اساسيات الحراريات والموائع

אאאאאאאא

١٦٠١٦٠

א ١٦٠

אאאא

،،אא،אW

אא א א א אאאאאא،אאאאאאא

אאאא אאאאאאאWא

אאK

אאאאאאא א ،א אא

אאאאאא،אאא א ،א אא א א אא א א א א א א א

אא،אאאא،אK

א א ?אאאא ?? ?Kאאאאאאאא

אאאאאאא،א ،א א אא

Kאאאאא

؛ א אא אאK

אאאא

א ١٦٠

אאאא

אאאאאאKאאא–אFאאאEאאFאאE

אאא–אאא،אאאKאא،

א١אאאא Jא JFאאEאאאאFאאאKE

אאאאאאאאאאאFאאאEאאאאאKא

אאאאאאאאאאאאאFאKEאאא

אאאאאאאאK

١אW

אאאאFאאאEאאFאאEאאאאא

א ١٦٠

אאאא

אאאאאKאאאאאאאאאאKא

אאאאאKאאאאא،K

אאאW

אאאאFאאE–אא–FאאאאKEאאWאtimeא،distance،אmassFאאkg

NEאאאאאא،אאtemperature،א،אא،אאK

אאאאאאSIאs،אm،אאkg،אKFאא

oCE،אc،אA،אmol،אאKא١אאאאK

א א א L m

א m א kg

א t s

אא T K

אאi A

א - c

א - mol

١Wאאאאא

א ١٦٠

אאאא

אאאאאאאאאאאareaFE

אאאאm2،אvolumem3F؟אKEאאאאאאאvelocity

smא،acceleration2s

mא،forceאNFא

אא2smkgEאאאא

א،energyFאאאEאJFאאאmN ⋅2

2

smkg ⋅E،אאFאאאאE

powerאאW FאאאsJ3

2

smkg ⋅KEא

٢אאאאאאאK

א א א A m2

א V m3

א v א m/s

א a m/s2

א F N

א E J

א P א W

٢Wאאאא

،אאאאאאאאא

אאאאאאאFאKEאאאא

אKאאאאאא

א ١٦٠

אאאא

FאNאJאאWEאאאאאאאK

١W אאworkFאאEא

10mאא502scm؟

אW אZא×א

LFW ×= אZ10m

אZא×א amF ×=

אZZ0.25×1000 kg Z250kg אZ502s

cmZ502scm÷100

mcmZ502s

cm×100

1cmmZ0.52s

m א

N 125sm 5.0kg 250

amF

2

=

×=

×=

אא

J 1250m 10 N 125

LFW

=×=

×=

٥

אאאא

אאאאאאאא

אא

١

א ١٦٠ אא אאאא אא

- ١ -

אא אאW

אאאאאאאאא

אאW אאא • אא • אאאא • אאאא • אא • אאא • א

אאW ١٠א

אאW אאאא

אא:

• אאא


- ٢ -

אא א

אאאאאאאK

אאאאאאאאאאאאאאאאאאאאאאאא

אאאאאאאאאאא

אK

א אאאאאאא

אאאאאאFאאאאאאEK

א אאאאא


אאאאאאאK אא،

،F1Eאא،אאא


- ٣ -

אF/AאF אאאאא

١Wא

אאא אאאאאW

)z (z g P - P 2112 −= ρ

P2 א(N/m2) 2 P1 א(N/m2) 1 ρ אF(kg/m3 g אא9.8 m/s2

z1אא1א (m) z2א2אאאא (m)

אאאאאאאא



- ٤ -

אאאאאאאאאאKאאאאאFאאאE

אK

אא אאאאאא

אN/m2PaאאאאK،אאאאא

א3אm H2OFEא76אcm

HgFEא،אאאאאא

אאK

g m

PAgc

×

= mא

A א m = V X ρVאρא

V = A X h ،h אא אא

cgg X Xh P ρ

=


- ٥ -

אאאאאא

אאאאא101.3 kPaאאאא

Pabsolute= Pgauge+ Patm

Pabsolute،אאPgauge،אא Patmאא

א

אא،אאאאאאא

אK

א אאא

CאאאאאאאF2E

אKאאאאאאFאאEא7000atm אאאאאאK

P

P

٢Wא


- ٦ -

אא אUא

אאFאאאאEאאא

אאאאאאאF3E

٣Wאא

אאאאאא

Wאa, bאFאאאE

(1)---g

h g g

d g P d g Pcc

2f2

1f1

m

cgρρρ

++=+

d1= d2 +h،ρm ρfאאאFאאאE،

א(1)אא

)2(g

h g )-( PPc

fm21 −−−=−

ρρ


- ٧ -

(2)אאאאFאא(1)א(2)אאאא،ρf << ρm א(2)

)3(g

h g PPc

m21 −−−=−

ρ

אאא

אאאאאאאF4E

٤Wאאא

אאאאKP2 = Patmא(2)

)4(g

h g )-( PPc

fmatm1 −−−=−

ρρ

fρρρ<<−−−=− m

c

matm1 )5(

gh g PP

אאאאאאאא

אא


- ٨ -

אאא אאאאאאאא

אF5E

٥Wאאא

אאאאאאFאאKEP2 = 0א(3)

)6(g

h g )-( Pc

fm1 −−−=

ρρ

fρρρ<<−−−= m

c

m1 )7(

gh g P

אא

אאאאא،אאאאא

F٦E

٦Wאא


- ٩ -

אאh، hLאאאsinθ Lh

=אאθL אא

אאאא،אh =L sinθ


- ١٠ -

F1E

אאW • אאאאאא

אא

• אא • אאאאFאEאא • אאאא • אאאאא

(1)

אאאאא3.66m917 kg/m3אא3.05mאאא،0.61m،אא101.3 kPaאW

(1)3.05אmאא (2)אאאאא

Patm

P2


- ١١ -

אWא

אW ١K אאאאאאאא

אאאאא ( z1= 0 )

)z (z g

g ρ PP atm1c

1atm −=−

gc=1kgm/Ns2Patm=101.3X103Pa, ρ=917 kg/m3, g=9.8m/s2,zatm=3.05m

P1 = 101.3 X103 + 917X 9.8X3.05 = 1.29 X105 Pa

٢K א(1)אאאאאאא

אאא P1 =1.29 X105 Pa , ρ =1000 kg/m3, z1 = 0.61m, z2 =0

P2 = 1.29X 105 +0.61X 1000X 9.8 = 1.347X105 Pa


- ١٢ -

(2) ،אאאאאא28.76 in

אW

אאא28.76 in אW

אcgh g ρ P =

ρHg=13600 kg/m3, h= 28.67 (in )X(2.54/100) m

P = 13600 X.9.8 X(28.67X2.54/100) = 97125 Pa

(3) ،אאאא1250 ft

א؟ אWאאא

אW אאאאא

אאא = 1000kg/m3, h= 1250 (ft) X0.3 mא


- ١٣ -

P= 1000X 9.8X 1250X0.3=367500 Pa (4)

אאאא،אאא3 0 psig،אאאא

؟א

خزان تغذية

مبادل حراريh

אW א،אאאא30 psig

אW אאא

P2 = 30 (psig)X(101.3X103/14.7) Pa + Patm

אאאאא

) z(z g

g ρ PP 2atmc

atm2 −=−

ρ = 1000 kg/m3, h = zatm – z2

h = 30 (psig)X(101.3X103/14.7)/ (1000X9.8)= 20.67m (5)

