Determine Heat Load
Obtain flowrate (W ), inlet, outlet temperatures and fouling factor for both hot and cold
stream. Calculate physical properties like density (ρ), viscosity (μ), specific heat (C
p
) and thermal conductivity (k) at mean temperature. Determine heat load by energy balances on two streams.
Q = m
H
.Cp
H
(T
Hot In
 T
Hot Out
) = m
C
.Cp
C
(t
Cold Out
 t
Cold In
)
where, m
H
, m
C
: Mass flow rate of Hot and Cold Stream Cp
H
, Cp
C
: Specific Heat of Hot and Cold Stream T
Hot In
, T
Hot Out
: Inlet and outlet temperature of Hot Stream t
Cold In
, t
Cold Out
: Inlet and outlet temperature of Cold Stream
Calculate Logarithmic Mean Temperature Difference (LMTD)
LMTD = (ΔT1

ΔT2)/ln( ΔT1 / ΔT2)
For Countercurrent flow
ΔT1 = T
Hot In
 t
Cold Out
ΔT2 = T
Hot Out
 t
Cold In
For Cocurrent flow
ΔT1 = T
Hot In
 t
Cold In
ΔT2 = T
Hot Out
 t
Cold Out
Calculate Film Coefficient
Allocate hot and cold streams either in inner tube or annular space. General criteria for fluid placement in inner tube is corrosive fluid, cooling water, fouling fluid, hotter fluid and higher pressure stream. Calculate equivalent diameter (D
e
) and flow area (A
f
) for both streams.
Inner Tube
D
e
= D
i
A
f
= π D
i
²/4
Annular Space
D
e
= D
1
 D
o
A
f
= π (D
1
²  D
o
²)/4
where, D
i
: Inside Pipe Inner Diameter D
o
: Inside Pipe Outer Diameter D
1
: Outside Pipe Inner Diameter Calculate velocity (V), Reynolds No. (Re) and Prandtl No. (Pr) number for each stream.
V = W / ( ρ A
f
)
Re = D
e
V ρ / μ
Pr = C
p
μ / k
For first iteration a Length of double pipe exchanger is assumed and heat transfer coefficient
is calculated. Viscosity correction factor (μ / μ
w
)
0.14
due to wall temperature is considered 1. For Laminar Flow (Re <= 2300), Seider Tate equation is used.
Nu = 1.86 (Re.Pr.D
e
/L )
1/3
(μ/ μ
w
)
0.14
For Transient & Turbulent Flow (Re > 2300), Petukhov and Kirillov equation modified by Gnielinski can be used.
Nu = (f/8)(Re  1000)Pr(1 + D
e
/L)
2/3
/[1 + 12.7(f/8)
0.5
(Pr
2/3

1)]*(μ/μ
w
)
0.14
f = (0.782* ln(Re)  1.51)
2
where, L : Length of Double Pipe Exchanger
μ
w
: Viscosity of fluid at wall temperature Nu : Nusselts Number (h.D
e
/ k)
Estimate Wall Temperature
Wall temperature is calculated as following.
T
W
= (h
i
t
Ave
+ h
o
T
Ave
D
o
/D
i
)/(h
i
+ h
o
D
o
/D
i
)
where, h
i
: Film coefficient Inner pipe h
o
: Film coefficient for Annular pipe t
Ave
: Mean temperature for Inner pipe fluid stream T
Ave
: Mean temperature for Annular fluid stream Viscosity is calculated for both streams at wall temperature and heat transfer coefficient is multiplied by viscosity correction factor.
Overall Heat Transfer Coefficient
Overall heat transfer coefficient (U) is calculated as following.
1/U = D
o
/h
i
.D
i
+ D
o
.ln(D
o
/D
i
)/2k
t
+ 1/h
o
+ R
i
.D
o
/D
i
+ R
o
where, R
i
: Fouling factor Inner pipe R
o
: Fouling factor for Annular pipe k
t
: Thermal conductivity of tube material Calculate Area and length of double pipe exchanger as following.
Area = Q / (U * LMTD )
L = Area / π * D
o
Compare this length with the assumed length, if considerable difference is there use this length and repeat above steps, till there is no change in length calculated. Number of hair pin required is estimated as following.
N
Hairpin
= L / ( 2 * Length
Hairpin
)
Calculate Pressure Drop
Pressure drop in straight section of pipe is calculated as following.
ΔP
S
= = f.L.G²/(7.5x10
12
.D
e
.SG.(μ/ μ
w
)
0.14
)
where,
ΔP : Pressure Drop in PSI
SG : Specific Gravity of fluid G : Mass Flux ( W / A
f
) in lb/h.ft² For Laminar flow in inner pipe, friction factor can be computed as following.
f = 64/Re
For Laminar flow in annular pipe.
f = (64 / Re) * [ (1 
κ²) / ( 1 + κ² + (1

κ²) / ln κ) ]
κ = D
o
/ D
1
For turbulent flow in both pipe and annular pipe
f = 0.3673 * Re
0.2314
Pressure Drop due to Direction Changes
For Laminar Flow
ΔP
R
= 2.0x10
13
. (2N
Hairpin
 1 ).G²/SG
For Turbulent Flow
ΔP
R
= 1.6x10
13
. (2N
Hairpin
 1 ).G²/SG
Total Pressure Drop
ΔP
Total
= ΔP
S
+ ΔP
R
Spreadsheet for Double Pipe Exchanger Design