AME 3363 Information Sheet

Properties of Water (Liquid-Vapor) v = (1 - x)vf + xvg = vf + x(vg - vf) u = (1 - x)uf + xug = uf + x(ug - uf) h = (1 - x)hf + xhg = hf + x(hg - hf) s = (1 - x)sf + xsg = sf + x(sg - sf) Ideal Gases pv = RT, pV = mRT, k = cp/cv, cp = cv + R

Rair = 0.287 kJ/kgK, kair= 1.4 Steady-Flow Processes

i em m (Conservation of Mass)

2 2

e i

C V C V e e e i i i

V VQ W m (h g z ) m (h g z )

2 2 (Conservation of Energy)

Isentropic Processes

k 1k 1

k2 2 1

1 1 2

T p v

T p v

(constant specific heats)

2 r 2

1 r1

p p,

p p

2 r 2

1 r1

v v

v v

(variable specific heats)

Ideal Otto Cycle 1-2 isentropic compression 2-3 constant-volume heat addition 3-4 isentropic expansion 4-1 constant-volume heat rejection Ideal Diesel Cycle 1-2 isentropic compression 2-3 constant-pressure heat addition 3-4 isentropic expansion 4-1 constant-volume heat rejection Ideal Brayton Cycle 1-2 isentropic compression 2-3 constant-pressure heat addition 3-4 isentropic expansion 4-1 constant-pressure heat rejection Ideal Rankine Cycle 1-2 isentropic compression 2-3 constant-pressure heat addition 3-4 isentropic expansion 4-1 constant-pressure heat rejection Vapor Compression Refrigeration Cycles

1-2 Isentropic compression in a compressor 2-3 constant-pressure heat rejection in a condenser 3-4 throttling in an expansion valve 4-1 constant-pressure heat absorption in an evaporator

Performance inputrequired

outputdesiredγ

Isentropic Efficiency

a 1 2 a

t

s 1 2 s

w h h

w h h

(Turbines)

s 2 s 1

p

a 2 a 1

w h h

w h h

(Compressors, pumps)

Atmospheric Air

Specific humidity g

g

v

v

a

v

PP

P622.0

PP

P622.0

m

m

φ

φω

Relative humidity gg

v

g

v

P)622.0(

P

P

P

m

m

ω

ωφ

Total Pressure P = Pa + Pv Total Enthalpy h = ha + ωhv Dew Point TDP = Tsat@Pv

Thermal Resistance kA

LR (plane walls),

kL2

)r/rln(R

io

π (cylindrical walls)

Heat Exchangers

Q = UA (LMTD) = mcp(To - Ti), LMTD = [(ΔTi) - (ΔTo)] / [ ln(ΔTi /ΔTo)]

(LMTD)cross-flow = F (LMTD)counter-flow

F = function of (P, R)

P = [t2 – t1] / [T1 – t1], R = [T1 – T2] / [t2 – t1],

max

actual

Q

Qε , )TT()cm(Q

in,cin,hminpmax

,)cm(

UANTU

minp

.C

CC

max

min

Boiling and Condensation

Nucleate Pool Boiling

32/1

Pr

)()(

n

lfgsf

satsplvl

fgl

hC

TTc

σ

ρρghμq

Critical Heat Flux 4/1

2

max )(vlvfgcr

ρρρgσhCq

Minimum Heat Flux

4/1

2)(

)(09.0

vl

vl

fgv

ρρ

ρρgσhρq

Film Boiling for Cylinders )()(

)](4.0)[(62.0

2/13

sats

satsv

satspvfgvlvvTT

TTDμ

TTchρρρgkq

Total Heat Transfer in Film Boiling )(4

3

4

3 44

sats

TTεσqqqqfilmradfilmtotal

Wave-Free Film Condensation

4/13*

)(

)(

943.0

LTTμ

khρρρg

h

ssatl

lvll fg

Re ≤ 30

82.0

2 4/33

4Re

h

k

ν

g l

l

Wavy Film Condensation

3/1

222.12.5Re08.1

Re

l

l

ν

gkh 30 < Re < 1800

82.0

2*

)(7.381.4Re

lfgl

ssatlv

ν

g

hμ

TTLk

Film Condensation over Horizontal Tubes

4/13*

)(

)(

729.0

NDTTμ

khρρρg

h

ssatl

lvll fg

AME 3363 – HW # 8