א،אאאאא763mmHgאא،mmHgאא


- ١٤ -

אW

אא،אאאאאאא אW

אאאאא P1= Patm

c

matm g

h g ρ P = Patm = 763 (mm Hg) X 101.3 X 103/760 Pa, h = 6.57m

ρm = (763 X 101.3 X 103)/(760 X 9.8 X 6.75) = 1579.5 kg/m3

אא

c

fmba g

h g )ρ-(ρ P-P =

ρm = 1579.5 kg/m3, ρf = 1000 kg/m3 , h = 0.21m

Pa – Pb = (1579.5- 1000) X 9.8 X 0.21= 1192.6 Pa


- ١٥ -

אא

א

א אאאאאא

אאאאאאאאא

אאאאאאאאא،אאא

אאאאאאאאאF

اجتاه احلركة

FF

אאאאאאאאא

אאאאאא،א

אAFτ =A אא

אא

אאFאאאאE،אאא

vאyאאאאא،µאאאאאאא


- ١٦ -

Kאאאא،אאאאאא

אאאאאאאאאאאאK

אאא אאאאאאPa.s

Fkg/(m.spoiseאאdyn.s/cm2gm/cm.s

אאאאא

אאאאאאKאאאאKאאאאאאאא

אאאאאאא،אאאאא

אאאאאאאאK

אא،אאאאאא1000 kPa אאאאאאאא


אF1E


- ١٧ -

אא

אא

אאאא،אאאאא

אאWאאאאאאא

Kאאאאאאאאאאאאא

אאאאאK

אאאאאא،


אא،א،אאאאא

Fא7 EK

אאאאאאאאאאאא

אאFאEFReE

µD vρ Re =


- ١٨ -

ρ،א V،אD،אאאµא،אאאאאאאאא

Re < 2100א،אRe > 4000אאאאאאאאאאאאא

٧Wא(a)אא(b)

א

אאאאאאאאאאאאאW

t)z,y,P(x, Pt)z,y,ρ(x, ρ t)z,y,v(x,v

===

אאאאאאאאאא،אא–א

אאאא


- ١٩ -

P(x) Pρ(x) ρ v(y)v

===

x،אאy אאאא،

אאאאאאאאאאאK

אאאאאאWאאאאאאאאאאאאאא

אאאFאEאאאא

אאאאאאאאאאא…Kאאאאאאא

אאK


- ٢٠ -

אאא אאא

אאאא

א،אאאאאW،אאאאא

אא אאאאאאאאK

א(1) (2)א(8)

٨Wאאא

אאא(1)אאZאאא(2)

א

21 m m && =

m&אא(kg/s)אאא،אאאאW

2 211 ρV ρ V && =


- ٢١ -

V&אא(m3/s)אאאאאW

222111 ρA v ρ A v =

1vאא(1)א A1א(1)

v 2אא(2)א A2א(2)

אאאאאאא

אאא אאFW1(אא

אאg z(J/kg)z،א(2)אאאאvv2/2(J/kg)،(3)אא

אP/ρ(J/kg) Pא1/ρ،אאאאאאאא(1)(2)א

אאאW

222

21

21

1 z g v21

ρP z g v

21

ρP

++=++

W אאאאא

אF9Eאv1A1אP1

אאאA2אP2אP1-P2Kאאא(1)(2)


- ٢٢ -

2 2 11 AvA v =

2

112 A

A v v =

٩W

א(1)(2)אאz1=z2

v21

ρP v

21

ρP 2

222

11 +=+

v2

A

A v 21

ρP v

21

ρP

22

21

2122

11 +=+

[ ]2

1- /AA vρ P - P22

21

21

21 =

[ ]1- ) /A(A 2

ρP - P v

221

211 =

[ ] ) /A(A-1 2

ρP - P v

221

212 =

2211 A vA v V ==&


- ٢٣ -

א



אא،אאאאאאvאvאαאאאα

אאאא،α =0.5אאα=1אאאW

f222

2p1

21

1 hz g v 21

ρP w z g v

21

ρP

+++=+++αα

אאא(wp)אאאאא(hf)אאא

אאאאאאאK

אא אאאאאאאאא

א ωτאאKאאאאLאאDF10Ev


- ٢٤ -

D

L

اجتاه احلركة

τw

v

١٠Wאאא

אאאא(hs) W

D2L v f 4J/kg)(h

2

s =

fאאאאKאאאא(2)א

אאאK

א אאאאW

Re16 f =א

אאאאאאKאאאאאאFε/DEεא

F11EאאאאאאאאאK


- ٢٥ -

D ε

١١Wא

אא אאאאאאא

אאאאאאF12Eאאאאאא

ــاجئ ضيق مف ــاجئ اتساع مف

صمامــريان اجتاه الس

١٢Wאא

אא(h D)אאאW

2 vJ/kg)(h

2

D K=

KאאF3E

אאאאאאאאK،

אאאאאKאאאאאאאאFאאE


- ٢٦ -

אא אאאאא

אאאאאא،

א

shρP

=∆

∆P א،ρ אא∆ Pאאאאאאא JאW

2D vL 32 P µ

=∆

אאאאאK Jא

אv LP

∝∆אאn

v LP

∝∆nא1.7-2

אאאאאKאאאאאאאW

Ds h hρP

+=∆


- ٢٧ -

אא אא

אאאאאא

אאאאאאאK Wא אאאאא

אאאWא،אאאאKאא

אאאאאאא،אאאא

אא،אאאאאאאאאאא

K

אא אאWאאאא

אאאאאאאאאאאאאאאא

אאאא)13(אאK


- ٢٨ -

١٣Wאאא

Wא אאאאאאאאא

אאאאאאK

אאאא

Wאאאאאאאאא

F14EאאאאK

١٤Wאא


- ٢٩ -

אאאאאאאאאאאאאאאאF15KE

١٥Wאאא

אאא אאאאאאאF16E

אאאאאאאאא(1) אאאא(2)

(3)אא(4)Kאאאאאאאא

אאאאאאא،אK التصريف

الدفاع

األرياش

الدخول

١٦Wאאא


- ٣٠ -

אאאא אאאאאאאאאאא

אאאאאאKאאאא(zs) א

אאאK


- ٣١ -

(2) (1)

1030 kg/m32.12 cp0.605 kg/s63.5mmא،W

(a)א،

(b)א2100אאא

אW

µD v ρRe = (a)

ρ = 1030 kg/m3 , µ =2.12X10-3 Pa.s , D = 0.0635 m, v = ??

A v ρ mنستخدم vلحساب =&

232

m 1017.34

πDA −×== , = m& 0.605 kg/s

m/s 185.01017.31030

605.0v 3 =××

= −

4000 5.57071012.2

0.0635 0.185 1030Re 3 >=×

××=

−

אא

31012.20.0635 v 10302100Re

−×××

== (b)

m/s 0.068 0635.01030

10 12.22100v-3

=×

××=


- ٣٢ -

(2) 829 kg/m3אאא

m3/s1.388 X10-3אא(1)(2)אאא(3)،א

FaE אאא(1) א(2)א(3)אא FbE אא(1)א א(2)א(3)

אW aK s/m 10 1.388V 3-3×=&אאא(1) ρ V m1 ×= &&

kg /m3, ρ = 892s/m101.388V 3-3×=& s/kg 1.238 m1 =∴ &

אאא(1)אאא(2)אאאא،(3)אאאא

(2)אאאא

s/kg 0.619 2

1.238 2m m 1

3 ===∴&

& bK ،אאא

2321

11 m 10027.24D πA ),

10054.22(D −×==×=

2322

22 m 1056.44D πA ),

10054.23(D −×==×=

2323

33 m 1014.14D πA ),

10054.25.1(D −×==×=

(1)


- ٣٣ -

111 A ρ v m ××=& m1&،A1،ρ

m/s 685.089210027.2

238.1ρ A

mv 31

11 =

××=

×=

−

&

m/s 304.08921056.4

238.1ρ A

mv 32

22 =

××=

×=

−

&

m/s 218.18921014.1

238.1ρ A

mv 33

33 =

××=

×=

−

&

(3)

א10 cmא19 m/sאא7cmא10 m/sאאאא15 cm،

FאאEאאאא،

1

2 3

אW

213 mmm &&& += Avρ Avρ Avρ 221133 += Av Av Av 221133 +=

3v A1, A2, A3 = 0.15m D1= 0.1m, D2 = 0.07m, D3

2321

1 m 10854.74D πA −×==


- ٣٤ -

2322

2 m 10848.34D πA −×==

223

3 m 018.04D πA ==

A1, A2, A3, 321 v,v,v אא

m/s 428.10018.0

10 848.31010 7.8519v -3-3

3 =××+××

=∴

(4)

