans er 2 on the syste. can be neglected or

ass2.ed to be e:2al or both bodies/

Fig2re 1!% D# 4 =D# n

'o.e errors d2ring the realiKation o this e- eri.ent 4o2ld incl2de the absence o an

ins2lating .aterial on the bars to ens2re a 2rely cond2ctive behavior o the bars/ 'ince the

bars 4ere e- osed to the a.bient air, art o the heat 4as lost to the a.bient 4hich co2ld

have altered the .eas2re.ents ta en/


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Coffee cu! station $, st atte"!t%

&aterials list

+arge Co ee Ma er

Q co ee c2 s 4ith lids

1 C2 ins2lating sleeve

'tirring stic s

1 Higital #her.o.eter

# !eri"ent +etu! and !rocedure

#he co ee cara e 4as illed 4ith 4ater and o2red into the co ee .a er, in the .eanti.e,the si- co ee c2 s 4ere identi ied by letters 2sing a .ar er to 4rite on the. and 4ere set

in di erent con ig2rations as sho4n in Fig2re 13 / #he descri tion o the c2 s is as ollo4s%

A;+id on 4ith ins2lating 7ac et

B;+id on

C;)o lid

H; )o lid and blo4n on

(;)o lid and stirred 4ith a stic constantly

F; )o lid and stirred 4ith stic constantly and blo4n on

Fig2re 13% 'et 2 o the co ee station e- eri.ent

'i- di erent ti.ers 4ere set, one or each co ee c2 , then the hot 4ater 4as o2red in

every c2 at a de th o 58/8 .. into each c2 / #he digital ther.o.eter 4as introd2ced in


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the irst c2 and once the reading 4as stable, the ti.er corres onding to that c2 4as

started, the sa.e roced2re 4as re eated or all si- c2 s, every .e.ber o the tea. 4as

res onsible or setting the ti.er corres onding to that c2 , and blo4ing=stirring de ending

on the case/ Readings 4ere ta en d2ring 1" .in2tes or every c2 and 4ere recorded on a

table ti.e and te. erat2re, see Fig2re 10 / Once the 1" .in2tes had assed, one o the

c2 s 4as .eas2red 2sing a cali er and the ollo4ing di.ensions 4ere obtained/

Hia.eter on to ; 3 in

Hia.eter on the botto.; ! in

Dall thic ness; 1=1Q in

$eight o the c2 ; 0 1=@in

Also the te. erat2re o the roo. 4as .eas2red 2sing the sa.e ther.o.eter o the

e- eri.ent and it 4as o2nd to be 88 SF/

Fig2re 10% c2 ( being stirred as the te. erat2re is read


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5esults

Fig2re 15% #e. erat2re .eas2re.ents o co ee c2 e- eri.ent, irst atte. t

Discussion

#he data obtained ro. this e- eri.ent sho4s a very erratic behavior, there are ea s o

te. erat2re that raise above the revio2s val2es o te. erat2re or the sa.e c2 , this can

be observed in the gra h o Fig2re 15, the c2rve corres onding to )o lid and blo4n

descends 2ntil a val2e o Q! Celsi2s and then increases to a val2e o QQ/Q Celsi2s in the ne-t

reading, as i heat 4as being in 2t to the syste. 4hich 4as not the case / A si.ilar

sit2ation is notice on the 2r le line corres onding to the )o +id and blo4n scenario/

#his 2nty ical behavior o the res2lts co2ld be d2e to the act that the sa.e ther.o.eter

4as being 2sed to .eas2re the te. erat2re o all si- c2 s, so by the .o.ent the

ther.o.eter is 2t in the ne-t c2 , it is already hot given it 4as already 2t into another

c2 4hose te. erat2re co2ld be higher or lo4er, and i not eno2gh ti.e is allo4ed or the

te. erat2re to stabiliKe, the reading 4o2ld be inacc2rate, also, the ti.e li.itations to do the

e- eri.ent didn6t allo4 to ta e eno2gh readings to create a .ore reliable database/

*iven the 2nreliability o this data, it 4as decided to redo the e- eri.ent doing so.e s.all

