This presentation is made to provide the overall conceptual knowledge on Chilton Colburn Analogy. It includes basis, importance, assumption, advantages, limitations and applications in addition to the derivation. Make It Useful!

1. Syed Hameed Anwar Sahib V

2. B A S I S
Based on experimental data for gases and liquids in
both the laminar and turbulent flow regions
I M P ORTA N C E
Lies in heat transfer characterization for flows having
Prandtl Number not equal to unity

3. U S UA L F O R M A N D I T S U S E
jH = jD = a function of Re, Geometry and Boundary Conditions
has proven to be useful for transverse flow around cylinders,
flow through packed beds and flow in tubes at high Reynolds
Numbers
A S S U M PTION
Pr ≠ Sc ≠1 ; No form drag exit condition
where,
Pr = Prandtl Number = Momentum Diffusivity/Thermal Diffusivity = Cpμ/k
Sc = Schmidt Number = Momentum Diffusivity/Mass Diffusivity = μ/ρDAB

4. D E R I VAT I O N
From Sieder Tate Equation for turbulent flow,
Nu = 0.023 Re0.8 Pr⅓ (μ/μw)0.14 , 0.7 ≤ Pr ≤ 16700 , Re > 10000 (1)
where,
Nu = Nusselt Number = Resistance to Conduction/Resistance to Convection = hL/k
Re = Reynolds Number = Inertial Force/Viscous Force = Dvρ/μ
Pr = Prandtl Number = Momentum Diffusivity/Thermal Diffusivity = Cpμ/k
Dividing equation (1) by RePr,
Nu/RePr = 0.023 (Re0.8 Pr⅓ (μ/μw)0.14/RePr)
Rearranging,
St Pr⅔ (μ/μw)0.14 = 0.023 Re-0.2
For turbulent flow region, an empirical relation of f and Re,
f/2 = 0.023 Re-0.2
f/2 = St Pr⅔ (μ/μw)0.14 = 0.023 Re-0.2 jH = j-factor for Heat Transfer

5. D E R I VAT I O N
Similarly, Relating Mass and Momentum Transfer using Mass Transfer Equation,
kc
’D/DAB = 0.023 Re0.8 Sc⅓
Dividing equation (2) by ReSc,
kc
’/v Sc⅔ Re0.03 = 0.023 Re-0.2 jD = j-factor for Diffusivity
Simplified Form of Chilton Colburn Analogy
This analogy is also known as Modified Reynolds Analogy
where,
StH = Nu/RePr = Heat/Thermal Capacity and StM = Sh/ReSc = Mass/Density*Velocity
(2)
f/2 = StH Pr⅔ = jH = StM Sc⅔ = jD | 0.6 < Pr < 60 , 0.6 < Sc < 3000

6. VA L I D I T Y
 Validity of Chilton Colburn Analogy depends on property
of the fluid and length of the plate
 This analogy is valid for flow around spheres only when Nu
and Sh are replaced by (Nu-2) and (Sh-2)
 This analogy is not valid below Re = 10000

7. C H I LTON CO L B URN J - FAC TORS
F O R H E AT A N D M A S S T R A N S F ER
Heat Transfer quantities
(Pure Fluids)
Binary Mass Transfer
quantities
(Isothermal Fluids)
MOLAR UNITS
Binary Mass Transfer
quantities
(Isothermal Fluids)
MASS UNITS
jH = Nu Re-1 Pr-⅓
= h/ρCpv (Cpμ/k)2/3
jD = Sh Re-1 Sc-⅓
= k/cv (μ/ρDAB)2/3
jD = Sh Re-1 Sc-⅓
= k/ρv (μ/ρDAB)2/3

8. C H I LTO N CO L B U R N A N A LO G Y
F O R F LO W S W I T H A N D W I T H O U T
F O R M D R AG
 For flow past a flat plate or a pipe where no form drag is
present,
f/2 = jH = jD
 For flow in packed beds or other blunt objects where
form drag is present,
f/2 > jH or jD
and jH = jD

9. D I M E NS IONLESS G R O U P S
F O R H E AT A N D M A S S T R A N S F ER
Heat Transfer quantities
(Pure Fluids)
Binary Mass Transfer quantities
(Isothermal Fluids)
MOLAR UNITS
Binary Mass Transfer quantities
(Isothermal Fluids)
MASS UNITS
Re = Lvρ/μ
Fr = v²/gL
Nu = hL/k
Pr = Cpμ/k
Gr = L³ρ²gβ∆T/μ²
Pé = LvCp/k
Sh = kL/cDAB
Sc = μ/ρDAB
Gr = L³ρ²gε∆x/μ²
Pé = Lv/DAB
Sh = kL/ρDAB
Sc = μ/ρDAB
Gr = L³ρ²gε∆w/μ²
Pé = Lv/DAB

10. C H I LTON CO L B URN A N A LO G Y
F O R LO N G S M O OTH T U B E S
In highly turbulent range (Re > 10000), the heat transfer ordinate
agrees approximately with f/2 for the long smooth pipes under
consideration
f/2 = jH
where,
jH = Nu Re-1 Pr-⅓ = h/ρCpv (Cpμ/k)2/3 = hS/wCp (Cpμ/k)2/3
where,
S = Area of the tube cross section
w = Mass flowrate through the tube
f/2 is obtainable using Re = Dw/Sμ

11. A D VA N TA G E S
Useful to find each term for highly turbulent flow as f equation is known
f = 0.058 Re-1/5
L I M I TAT I O N S
1. Only applicable when no form drag is present in flows
2. Only applicable to conditions 0.6 < Pr < 60 , 0.6 < Sc < 3000
3. Not applicable to heavy oils (Pr>60) and liquid metals (Pr<0.6)
A P P L I C AT I O N S
1. Evaluation of heat transfer in internal forced flow
2. Heat Exchanger Design
3. Reactor Design