אא1.15אא،50 mmאאא4.5mאאא

אאאאאא،

2

4.75 m

D =50 mm1

אW

א Wאאאאאאא

אFאאאאEאאאא

אאאאאאאא אW

אאF(1)אEאאאF(2)אE


- ٣٥ -

222

21

21

1 z g v21

ρP z g v

21

ρP

++=++

P1 = Patm FאאאאE , v1 = 0 FאאאE P2 = Patm ,v2 = ?

z2 = 0, z1 = 4.57 m FאאאE

W m/s 9.46 4.57 9.8 2 z g 2v 12 =××==

(5) אאאא6.31X 10-3 m3/sFאאKE

אאאא،א،אאאאא20 m

א،אאא0.75אא0.55א1000 kg/m3א0.001 Pa.sא،אW

aE אא bE אא cE א dE א eE אאאא fE אאאא gE אאאא hE אאאא iE אאא 65 % jE אא


- ٣٦ -

20 m

خط التفريغ

خط السحب

אW

אאאאFאEאאאאאא،אFאEאאאאא

aE א،אא

D = 4 X 2.54/100 m, 4D π A

2

= = 8.107 X 10-3 m2

m/s 0.778 10107.8

1031.6AV v 3

3

=×

×==

−

−&

bE אאא

D = 2 X 2.54/100 m, 4D π A

2

= =2.027 X 10-3 m2

m/s 3.113 10027.2

1031.6AV v 3

3

=×

×==

−

−&

cE א

µD v ρ Re =

ρ = 1000 kg/m3, v = 0.778 m/s, D = 4 X 2.54/100, µ = 0.001 Pa.s

79044 100 001.0

2.54 4 0.778 1000 Re =×

×××=


- ٣٧ -

dE (cא

µD v ρ Re =

ρ = 1000 kg/m3, v = 3.113 m/s, D = 2 X 2.54/100, µ = 0.001 Pa.s

140 158 100001.0

2.54 2 3.113 1000 Re =×

×××=

eE אאא

D2v L f 4 h

2

s = Re =79044, אא, f = 0.0045 ( Fאא

L = (20 ft/3.2808) = 6.096 m, m/s0.778v = , D = 4 X (2.54/100)

א

J/Kg 0.327

1002.54 4 2

(0.778) 6.096 0.0045 4 h2

s =××

×××=

fE אאא

Re = 158140, f = 0.0040, L = (125+10+34+50) ft /3.2808) = 66.752m,

m/s3.113v = D = 2 X (2.54/100)

J/Kg 101.871

1002.54 2 2

(3.113) 66.752 0.0040 4 h2

s =××

×××=

gE אאא

2v)K K (h

2

nContractioElbowD ×+=

m/s 0.778v = KContraction = 0.55,KElbow= 0.75,


- ٣٨ -

J/kg 0.393 2

(0.778))0.55 0.75(h2

D =×+=

hE אאאא

2v K 2h

2

ElbowD ××= m/s 0.778v =KElbow= 0.75,

J/kg 7.268(3.113) 0.75h 2D =×=

iE אZη

m WP &× η،אη = 0.65

kg/s 6.31 100010 6.31 ρVm -3 =××=×= &&

Wpאא(1) אאאא(2)א

f2

222

P1

211 h z g v

21

ρPW z g v

21

ρP

+++=+++αα

P1 =P2 =Patm

0vv 21 == z1 = 0, z2 = 20 m FאאאאאE

hf = hs א H hD 109.859 = 7.268+ 0.393 + 0.327+101.871= א J/kg

α =1 FאאE

J/kg 859.305859.109208.9W =+×=P kg/s 6.31m =& , η =0.65 Wp,

א = 2.97kW W 486.29690.65

6.31 859.305==

×

jE אא،אאאאא(1)(2)


- ٣٩ -

1 2

(1)אא،א(2)א

P2 –P1 = ?, WP = 302.2 J/kg, hf = 0, z1 = z2

WP =(P2 –P1) / ρ, P2 –P1 = 302.2 J/kg Wאא(1)אאאאא

א(2)א אא אאאKאאאא

אא


- ٤٠ -

א(1)א אאא

١K אאא • אאאאא • אאאא • אאאא ٢K אאא • אא • אאאא • אא ٣K אא • אאאאאא • אאאאאא • אאאאא • אא ٤K אא • • • ٥K אאאא • • •


- ٤١ -

אא(1) אאא

١K אאא • אאאאא • אאאא o אאאא ٢K אאא • אא o אאאא • אא ٣K אא o אאאאאא • אאאאאא • אאאאא • אא ٤K אא o • • ٥K אאאא • o •


- ٤٢ -

א(2)א אאא

١K א

• אאאאאאאאאא

אאאאאאאאא •


٢K אא

• אאא

• אאא

• אאא

٣K אא

• אאא

• אאא

• אאאא

٤K אא

• א

• א

• א

٥K אאאא

• אאאא

• אאאא

• אא


- ٤٣ -

אא(2) אאא

١K א


o אאאאאאאאא


٢K אא

• אאא

o אאא

• אאא

٣K אא

• אאא

• אאא

o אאאא

٤K אא

o א

• א

• א

٥K אאאא

• אאאא

o אאאא

• אא

אאאאאא

אאאאאאאא

א

א

א

٢

א ١٦٠ אא אאאא אאא

- ٤٤ -

אאW אאאאאאאא

אאW אאאW • אאאאא • אאאאאאאאאא • אאאא • אאאאאאא

אאW ١٥א

אאW אאאא

אא:

• אאא


- ٤٥ -

אאWאאאאאThermodynamics

אא،אאאאאאאאאKאאאאא


אאאאKאאאאאאאאאא

אאאאאאאאאאK

אאאא System: אאאא אאSurroundings W אאאאא

אBoundariesWאאאאא

אW אאW אאאאא،

אאאאאאאאאאאF١KE

غاز أو سائل mكتلته

ال كتلة

١Wאאאא

אאאאאאאאאא


- ٤٦ -

אאאאאאF2EאאKאאאworking fluidאאאאאKא

אאאאFFאEאאאאאE

حدود متحركة

حدود ثابتةغاز

2 kg 1m3

غاز 2 kg

3m3

حرارة

٢Wאאאא

אאאW אאאא

אא Open Systems: אאאאאאאאאאאא ) 3شكل(

كتلة

الطاقة

٣Wאא


- ٤٧ -

אאProperties of a System : אאאאאאאאPאאTאVאmKKאא

WKאאאאאא(extensive and intensive properties)Kאאאאאא،א،א

אKאאאאאאאאאאאאאאאא

אאאV/m

אW אאאאא،אאאאא

אK،אאאאאאאא1m33m3،

אאאאW אאאאאאאאאThermodynamic process אאאאאאPathאאאאא

אאאאאאאKאאW

• א Reversible processes: אא אאאא

אאא • אIrreversible processesW

אאאאאאK ،אאאא

אאאאאאא


- ٤٨ -

אKאאאFאEאאאאאאFאKEאאאא

אאאאאאאKאאאאאאKאא

א،אאאאאאאא

אאאאאאא

אאאאאאאאאאאאאא

אאאKאאאאאאאאאאא

אFאEאאFאEאאאK

غاز

٤W

אאאאאKאא

אאאKאאאאאאא


- ٤٩ -

אאאאא،אאאאא

אאאאאאאKאאאא

אאKאאאאאK


؟אאאאא،אאאאא

אאאאאאאאאאאאאK


- ٥٠ -

אאWאאאאאאאאאאאאאאאאK

אאאאאאאאאאאאא(5)א

p

v

٥W


- ٥١ -

אא אאאא

אאאאאאאא،אא

אKאאאאKאאאאאאאא

אאאאאאKאאאאאאאא

אאאאאאאאאאKאאאאאא

אאאאאאKאאאאאאאאא

אאאאאאאאאאאאאאאאא

אאאאKאאאאאאאאא

אאאאאאאאאאאאאא

F(6Kאאאאאאאאאאאאא

Q (+)

(-)

(-)