.odi ications to the roced2re/

Coffee cu! station $- nd atte"!t%

&aterials list

1 co ee c2


23/34

1 lid

1 stirring stic

1 ti.er

1 Higital #her.o.eter

1 Co ee Ma er

1 C2 ins2lating 7ac et

Fig2re 1Q% irst co ee c2 lid on and ins2lating sleeve

Fig2re 18% Higital ther.o.eter # !eri"ent +etu! and !rocedure

Be ore the beginning o the e- eri.ent, the air conditioner o the roo. 4as sh2t do4n so

that it 4ill not a ect the .eas2re.ents 4hen the a=c t2rns on/

One co ee c2 4as set at the ti.e as ollo4s%


24/34

1st +id on and ins2lating sleeve A

! nd +id on B

3rd )o +id C

0 th )o +id and blo4n H

5 th )o lid and stirred (

Qth )o lid and stirred and blo4n F

$ot 4ater 4as o2red into the c2 , the digital ther.o.eter 4as introd2ced in the c2 and

once the reading 4as stable the ti.er 4as started, ta ing readings every 3" seconds d2ring

the ollo4ing 1" .in2tes and recording the data in a table, the sa.e roced2re 4as re eated

or every set2 2ntil co. lete the Q di erent con ig2rations/

5esults

Fig2re 1@% #e. erat2re readings ro. the di erent co ee c2 s

Discussion

*iven the si- con ig2rations disc2ssed above, 4e 4anted to co. ere ho4 the heat trans er

increases or decreases in every sit2ation co. ared to the c2 that only has a lid/

'ince the hot 4ater is s2rro2nded by a l2id .edia air and there is a di erence in

te. erat2re bet4een the 4ater and the air, 4e no4 that 4e are dealing 4ith a sit2ation o


25/34

heat trans er by convection ! , so 4e can a ly )e4ton6s cooling la4 to address the

roble. o inding the rate o heat trans er/ Recalling the or.2la o heat trans er by

convection%

dQdt = hA(T s− T ∞)

and

dQ=− m c p dT

'2bstit2ting 4e have

− mc pdT dt = hA(T s− T ∞)

dT dt

= − hAmc p

(T s− T ∞)

'ince the ter.hA

mc p is a constant, 4e can call it 4hich yields%

dT dt =− k (T s− T ∞)

'olving the di erential e:2ation 4e obtain%

T s= T ∞+(T i− T ∞)e−kt

Dere Ts is the te. erat2re o the s2r ace at the instant t and #i is the initial te. erat2re o

the s2r ace/ 'ince in o2r e- eri.ent the val2e o te. erat2re o the 4ater is no4n at every

instant, it is ossible to solve or the constant o every con ig2ration/

'olving or res2lts


26/34

k =ln (T i− T ∞T s− T ∞)

t

Calc2lating the at every instant or every con ig2ration and co. 2ting the .ean andcorres onding standard deviation 2sing Matlab, the .ean val2e o or every case 4as

obtained/

#able 0%al2e o constant or every sit2ation

C2 stdA "/"""! "/"""1B "/"""! "/"""1C "/"""5 "/"""1H "/""1! "/"""3

( "/"""Q "/"""1F "/""15 "/"""0

I 4e redict the val2es o te. erat2re based on the obtained 2sing the e:2ation

T s= T ∞+(T i− T ∞)e−kt and lot the redicted val2es and the act2al e- eri.ental val2es

vs ti.e 4e obtain the ollo4ing gra h/

Fig2re 1?% Act2al vs Predicted val2es


27/34

Fro. Fig2re 1? it can be noticed that the redicted val2e it6s very close to .eas2red val2es

4hen the sit2ation it6s ri.arily convective i/e/ stirring, blo4ing, blo4ing and stirring /

And it6s .ore inacc2rate 4hen ins2lators are added to the syste. +id and 7ac et, and 72st+id /

)o4 it is ossible to deter.ine the h or every con ig2ration%

h=mk c p

A

Dhere . is the .ass o 4ater, A is the area o convection and c is the s eci ic heat o the

4ater/ 'o in concl2sion, this e- eri.ent set2 it6s an acc2rate 4ay to esti.ate the val2e o the convection coe icient as long as the convection is the redo.inant .echanis. o heat

trans er and the e ects o radiation and cond2ction can be neglected/

#he error o2nd ro. case 1 and case ! it6s d2e to the considerable e ect o the ins2lators,

or e-a. le, 4hen the c2 is covered 4ith the lid, the heat it6s trans erred irst to the air

inside the c2 and then it6s trans erred by cond2ction thro2gh the lid to the environ.ent,

4here inally the heat is dissi ated by nat2ral convection/

#able 5% Convection area, h and co. arison o rate o heat trans er

C2 Convection Area

.!

