Given data: Thi := 250 °C Tci := 30 °C mh := 0.15 kg s mc := 0.6 kg s

cph := 2000

J kg⋅ K

cpc := 1000

J kg⋅ K

U := 1000

W m K

2

Finding Heat Exchanger Area(A0):

2

Cc := mc⋅ cpc = 600

m ⋅ kg K⋅ s

3

Ch := mh⋅ cph = 300

m ⋅ kg K⋅ s

3

2

Tco :=

mh⋅ cph⋅ Thi + mc⋅ cpc⋅ Tci mh⋅ cph + mc⋅ cpc

4

= 103.333 °C

Tho := Tco

Q := Ch⋅ ( Thi − Tho) = 4.4 × 10 W Thi − Tco − ( Tho − Tci) Thi − Tco ln Tho − Tci Cc Ch Ch Cc ε0 := if ( Cc < Ch) otherwise = 0.5

∆Tlm :=

= 105.798 ∆°C

C0 :=

Taking C0=Cmin/Cmax

Cmin :=

Cc if Cc < Ch Ch otherwise

Q Cmin⋅ ( Thi − Tci)

= 0.667

HEX effectiveness

ln NTU :=

1 − ε0 = 1.386

1 − C0

1 − C0⋅ ε0

Hence A0 := NTU⋅

Cmin U

= 0.416 m

2

Problelm 3.7

Given data: Do := 25.4mm Tci := −7 °C mh := 0.6 kg s mc := 2.4 kg s Tco := 0 °C

cph := 4180

J kg⋅ K

cpc := 5200

J kg⋅ K

U := 120

W m K

2

Thi := 85 °C

a) Finding Heat Exchanger Area(A0) for a Cross Flow:

2 4 m ⋅ kg 2 3 m ⋅ kg

Cc := mc⋅ cpc = 1.248 × 10

K⋅ s

3

Ch := mh⋅ cph = 2.508 × 10

K⋅ s

3

Q := Cc⋅ ( Tco − Tci) = 8.736 × 10 W

4

Cmin :=

Cc if Cc < Ch Ch otherwise

Qmax := Cmin⋅ ( Thi − Tci) = 2.307 × 10 W

5

C0 :=

Cc Ch Ch Cc

if ( Cc < Ch) otherwise

= 0.201

Taking C0=Cmin/Cmax

ε0 :=

Q Qmax

= 0.379

HEX effectiveness

ln NTU :=

1 − ε0 = 0.496

1 − C0

1 − C0⋅ ε0

Hence A0 := NTU⋅

Cmin U

= 10.375 m

2

Problelm 3.7

Given data: Do := 25.4mm Tci := −7 °C mh := 0.6 kg s mc := 2.4 kg s Tco := 0 °C

cph := 4180

J kg⋅ K

cpc := 5200

J kg⋅ K

U := 120

W m K

2

Thi := 85 °C

b) Finding Heat Exchanger Area(A0) for a 1-2 TEMA E:

2 4 m ⋅ kg 2 3 m ⋅ kg

Cc := mc⋅ cpc = 1.248 × 10

K⋅ s

3

Ch := mh⋅ cph = 2.508 × 10

K⋅ s

3

Q := Cc⋅ ( Tco − Tci) = 8.736 × 10 W

4

Cmin :=

Cc if Cc < Ch Ch otherwise

Qmax := Cmin⋅ ( Thi − Tci) = 2.307 × 10 W

5

C0 :=

Cc Ch Ch Cc

if ( Cc < Ch) otherwise

= 0.201

Taking C0=Cmin/Cmax

ε0 :=

Q Qmax

= 0.379

HEX effectiveness

Guess: given

NTU' := 0.1

( 1 + C0) + 1 + C0

(

2

)

0.5

0.5 1 + e− NTU'⋅ ( 1+C02) 2 = ⋅ 0.5 ε0 1 − e− NTU'⋅ ( 1+C02)

NTU := find( NTU')

NTU = 0.501 Cmin U

2

Hence A0 := NTU⋅

= 10.463 m

,