(+)W

٦Wאאאאא


- ٥٢ -

אא

אאאאאאF אdsאאאW

∫=S

0

ds F W

אאאאאWא،אKאאא

אאאא؟

אאאא،אאאאאאPאVאA،

אאאP-dP Kאאא dVאאאאאאPא ds

(7)

A

P

غاز

ds

٧Wא

אאאאאאא

∫∫∫ ===2

1

V

V

S

0

S

0b PdVdsPA ds F W

F = P A، dV = A ds V1, V2 אאאאאא،אא(Wb )אאdV،


- ٥٣ -

אאאאא dVא،אאאא

אKא،אאאא

Wאאאאאא

אIsobaric Process


אאW P = constא

)V(V PPdV W 12

V

Vb

2

1

−== ∫

אא(J)Jouleאאאאאאאא

QFאEFאEא)٨(

P

غاز

Patm مكبس حر

Q ٨Wא


- ٥٤ -

אאIsothermal Process

אאאאFאאא

אKא(9)א،W P V = const אא

P

غاز

F

Q ٩Wאאא

אאאאאאאW

Vconst P =

⎟⎟⎠

⎞⎜⎜⎝

⎛×=⎟⎟

⎠

⎞⎜⎜⎝

⎛×=== ∫∫

2

1

1

2V

V

V

Vb P

Plnconst VVln const

VdVconst dV

Vconst W

2

1

2

1

אא Polytropic Process

אאאאאאאא،אאאאאאאW


- ٥٥ -

P Vn = constnPVאאאא

n-11V 1P2V 2P

n-1

n-11V - n-1

2Vconst bW

−==

אn=0אאאאn =1אאאKאאאא

א

אאאא Isochoric Process

אdV=0)٠Z(WbאאאאאאV=

constאאאK

אאאאW אאאאאאאא

אאאאאאאאאאאאאאאK

אא אאאאFאאאא

אEאאאאאאאאKאאאWP V = n R T،P

،אאV،אאn،אRאאאJ/mol K 8.314אSITאאאKאאאא



- ٥٦ -

אאא אאאאאאאKאא،

אאאאאKאאאאאאאאאאאK

אאאאאKא

אאאא(20oC)אא1אatm אאאאאאא،א

(compressed liquid) אאאKאאאאאאא100oCא

(saturated liquid) אאאאאאא(saturated vapor) אאאאא

אאאאאאאאאאאאאא(superheated

vapor)Kאאאאא T-V(10)K

T oC

V

20

100

Compressed Liquid

Saturated Liquid mixture

Superheated vapor

١٠Wאאאא


- ٥٧ -

אאאאאW،،،Kא

אאאאאאאאאאאאאKא

אאא saturated steam tablesאאאאאא

אאKאאאאאאאאאאFאE) T( ocאאאאא

אPsat ( kPa) אאאאאא vf, vg (m3/kg)אאאאאאאאא

אא (kJ/kg) uf, ug, hf, hgKאאאאאאאsuperheated steam tablesאא

אאאאאאאאאאK

אא אאאא

א،אאאאאאאאאאאאאאאאאאאא

אאא١K


- ٥٨ -

الخواص

المعطاة حمصبخار م بخار مشبع خليط مشبع سائل مشبع سائل بارد

T, P P > Psat at T P = Psat at T P = Psat at T P = Psat at T P < Psat at T

T< Tsat at P T = Tsat at P T = Tsat at P T = Tsat at P T > Tsaat P

v, (T or

P) v < vf at T or P v = vf at T or P vf <v<vg at T or P v = vg at T or P

v > vg at T

or P

u, (T or

P) u < uf at T or P u = uf at T or P uf <u <ug at T or P u = ug at T or P

u > ug at T

or P

h, (T or

P) h < h f at T or P h = hf at T or P hf <h <hg at T or P h = hg at T or P

h > hg at T

or P

١Wאאא


- ٥٩ -

אא אאאא

אאW

אאאא א אאאאאאאK

א אאאא K אאאאאאא

א،אאאאאאאאאK

∆אאH∆אאאZ٠

אאאZאאאאאאאאאאא،אZאאא

א אא אא Kאא אאאאאאאאא

אאאאאאא W-QU =∆

U ∆אאאאא

א אאאאאא אא

אKאאאאאאאאאK

אW H = U + PV


- ٦٠ -

אא h = u + Pv

אא d(PV)dU dH +=

dPVdVPdU dH ++=

אאאV dP = 0 אאאאאאאאdU = δQ - δWbδWb

= P dV dH = δQ

∆H = Q אאאאא

∆h = q qאאאFאאאאE

אאא P dV = 0א

∆H = ∆U + P ∆V ∆h = ∆u + P ∆v

אאאא

∆H = ∆U ∆h = ∆u


- ٦١ -

אאא אאאאאאאאא

אאאאאאאאאאאאאKאאאאא

אאKאאאאאאW

١. אאאCvאאאאאאאאאאא q = ∆u

du /dT Cv = و

٢K אאאWאאאאאאאאאאאאא

Q = ∆h CP = dh / dT

אאאאאא،אאאאאאאאא

אא

אאאאאאא

אא א א אא א א א א א א א Kא א א

אאאאאאאאאאאאאK

dT (T)C u 2

1

T

Tv∫=∆

dT (T)C h 2

1

T

TP∫=∆


- ٦٢ -

אאאCpאאאאאאאC p – Cv = R אאK

אאאאא א א א א א

א، אא אא W،אא،א ،אא،א

אאאא،א،אKאאאאאאאא א F،א אא

א ،א ،א،א E א א אאאאאאאאאW

⎥⎦

⎤⎢⎣

⎡−+

−+−= )z(z g

2u uhh m W- Q 12

21

22

12&&&

⎥⎦

⎤⎢⎣

⎡−+

−+−= )z(z g

2u uhh w- q 12

21

22

12

אאאאאא(J/s) = Q&

אFאEאאאאא(J/s)=W&

אא= (kg/s)m&

אאאא(h2) א(h1)(J/kg)∆ h = h2-h1=

אאאאF (J/kg=2

u u 21

22 −∆k e =

אאאא(J/kg))z(z g 12 −∆pe =

אאאאא(J/kg)q =

אאאאאw = (J/kg)


- ٦٣ -

אאא אאאא

אאאאאאא

אאאאאאאאK،אאאWא

؟אאאאאאאKאאאאאאאאא

אאאאאאKאאאאאאאאאאKאאאא

אאאאאאאאKאאא،אאאא

אאאאאאאאאאאאאאKאאא

אאאאאKאאאאאאאאאא

FאאאאאEאאאאאאאאאאK


אאKאאאK

אא

אא(11)KאאאאאאKאא


- ٦٤ -


غالية

مضخة

مكثف

تربينة

Win Wout

Qout

Qin

١١Wאא

אאאאאQin אאQout אKא

אKאאא (η)אאאאאא

inputheat totaloutputnet work η =

א∆U = 0net work output = Qin - Qout

in

out

QQ -1 η =


- ٦٥ -

(3) אאW

• אאFE • אאא • אאאאZ • אאאאאא • אאאFאאאאEאF

אאאאEאאאא

• אאאאא • אא • אאא • אאאאאאאאאא

(1) אאאPV1.4 =constא،

א2kgאאא100kPaא300Kאאא700Kאא،

אW

١K אאא

٢K אאאאאCv20.804 kJ/ kmol K

٣K אאא


- ٦٦ -

אW אW

• אWא

• אאn =1.4Fn١E

١. n1

)T- (T R m n-1

V PV PW 121122b −

=−

=

m אWאLאאZ2/28Z0.0714 k mol

R = 8.314 kJ /mol K, T2 = 700 K, T1 = 300 K Wb = -593.62 Jאאא

א

٢K אאאאא ∆Uאא،

∫=∆2

1

T

T v dT C U

∆U = Cv (T2 –T1) Cv = 20.804 kJ/mol K

∆U = 20.804 (700 -300) = 8321.6 kJ/kmol X0.0714 kmol = 594.16 KJ ٣K אאאאאאאא

∆U = Q –W , Q = ∆U + W = 594.16 -593.62 = 0.54 kJ


- ٦٧ -

(2)

