OIL

WATER

OilTh,in = 100 °Ccp,h = 1.9 kJ/kgKmh = 2.6 kg/s

WaterTc,in = 40 °C; Tc, out = 80 °Ccp,h = 4.18 kJ/kgKmh = 1.0 kg/s

Th,in = 100 °C

Tc,in = 40 °CTc,out = 80 °C

1. Energy Balance

Qcold = mc⸱cp,c⸱ΔTc = 167200 W

Qhot = Qcold

Qhot = mh⸱cp,h⸱ΔTh

Th,out = Th,in - Qhot/mh⸱cp,h = 66.15 °C

2. Effectiveness method

ε = f(Cmin/Cmax, NTU) = 0.67

Cc = mc⸱cp,c = 4180 W/K = Cmin

Ch = mh⸱cp,h = 4940 W/K = Cmax

Cmin/Cmax = 0.85

NTU = UA/Cmin = 2.2 U = Cmin ⸱ NTU/A = 460 W/m2K

LMTC =

3. LMTD method

P = 0.67

R = 0.85F = 0.80 U = 455 W/m2K

Mercury

Water

Th,in = 65.6 °C

Tc,in = 21.1 °C

Th,out = 53.3 °CMercuryTh,in = 65.6 °C; Th,out = 53.3 °Ccp,h = 139,4 J/kgKmh = 0.83 kg/s

WaterTc,in = 21.1 °Ccp,h = 4.18 kJ/kgKmh = 0.028 kg/s

1. Energy Balance

Qhot = mh⸱cp,h⸱ΔTh = 1415 W

Qhot = Qcold

Qcold = mc⸱cp,c⸱ΔTc

Tc,in = Tc,out + Qcold/mc⸱cp,c = 33.2 °C

2. LMTD method

F = 1(it is a perfectly countercurrent arrangement)

LMTD = 32.6 K

A = 0.145 m2

Rfouling = U-1fouling - U

-1design

U-1design = ∑Ri

U-1fouling = ∑Ri + Rfouling

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Th,in = 160 °C

Tc,in = 25.0 °C

Th,out = 70.0 °C

Tc,out = 80.0 °C

Fouling condition

Qfouling = 0.7 Qdesign

Th,out,fouling = 90 °C

1. Energy Balance

Qfouling = 0.7 Qdesign

mcp(Tc,out,fouling - Tc,in) = 0.7mcp(Tc,out - Tc,in)

Tc,out,fouling = 0.7Tc,out + 0.3Tc,in = 63.5 °C

2. LMTD

LMTDdesign = 60.8 K

LMTDfouling = 79.7 K

3. Correction factors

Pdesign = 0.67

Rdesign = 0.61

Fdesign = 0.80

Pfouling = 0.52

Rfouling = 0.55

Ffouling = 0.95

4. Energy Balance + LMTD

Qfouling = 0.7 Qdesign

Ufouling A LMTDfouling Ffouling= 0.7 Udesign A LMTDdesign Fdesign

Ufouling = 0.7 Udesign LMTDdesign / LMTDfouling Fdesign / Ffouling= 899 W/m2K

5. Fouling resistance

Rfouling = U-1fouling - U

-1design = 6.1235e-04 m2K/W

WaterTc,in = 17 °CTc,out = 27 °Ccp,h = 4.18 kJ/kgK

SteamTh,in = Th,out = 40°Chlv = 2406 kJ/kg

1. Energy Balance

Q = msteamhlv = 6.6833e+05 kW

mwater = Q/(cpΔT)water = 1.5989e+04 kg/s

2. Effectiveness

ε = ΔTwater/ΔTmax = 0.43478NTU = UA/Cmin = 0.57

A = Cmin ⸱ NTU/U = 8105.4 m2