h <


28/34

.aterial o the c2 , so in c2 A 7ac et and +id , the area o convection it6s 72st the ortion

o area o the level o li:2id that raises above the ins2lating 7ac et, since the s2r ace o the

li:2id itsel it6s not in contact 4ith the s2rro2ndings rovided the lid is on, on the other

hand one the lid and 7ac et are re.oved, this increases the area o the convection since no4

the 4all area in contact 4ith the li:2id it6s e- osed to the a.bient and the s2r ace area o

the li:2id it6s also e- osed/ '2r risingly the coe icient h in case A it6s greater than the one

in case B no 7ac et , b2t the rod2ct hA it6s s.aller, this is 4hat .a es the rate o heat

trans er in sit2ation A being s.aller than B

Fig2re !"% Co. arison o the rate o heat trans er vs ti.e

Ther"ocou!le # !eri"ent

&aterials List

1 Ard2ino H2e O( +ab Board

1 O( +ab Board o4er ada ter

1 Hell +a to

1 Hell +a to o4er ada ter

Ard2ino so t4are on the la to

HataPlot3 so t4are on the la to

1 .icro U'B serial cable

1 ty e #her.oco2 le 4ith 05 c. leads

1 'hort solid !!ga 4ire stri ed 5 .. on each end

#ransistor Unit


29/34

11/3 W $eat Resistor

1 Clothes in

# !eri"ent setu! and !rocedure

#he la to and O( lab board 4ere l2gged into the 4all, and the U'B cable 4as connected

ro. the O( lab Board U'B ort na.ed PRO* U'* to the +a to , then the yello4 4ire o

the ther.oco2 le 4as inserted in the in BR* on 72. er &3, the other 4ire o the

ther.oco2 le 4as inserted in in >BR* 4ith a short 72. er cable connected to the gro2nd

in, then the alligator 4ire 4as connected to a gro2nd in on &3 as sho4n in Fig2re !1 /

Fig2re !1% Connection o the ther.oco2 le and 72. er cable to the O( lab Board

)o4 the resistor end o the transistor 2nit 4as attached to in H=P @ on the board and the

blac alligator cli 4as attached to one o the leads o the heater resistor Fig2re !3

Fig2re !!% Connection o the transistor6s 2nit resistor

&3

&2. er 4ireAlligator 4ire#her.oco2 le

ello4 4ire o

ther.oco2 le

#ransistor

2nit6s resistor

#ransistor 2nit


30/34

Fig2re !3% Connection o the heater resistor

#he red alligator cli ro. the transistor 2nit 4as then connected to the 2se on the O( lab

Board as sho4n in Fig2re !0 , and the ther.oco2 le 4as held in contact 4ith the heater

resistor 2sing the clothes in Fig2re !3 /

Fig2re !0% #ransistor 2nit connected to 2se

#he .ain idea o this e- eri.ent it6s to rove that it is ossible to ad72st the te. erat2re o

a roo., boiler, tan , etc, by .oving a otentio.eter to a di erent location, 4hich controls

the intensity o c2rrent that asses thro2gh a heater resistor/ #he ther.oco2 le in contact

4ith the heater resistor rovides the data read by the board 4hich is converted in the code

Alligator clico.ing ro.

gro2nd

#her.oco2 le$eater resistor

Alligator co.ing ro.

transistor 2nit

#ransistor6sAlligator cli

connected to 2se


31/34

to a val2e o te. erat2re, also the osition o the otentio.eter is read and 4ritten to the

c2rrent to increase, sto or decrease the intensity de ending on the case, the readings 4ere

collected thro2gh the Ard2ino6s serial .onitor and asted into a ne4 te-t doc2.ent or

storage and 2rther analysis/

5esults

Fig2re !5% #e. erat2re and otentio.eter osition vs ti.e

Discussion

Co..ented code 2sed in the lab%

== set 2 global sco e variables or the .oving average calc2lationint iXdataPosition ;"E==initialiKe variable

loat aX XReadings 5"" Evoid set2 Y'erial/begin ?Q"" E== initialiKe serial co.2nication at ?Q"" ba2dsanalogReadResol2tion 1! E==set resol2tion on analog read to 1!