א8 kgאא500 kPaoC300א،אא70%אK

א ١K אאא ٢K אאאא ٣K אא ٤K אאא

אW אW

• א • אא • אאאW • אאWאאאאFא

70%אאאאאאאE • א ١K א

Wb = P (V2 –V1) אV1אאא V2אאא

W אאv1 500 kPaC 300o0.5226 m3/kg

V1 = 0.5226 m3 /kg X 8 kg = 4.18 m3 v2אW

v2 = (1-x) vf + x vg אאvf vgאאF

אEאאאKxאאאאא


- ٦٨ -

) P = 0.4758 (~0.5 MPa،vf =0.001091 m3/kg= 0.3928 m3/kg vgx = 0.3W= 0.12 m3/kg v2

V2 = 0.12 X 8 = 0.96 m3 ∴ Wb = 500 kPa X (0.96 – 4.18) = -1610 kJ

אאאא ٢K אאאאU1 - ∆U=U2

א1 V U1אאא U1 = 2802.9 X 8 = 22423.2 kJ

אV2U2אאא u2 = (1-x) uf + x ug = 0.7X 631.68 + 0.3 X 2559.5= 1216.3 kJ/kg

U2 = 1216.3 X8 = 9730.7 kJ ∆U = 9730.7 – 22423.2 = -12692 kJ

אאאאא (3)

א25000 kg/hr8MPa450oC30kPaאאאא، 4MWאאאאא،

אא אW

אW ،אאאא،א

)h(h m W- Q 12 −= &&&

h1 h2 אאאאF1אEאאאאאאא

אאKאא8MPa אאאאא 295oCFאאאEאאאאאא

K

אאאאF(P= 8MPa, 450oCh1 = 3272.0 kJ/kg

אאאאFkPa h2 = hg = 2626.8 kJ/kg ( P = 30


- ٦٩ -

W&א4MWm&אא25000 kg/hrאאאאא

)h(h m W Q 12 −+= &&&

kW -408053272)-(2626.8 360

25000 10 4 Q 3 =+×=&

אאאא


- ٧٠ -

א(3)א אאא

١K אאא • א • א • אאא ٢K אא • אא • אאא • אאא ٣K א • • • ٤K אאאא101.3 kPaא120oC • • • ٥K א • א • א • א


- ٧١ -

אא(3) אאא

١K אאא • א o א • אאא ٢K אא o אא • אאא • אאא ٣K א • • o ٤K אאאא101.3 kPaא120oC o • • ٥K א • א • א o א

אאאאאא

אאאאאאאא

אא

א

٣


- ٧٢ -

אאWאאאאאאאאא

אאW אאא

• אאא • אאאאאא • אאאאאאא אאאא •

אאW ١٥א

אאW אאאא

אאW

Gאאא


- ٧٣ -

Wאא

אאHeatאאEnergyאאאאאTemperatureאKאא،א،א

،א،אאא،אאאאאאאאאFאאאאאאE،

אאFאאאאאאEאא،FאאאאאאאאאEאא،א،אא،Fא

אE،אא،K א،אK

אא،אאאKאאא

אFאאאאEאאKאאאאאא

אאאKאאאאאאאאאאKא؛

אא،אאאאא،אאK

אאאאאאאKאאא Heat TransferF١אEא،

אאאאFאאאHeat ConductionEאאאאאFאאאHeat ConvectionEאאאאאFאאאHeat

RadiationKEאאאHeat Conductionאאאאאא،אFEKאאא Heat

ConvectionאאאKאHeat Radiationאאא Jא JאFא


- ٧٤ -

אאאאאKEאאאאK

١אW،אאאאאאא


- ٧٥ -

אא אאא

אאF٢אEאאאא

אאאאאאאאאאKאאאאאאאK

אאאאאאאאאאKאאאאאאא

אאאאאאK

50 oC

15 oC

Q

50 oCQ

15 oC

Q50 oC

ماء بارد10 oC

أ

ب

٢אW J،אאא Jאאא


- ٧٦ -

א،אאאאא٢אאאאאאאאאאאאאא

FאאאאאאאKE٣אאאאאאא

אKאאאTHאאא،TLKאא J•

Q JאאאאTHTLאאKאאאאאLא،א

אאFאאEאאאאאאAKאkאאאאFא

؟אאאאEאאאאK

٣אWאאא


אאאאאT∆Fא∆،אLH TTT −=∆KEאAKאאא

Q .TH TL

L

A

k


- ٧٧ -

אאאkKאאאאאאאאKאאא

אאא

TLA kQ ∆=

• F١E

אאQאFא؟EאJouleJKאאא•

Qא١אאאאאאאאאא،א

sJK١א

אאא،אאאא•

QאאאT∆אאאאאאא

LA kKאאא،אאאאאא

אאאאאאאאאאאKאאF

LA kEא

CWo

אאאאאאאאאKאאאk

א،אאK ١WאאאאF٤אE2 cm

1 mא0.5 mאאא10 oCאא40 oCFאאW

CmW°

k = 80 E K

אWאאאאאאא

C30C) 1040(

C 10C 40TTT LH

°=°−=

°−°=−=∆


- ٧٨ -

אאאאא Jאאאאא J

m 02.0

mcm 100

cm 2cm 2L ===


2m 5.0m 5.0m 1Aالطول االرتفاع

=

×=×=

אאאאאאאאאF١אE

٤א

Q = ? . 10 oC

2 cm

1 m

k

40 oC

0.5 m

sMJ 60.0

MW 60.0

KW 60

W60000

C 30 m 0.02

m 5.0C m

W 80

TLA kQ

2

=

=

=

=

°××

°=

∆=•


- ٧٩ -

אאאאFQאJEאFאtimetא s Eאאאאא

אא

tQQ•

= F٢E

٢W אאאאאאאאאאאאK

אWאאאאאאא

s 7200

mins60

hrmin 60 hr 2hr 2t =××==

hrminKאאא

אא60000 J/sאאאא

MJ 324J 432000000

s 7200 sJ 60000

tQQ

==

×=

=•

אאאאא

אKאאאאא،אאKאאאא?אאאא?

?אאאHeat Flux ?•

q2mW


- ٨٠ -

TL k

A

TLA k

AQq

∆=

∆=

=

••

F٣E

٣W אאאאheat fluxאאא١K

אWאאאאאא

2mW120000

C 30 m 0.02C m

W 80

TL

kq

=

°×°=

∆=•

אאאאאאאא١אא

2

2

mW120000

m 0.5W 60000

AQq

=

=

=

••

אאW

אLA kא١אאאאאאאאkFאאE

אAאLאאא،אאאאאKאאאאאא


- ٨١ -

אא،אKאאא،אאאאא

אאK

٤WאאאW JF

CmW°

k = 420E 100 cm2 10 cm

JFCm

W°

k = 80E 1 m2 5 cm

JאאFCm

W°

k = 0.5E 10 m2 5 cm

אWאFkE،אאאאא

فضةحديدطوب k k k ⟩⟩

א––אALא k

LA k

אאאאאאאZ

C W42.0°

אאאאZC

W4°

אאאאאZC

W95.4°

אאאאkאא،אאK

אאא–א–אאK


- ٨٢ -

א٤אאאא אאאאאא٤Z

W C38.2 °

אאאאZW C25.0 °

אאאאאZW C2.0 °

אאאאאאאא

אאאאאאFאKEאאRא٢א

RTQ ∆

=• F٤E

RאאאאF

LA kE

A kL

LA k

1R == F٥E

אאאאאאW אאאKאאאאאא،א٥

אאאאאאKאאאcomposite materialאאאאאא

אK


- ٨٣ -

٥אWאאאאא

א٥אאאא

אאאKאאאאאאאאאKאאאאא

א٤א

3

L2

2

21

1

1H

RTT

RTT

RTT

RTQ −

=−

=−

=∆

=•

33

33 A k

LR = ,

22

22 A k

LR = , 11

11 A k

LR =

אא٥אא321 AAA ==

אאאK

T4

LB

A

kC

LA

kB kA

T3 T2 T1

LC

Q .


- ٨٤ -

אאאאאאאאאאאאאאFאא

،אאאEאאאאא

TotalRTQ ∆

=• F٦E

TotalRאאאאא

אאאאFאאאאאE

321Total RRRR ++= F٧E

٥W،אאאאאא

2BA

BA

m 1AAm 05.0LL

==

== Cm

W100k

CmW80k

B

A

o

o

=

=

C50T

C100T

2

1o

o

=

=

T2

LA

kB kA

T1

LB

Q .


- ٨٥ -

א Wאאא

C 5050100TTT 21o=−=−=∆

אאאאאאא

WC001125.0

10005.0

8005.0

A kL

A kL

RRR

BB

B

AA

A

BATotal

o

=

+=

+=

+=

אאאאאא

W 4.44444

001125.050

RTQ

Total

==∆

=•

אאאאF٦אKE

אאאאאאF٦Eאאאאאאאאא

321Total R1

R1

R1

R1

++=

133221

321Total RRRRRR

RRRR++

=⇒ F٨E


- ٨٦ -

אF٦WEאאאאא

אאאאא

אאאאF٨EאאאאאאאF٧Eאאאאא،

אאK

٦Wאא،אאאאאא

2

D

CB

A

m1Am 05.0L

m 1.0LLm 05.0L

=

===

=

CmW30k

CmW45k

CmW58k

CmW80k

D

C

B

A

o

o

o

o

=

=

=

=

C50T

C100T

L

Ho

o

=

=

T4

kC

kA

T3 T2

Q .

AA

kB T1 T2

AB

AC


- ٨٧ -

א Wאאא

C 5050100TTT LHo=−=−=∆

אאאאא

W C0.00063

A kL

RA

AA

°==

W C0.0017

A kL

RB

BB

°==

W C0.0022

A kL

RC

CC

°==

W C0.0017

A kL

RD

DD

°==

אאאאאאא

TL

LB = LC

A

kC

LA

kB kA

TH

LD

Q .

kD


- ٨٨ -

WC0.0033

0017.00022.00017.00022.00017.000063.0

RRR

RRR

RRRR

DCB

CBA

DBCATotal

o

=

++×

+=

++

+=

++=

אאאאאא

W 5.15151

0033.050

RTQ

Total

==∆

=•

אאאאW

אאאאאאHeat ExchangersKאאאF٧אEאאאא

K

٧אWא

אאאאאאאאאאAאאאאאא

אאא،אאא


- ٨٩ -

KאאאאאF١ J١EאאFאאאאא،d(r)E

אאאאאאא

T

rr

ln

k 2Q

i

o∆

π=

• l F٩E

πאא3.142

kאאאאאCm

Wo

lאm

orאאm

irאאאm lnאאאאFאE

אT∆אאאאאאאoC

١אאi

o

rr

ln

k 2 lπאאאאא

אאאאאאאא،אK

٧WאFCm

W380ko

=Eאא 20 mmא30 mm5 mא،50 oCאאאא25 oCK؟אאאאאFאא

אאאאאאאKE

א Wאאא

C 252550TTT LHo=−=−=∆


- ٩٠ -

אאאאא

WC340000.0

5 380 22030ln

k 2rr

lnR i

o

°=

××π×=

π= l

אאאא

kW 07.736W 736071.48

340000.025

RTQ ===

∆=

•


- ٩١ -

אא אאא

אFEאF٨אEאא

אאאאאאאאאאאאאאKאאאא

אאאאאאאאאאאאאאאKא

אאאאאאאאאאאאאאאא،אאאאאאאא

אאאאKKKאאאHeat ConvectionK

٨אWאאאאFE،אFE

אאאKאאאאF٨אE

אאאאאאאאאאאאאאא

אאאKאאF٨אEא

Q.

هواء25 oC

50 oC

)أ(

Q.

هواء25 oC

50 oC

)ب(


- ٩٢ -

KאאאאאאאאאאFאאEאא

אאא،אא

TLA kQتوصيل ∆=

•

אאאאאא

TA hQحمل ∆=• F١٠E

א١٠אא،אא

אאאאאאאFAhEאFLA kE

אאאkאLאאאאhKאאLאאאאאאאאא

אאאאאKאאאאא

א hא?אאא?אאאאאאאאאאאאאא

אאאאאאאאאKאאאhF

CmW2 °

EאאFאאאאאא

אאאאKEאאאאאhאאאאאאא

אאאאאאK


- ٩٣ -


Ah1R حمل = F١١E

אאאF١ J١١Eאאא

حملحمل R

T Q ∆=

• F١٢E

٨Wאא30 oCא250 oC

50 cm30 cmKאאאאhאאCm

W302o

אאאאאאאאK

א Wאאא

C 22030250TTT السطحالهواءo=−=−=∆

אאא

WC222.0

3.05.0301

A h1R حمل

o

=××

==

אאא

W 990222.0

220R

T Qحمل

حمل ==∆

=•


- ٩٤ -

אאא hW אאאhא

אאאאאאKא؛אאאK

אאאאאאאאאאאאאאאאhאאא

F١٠אKE

٩Wאאאאhאאאאאאאאאאאאאאא90א

Wאאא15 oCאא152 oC3 mm2 mK

א Wאאא

C 13715152TTT السلكالهواءo=−=−=∆

אאאאאא

i = 1.5 A

v = 60 VPowerin = i * v = 90 W

Qout = Powerin = 90 W.

T15 = الهواء oC

T152 = السلك oC


- ٩٥ -

2m 188.020.003 d A =××π=π= l

lאd،אאאאאאאאאאא

W90Q =

•

אאא

CmW 9.34

137188.090

T AQh

2o=

×=

∆=

•

،אאא

אא،אאאאאאאאhKאאאאאhKא

אאאאFאאאEאאאאאFאאEKאא

אאאאאאאאאאאאאhKאא

אא hKאאאאאK

WאאאאאאאאW

אאאאאאאאאאאאKאא٩

Lאאאאאא


- ٩٦ -

٩W

אאאאא

אא

TLA kQتوصيل ∆=

•

אאאאאא

אא

TA hQحمل ∆=•


kLh

TLA k

TA h

Q

Q

توصيل

حمل =∆

∆=•

•

h k U∞

TH

TL

L


- ٩٧ -

אF kLh E،אאאאאאא

FhLk،אE Nu

kLh Nu = F١٢E

אNu،אאאאאאאאא

Nu = 1אאFאEאאאאאאK

Wאאאא

אאאאאאאhW אאאאאאאאF

אEאFאKEאאאאאאאאאא

אאאKאא١٠אאאאאא

FאאאאאאאKEאאאאאא

אאאT∞אאאאאאא،אאאאאאKא

אאאThermal Boundary LayerKאאאאאאאאאא

אאאU∞אאאאא،אאאאאאK

אאאVelocity Boundary LayerK


- ٩٨ -

50 oC

Q

15 oCهواء بارد

١٠Wא

אא

אא،אאאאאאµאאkאאCpKאא

אאאאאאאFδt EאKאFאEאא

אאאF δv EאKא١١אאאאKאאאאא

אאאFאאאאאא،אאא1

t

v ⟩⟩δδEאאאא

Kאאאאאאאאאאאאא،אא

1 t

v ⟩⟩δδKאאאFאאא

אאEא،אאאאאאאא hKאאאאא

אFאµאאאkאאא CpEאאPr

kC

Pr pµ= F١٣E


- ٩٩ -

אאא١١Pr >> 1 א،Pr << 1KאאאאאאאPr = 0.7אK

١١Wאאאאאאא

אאאאא

WאW אF١٢Eאאאא

אאאאLaminar Flow،אא

אאאTransitional

Laminar Flow،אאאאאאאTurbulent FlowK

١٢Wאאאאא

املضطربمنطقة التدفق انتقاليةمنطقة منطقة التدفق الطبقي

U∞, T∞

ρ, µ

k, Cp δT δv

v = U∞

v = 0

T∞

Ts


- ١٠٠ -

אאאאρאאU∞µאאאlF١٢אKE

אאRe

µρ

= ∞ l URe F١٤E

ReFEאK

،אאאא500,000F 5 x 105 Re ≥KE

אאאFאNuאPrReE

אאאא hאאא؟Kאאאh Nu

kLh Nu =

אאא

Lk Nuh = F١٥E

אאאאkאאא L אאאאאאאאNu

אאאאאKNuאאאFאאאReאPrE

אאא،F5 x 105 Re <Eאאאא


- ١٠١ -

١٦E ) Nu = 0.664 Re1/2 Pr1/3 [ Rr ≥ 0.6 ]