inMode @,OU#PU# E== declare in n2.ber @ as an o2t 2tZvoid loo Y ==start loo== Read the voltage at the ther.oco2 le a. li ied in 2t

int sensor al2e;analogRead AQ E==Convert it to volts 4ith Kero re erenced to the Kero oint o the a. li ier loat X#CX olts; loat sensor al2e !"30/@3?=0"?5/" V!/?8 =??/" E ==!"30 is center o bridge

in 2t/==Read the voltage at the te. erat2re sensor in 2tint te. al2e;analogRead A8 E==convert the HA< reading into a val2e in degrees Celsi2s

loat XC&X#e. ; loat te. al2e =0"?5/" V!/?8 "/5@0?EXC&X#e. ; XC&X#e. ="/""Q!5 E== in degrees Celsi2s


32/34

== (-tre.ely si. li ied #her.oco2 le or.2laloat X#e. ; !0/385V X#CX oltsV1"""/" "/03@ XC&X#e. E

== Use a .oving average=='et one ele.ent in the array to the c2rrent readingaX XReadings iXdataPosition ; X#e. E==*et total o the reading

loat X#e. #otal;"Eor int iXco2nt;"E iXco2nt[5""E iXco2nt YX#e. #otal ;aX XReadings iXco2nt E

Z==incre.ent the array ositioniXdataPosition E==loo the array bac to the start 4hen it overr2nsi iXdataPosition\0?? iXdataPosition;"E

X#e. #otal; X#e. #otal=5""/"Eloat XsetPoint;analogRead A? E== read voltage ro. otentio.eter XsetPoint;!"/"V XsetPoint=0"?Q/" 35/"E== convert voltage into a scaled val2e

'erial/ rint X#e. #otal,3 E== rint te. erat2re to serial .onitor

'erial/ rint ],] E'erial/ rintln XsetPoint,3 E== rint otentio.eter^s osition to serial .onitor

loat Xo2t 2t o4er; XsetPoint X#e. #otal V1"/"E == Pro ortional control state.entint iXO2t ; constrain Xo2t 2t o4er XsetPoint 35/" V3/8 ,"/",!55/" EanalogDrite @,iXO2t E== #a es a v2l2e bet4een " and !55 to heat the resistor delay 1" E == 4ait 1" .s

#he oscillations e-hibited by the te. erat2re are ty ical o a ro ortional control s2ch as

the one that has been i. le.ented in the code, according to 3 , this error can be eli.inated by the i. le.entation o an integral control 4hich 4ill eli.inate the steady state error

derived ro. the ro ortional control/

In Fig2re !5 it can be seen that a variation on the osition o the otentio.eter has a direct

e ect on the te. erat2re read by the ther.oco2 le, this ha ens beca2se 4hen the osition

o the otentio.eter it6s changed, its voltage it6s read by the .icrocontroller board and 2sed

to 4rite a ne4 val2e o voltage on the o2t 2t in connected to the resistor 4hich 4ill

rod2ce a variation on the c2rrent that asses thro2gh the resistor/ $ere 4e ta e advantage

o &o2le6s e ect to generate heat in the resistor and heat 2 the ther.oco2 le/ $o4ever,

4hen the te. erat2re needs to be red2ced to the .ini.2., the only thing that can be done

it6s to sto the c2rrent going to the resistor and let it cool do4n by convection, 4hich

i. lies that 4e lac control on the cooling rocess/


33/34

A ter the disc2ssion sho4n above 4e can concl2de that an integral control loo it6s

necessary to red2ce the oscillations o the readings derived ro. the 2se o a ro ortional

control, ho4ever the desired e ect 4as achieved and this .ethod re resents a si. le 4ay

to address the roble. o te. erat2re control/ #his .ethodology rovides e ective control

on the increase o te. erat2re, b2t the cooling rocess 4ill de end on the s2rro2ndings o

the syste., since the resistor 4ill cool do4n by convection and cond2ction i it is in contact

4ith another body, and not beca2se o the e ect o a control variable/


34/34

(orks Cited

1 U/ Besson, #he $istory o Cooling +a4% Dhen the search or si. licity can be anobstacle, Pavia, Italy% ' ringer, !"1"/

! / Cengel, $eat and .ass trans er, !nd edition, Reno% Mc*ra4 $ill, !""8/

3 / &/ Astro., Control 'yste. Hesign, !""!/

0 ] asco/co.,] "8 11 !"15/ Online / Available% 444/ asco/co.= rodCatalog=#H=#H

@513Xheat cond2ction a arat2s/

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Heat transfer by conduction and convection, Lab report

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