אאאF5 x 105 Re >Eאאאא

١٧E ) Nu = 0.037 Re4/5 Pr1/3 [ 0.6≤ Pr ≤ 60 , 5x105 ≤ Re ≤ 107 ]

אאFאאאאEא

אאא

١٨E ) Nu = (0.037 Re4/5 – 871) Pr1/3 [ 0.6≤ Pr ≤ 60 , 5x105 ≤ Re ≤ 107 ]

אReF١ J١٤Eאאא،אאPrF١٣אEאאא،

אאאאאאאNuאאאא، hNuK

١٠Wאא8 m/sא 20 oCא 1.5 m6 mא134 oC

אאאאאאאאאK

אWאא20 oC אאא١Fאאאאאאאא

אTf = (T∞+Ts)/2 = 77 oCE

ρ = 1.009 kg/m3 µ = 2.08 x 10-5 kg/m Cp = 1008 J/kg oC k = 0.0297 W/m oC U∞ = 8 m/s L = 6 m


- ١٠٢ -

א

Re = ρ U∞ L / µ = 2,328,461.5 > 500,000

Pr = µ Cp / k = 0.705

אאאאFאאאE،אאא٦}٠٦٠

500000 107אאא١ J١٨NuאאאNuFא١٥E

אאאhאאאF١٠אE

Nu = (0.037 Re4/5 – 871) Pr1/3 = 3310.375 h = Nu k / L = 16.386 W/m2 oC

•

Q = h A (Ts - T∞) = 16812.4 W

אאאאאאאאא

Q () = •

Q ∆t = 121049280 J = 121.05 MJ

אאאאאא

אKאאאאאאאאאאאאאאאאא

אאKאאאNuF١٦א١٧١٨Eאא،

אאא.


- ١٠٣ -

אאאאאאאאאא אT ρ Cpk µ Pr

( K ) ( 3mkg ) (

CkgJo

) (Cm

Wo

) (sm

kg ) x 10-5 200 1.766 1003 0.0181 1.34 0.740 250 1.413 1003 0.0223 1.61 0.724 280 1.271 1004 0.0246 1.75 0.717 300 1.177 1005 0.0261 1.85 0.712 320 1.110 1006 0.0275 1.94 0.710 350 1.009 1008 0.0297 2.08 0.706 400 0.833 1013 0.0331 2.29 0.703 450 0.785 1020 0.0363 2.49 0.700 500 0.706 1029 0.0395 2.68 0.699 550 0.642 1039 0.0426 2.86 0.698 600 0.589 1051 0.0456 3.03 0.698

١Wאאאאאא

אאאאRUאאאאUW אאאאאאאFאE

אאאאאאKאאאאאאאאאאאא

אאאKא١٣אאאאאאKא

אאאאאאאאאאאאאאאאאאאאאא

אאאאאKאאאא

אאאאאאאאאאאאאאאאא


- ١٠٤ -

URT Q ∆

=• F١٩E

RUאאאאאאאאKאאא١٣אאאא

אאאאא

23211U RRRRRR ∞∞ ++++= F٢٠E

1R ∞אאאאאאFA h

1

1

E

1RאאאאאאFA k

L

1

1E

2RאאאאאאFA k

L

2

2E

3RאאאאאאFA k

L

3

3E

2R ∞אאאאאאFA h

1

2

E

١٣Wאאאאאאאא

TL

L2

A

h1

L1

k2 k1

TH

L3

Q .

k3

h2


- ١٠٥ -

אאאKאאאא

אאאאK אאאאUאאאאRU

אאאאאאFאאEאאFEאאא

TA UQ ∆=• F٢١E

א،א١٧אאאאU

23

3

2

2

1

11 h

Lk

Lk

Lk

hU ++++= F٢٢E

אאאF١٢אKE

אאאאאFאאEאאאאFאE

UR1A U = F٢٣E

אאFאאאWE אאאאאאאאF

אאאE>אאאא؟אאאאאאאאאאאK

אאא١٤אאאא


- ١٠٦ -

אאאאאאאאאאאאא،TA h Q ∆=

•

١٤Wאאאא

אאאאא

אאא،אאאאKאאאאאאאאא

אא

المحسنةالقاعدةالزعنفة QQQ•••

+= F٢٤E

אאאאאאאKאאאאאאאאFא

١٤Eאא

Ab

Tb T∞

q base

Ab

Tb

T∞

q base

q base

q fin

w

L t


- ١٠٧ -

( )∞

•

−= TTA Pk hQ bcالمحسنة F٢٥E

PאFP = 2 (w+t)E ACאAC = 2 (w+t)L )E Tbאאא ∞Tאאא

١١Wאאאא100א oC2 m2

אאאאא25 oCאאאCm

W2 o

50 ،

אאאאאאאאאאF

CmWo

k = 372 E אאL = 20 cm

אw = 10 cmt = 0.5 cmK

אWאאאאאFאE

kW 5.7W 7500

752372TA h Q

==

××=∆=

•

،אאאאא

אאאFאאEאא١ J٢٥אאאא

( )

( )[ ] ( )[ ] ( )kW 61.9

25100 2.01.0005.021.0005.02 273 05

TTA Pk hQ bcالمحسنة

=

−×+×+××=

−= ∞

•


- ١٠٨ -

אא אאאאא

אRadiationאאאF

EאאאKאאאאאאאאאאאאאאK

אאאאאאאאאאאאאאFאEאאאא

אK

אאאאאאאאאאKאאF١٥אE–אא–

אאא،אאאאאאאאאאאאK

١٥Wא


אאאFא١٦KEאאאאאאאאא

F300,000 km/hKE


- ١٠٩ -

١٦Wאאאאאא

אאאאWאemissivityא

absorptivityאreflectionאtransmitionKאemissivityאאאאאאא

אKאאאאאאאKאאאאאאא

אאא absorptivityא،אאאFאtransmitionEאFאא

אEאא،אאאאאFאreflectionEאאאאF١٧אKE،אא

אאאאFאאאאאאאאEא،אF

אאאKEאאאאאאאאאאKא

אK

30 oC

5 oC 900 oC


- ١١٠ -

١٧Wאאאאא

אאאאאאא emissivityא

absorptivityKאאאאאאאאאאKאא

אאFE،אאאאאאאאFKE

אאא؛אאאKאאאאאאאFא

אאא،אE JW

4smax T A Q α=

• F٢٦E

maxQ•אFאאאtotal emissive

energyE

أشعة ساقطة

منعكسةأشعة

ممتصةأشعة

مارةأشعة

أشعة منبعثة


- ١١١ -

α J428

K mW1067.5 −×

A אאא TsאאאאFK

oCE

א א אFאE 0.07

0.03 0.03 0.98 0.9 0.92 - 0.97

0.85 - 0.93 0.93 - 0.96

א 0.95 א 0,82 - 0.92

א 0.93 - 0.6 0.96

٢WאFεEאאא300 K

אא–אאא–אא

אאא٢٤אאאאאאאא

٢٤אKאאאεFאאאא،אאאאא٢אEאא

א


- ١١٢ -

4sT A Q αε=

• F٢٧E

١٢Wאאאאאאאא10 oCאא30 oCאא

1.4 א m2אא0.95K

אWאאאאFKE

K 28327310T

K 30327330Ts

=+=

=+=

∞

٢٦אאאאאאאא

( )( )

W1522833034.11067.595.0

TT A Q448

44s

=−××××=

−αε=−

∞

•

،אאאא

אאאKא٣אאאאK


- ١١٣ -

٣Wאאא

A1, T1, ε1

A2, T2, ε2

0AA

2

1 ≈ ( )42

411112 TTAQ −σε=&

A1, T1, ε1

A2, T2, ε2

21 AA =( )

111TTA

Q

21

42

411

12

−ε

+ε

−σ=&

r1 r2

2

1

2

1

rr

AA

= ( )

⎟⎟⎠

⎞⎜⎜⎝

⎛ε

ε−+

ε

−σ=

2

1

2

2

1

42

411

12

rr11

TTAQ&

r1

r2 2

2

1

2

1

rr

AA

⎟⎟⎠

⎞⎜⎜⎝

⎛=

( )2

2

1

2

2

1

42

411

12

rr11

TTAQ

⎟⎟⎠

⎞⎜⎜⎝

⎛ε

ε−+

ε

−σ=&

جسم صغري وسط جتويف ضخم

لوحان متوازيان كبريان جداً

كز اسطوانة ، طويلتان جداًاسطوانة يف مر

كرة يف مركز كرة


- ١١٤ -

١EFEFEאאW J Jא EF JאאאאאאאאאאאאאEF _אאאאאא EF –אאא EF –אאאאא،א

א EF

٢EאאאW J –אאאW ١E٢אEאא٣Eא Jאאא kאאאW ١E٢Eא٣E _אW

١K אאאאא ٢K אאאאא ٣K אאאאא ٤K אאא

JאאאאאW EKEoCEא

JאאאA k

Lאאא،W

EA h

LEA h1E

LT∆


- ١١٥ -

٣EאאאאאאאאW A = 1 m2

1T∞ = 45 oC h1 = 50 C m

Wo2

L1 = 5 cm k1 = 0.1 C m

Wo

L2 = 15 cm k2 = 0.6 C m

Wo

L3 = L4 k3 = 0.8 C m

Wo

L4 = 10 cm k4 = 0.5 C m

Wo

2T∞ = 25 oC h2 = 50 C m

Wo2

٤Eא60 oC5 m א20

oC 2 m/sאאאאאאK ٥EKאאאא30 oCא

אא10 oCאא1.75 m2 אא0.95 ،אאאאא؟

L1 L 3

L2

L4

k1 k2

k3

k4

T∞1 T∞2

h1 h2

A

Q = ?.

א ١٦٠ ١ אאאא

- ١١٦ -

(1) א

١. אא(X,Y)אאאאאא

٢. אאאא

٣. א א אאא א אאא

٤. א אאאא אאאאאcpFאE

W אאאאאא40oC1atm

אאW0.017cp אW0.7cp

א ١٦٠ ٢ אאאא

- ١١٧ -

(2) אאא

١K א

٢K א אא א ،אאא אאאאאא

٣K אאא،אאאאא

W אא،אאאRe =125000

אאאא1 cm Re = 1.3 X 10 5 אא

ε/D = (4.6 X 10-5/0.01) ~ 5X 10-3 f = 0.009

א ١٦٠ ٣ אאאא

- ١١٨ -

(3) אאאא

א 1 in = 2.54 cm 1 m = 3.2808 ft

א 1 L = 1000 cm3 1 m3 = 100 L

1 ft3 = 28.317 L א

1 gc = 980.6 g cm/ dyn s2 = 32.174 lbm .ft/ lbf .s2 = 1kg m/N s2

א 1 atm = 14.7 psia = 101.3 kPa = 760 mmHg

א

1 cp = 10-2 g/cm.s (poise) = 10-3 Pa.s = 10-3 kg/m.s = 10-3N.s/m2

א 1 hp = 0.745 kW, 1 J/s =1W

א ١٦٠ אא אאאא

- ١١٩ -

אא

1. Cengel,Y.A and Boles, M.A., “Thermodynamics, An Engineering Approach”, 2nd edition, McGraw –Hill Inc, 1994

2. Coulson, J.M. and Richardson, J.F, “Coulson Chemical Engineering Series”, 4th edition,

volume 1, Pergamon Press, 1991 3. Geankoplis, C., “Transport Processes and Unit Operations”, 3rd edition, McGraw-Hill

Inc, USA, 1993 4. Mccabe,W., Smith, J., Harriot, P., “Unit Operations of Chemical Engineering”,4th

edition, McGraw–Hill Inc, USA, 1985 5. Smith, J.M., and Van Ness, J.F., “Introduction to Chemical Engineering

Thermodynamics”, McGraw-Hill Inc, USA, 1987 6. Yunus A. Gengel, "Heat Transfer, a Practical Approach", McGraw –Hill Inc, 1998 7. Yunus A. Gengel, Robert H Turner, "Fundamentals of Thermal-Fluid Sciences",

McGraw-Hill Inc, 2001

א ١٦٠ א אאאא

א

אא ..................................................................................................................... J١ J

אאW .................................................................................................................. J١ J

אא ............................................................................................................... J٢ J

א ................................................................................................................ J٢ J

א .............................................................................................................. J٢ J

א .............................................................................................................. J٢ J

אא ............................................................................................................ J٤ J

אאאאאא ............................................................................ J٥ J

F1E ....................................................................................................... J١٠ J

אWא ................................................................................................. J١١ J

(2) .............................................................................................................. J١٢ J

אאא،אא28.76א in ...................................... J١٢ J

אא ........................................................................................................... J١٥ J

א ................................................................................................................. J١٥ J

................................................................................................... J١٥ J

אאא ........................................................................................... J١٦ J

אא ........................................................................................................... J١٧ J

אא ............................................................................................................. J١٧ J

אאא ........................................................................................................... J٢٠ J

אאא ................................................................................................. J٢٠ J

אא ..................................................................................................... J٢٠ J

1vאא(1)א ......................................................................... J٢١ J

A1א(1) ................................................................................................. J٢١ J

א .............................................................................. J٢٣ J

אא ..................................................................................................... J٢٣ J

אא .......................................................................................................... J٢٧ J


אא .................................................................................................... J٢٧ J

Wא ......................................................................................................... J٢٧ J

אא ......................................................................................................... J٢٧ J

Wא ......................................................................................................... J٢٨ J

אאאא ............................................................................................... J٢٨ J

אאא ................................................................................................ J٢٩ J

אאאא ........................................................................... J٣٠ J

(2) ...................................................................................................... J٣١ J

W .......................................................................................... J٣٥ J

א(1)א ........................................................................................................ J٤٠ J

אאא .................................................................................................. J٤٠ J

אא(1) ................................................................................................. J٤١ J

אאא .................................................................................................. J٤١ J

א(2)א ....................................................................................................... J٤٢ J

אאא ................................................................................................. J٤٢ J

אא(2) ................................................................................................ J٤٣ J

אאא ................................................................................................. J٤٣ J

אאW ......................................................................................................................... ٤٤

אאWאאאאאThermodynamics .................................... ٤٥

אא .................................................................................................................... ٥١

אאאא ....................................................................................... ٥١

א٥٩ .................................................................................................................... א

אאאא ............................................................................................. ٥٩

אאW ................................................................................................................. ٥٩

אא٦٣ ................................................................................................................... א

אאאא ................................................................................ ٦٣

(3) ............................................................................................................... ٦٥


אאW .......................................................................................................... ٦٥

א٧٠ ................................................................................................................ (3)א

אא٧٠ .......................................................................................................... א

אא(3) ......................................................................................................... ٧١

אא٧١ .......................................................................................................... א

Wאא ........................................................................................................ J٧٣ J

אא ............................................................................................................. J٧٥ J

אאא ....................................................................................................... J٧٥ J

אא ........................................................................................................... J٩١ J

אאא .......................................................................................................... J٩١ J

אא .......................................................................................................... J١٠٨ J

אאאאא ....................................................................................... J١٠٨ J

.......................................................................................................... J١١٤ J

W .................................................................................................................. J١١٦ J

W .................................................................................................................. J١١٧ J

א .................................................................................................................. J١١٨ J

א .................................................................................................................. J١١٨ J

א ................................................................................................ J١١٨ J

א .................................................................................................................. J١١٨ J

א ................................................................................................................ J١١٨ J

א .................................................................................................................. J١١٨ J

אא ................................................................................................................. J١١٩ J

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