---
title: "Convective mass transfer and analogies"
subject: "Heat Transfer"
chapter: 7
key: "semester_5/heat_transfer:convective-mass-transfer-analogy-correlations"
source: https://www.bctengineer.com/q/semester_5/heat_transfer/convective-mass-transfer-analogy-correlations
site: BCT Engineering
---

# Convective mass transfer and analogies

Heat Transfer · Chapter 7: Introduction to Mass Transfer

- Asked in: year not given, 6 marks
- Video: [UCSB ChE120C (MassTrasnfer) - Analogies to heat and momentum transport](https://www.youtube.com/watch?v=BS8_EbF-QTU) — Baron Peters
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/heat_transfer/convective-mass-transfer-analogy-correlations
- Whole chapter: https://www.bctengineer.com/md/semester_5/heat_transfer/chapter-7

## Question

Define the convective mass transfer coefficient. Explain the Schmidt, Sherwood and Lewis numbers. State the analogy between momentum, heat and mass transfer (Chilton-Colburn) and give two correlations used for convective mass transfer.

## Short answer

Convective mass transfer coefficient h_m: N_A = h_m (C_As – C_A∞). Sc = ν/D, Sh = h_m L/D, Le = α/D. Chilton-Colburn: (f/2) = St Pr^{2/3} = St_m Sc^{2/3}, thus h/h_m = ρ c_p Le^{2/3}. Correlations: laminar flat plate Sh_L = 0.664 Re_L^{1/2} Sc^{1/3}; turbulent tube Sh = 0.023 Re^{0.83} Sc^{0.44}.

## Answer

#### Convective mass transfer coefficient
When a fluid flows over a surface from which species A is transferred, the flux is written in the form of Newton's law of cooling:

$$
N_A = h_m\,(C_{As}-C_{A\infty})
$$

$h_m$ (m/s) is the convective mass transfer coefficient, found from correlations just like $h$.

#### Dimensionless numbers
| Number | Definition | Meaning |
|---|---|---|
| Schmidt, $Sc$ | $\dfrac{\nu}{D_{AB}}$ | Momentum diffusivity / mass diffusivity (mass analogue of $Pr$) |
| Sherwood, $Sh$ | $\dfrac{h_mL}{D_{AB}}$ | Convective / diffusive mass transfer (analogue of $Nu$) |
| Lewis, $Le$ | $\dfrac{\alpha}{D_{AB}} = \dfrac{Sc}{Pr}$ | Thermal diffusivity / mass diffusivity |
| Stanton (mass), $St_m$ | $\dfrac{h_m}{V}= \dfrac{Sh}{Re\,Sc}$ | Mass transfer / mass capacity of the stream |

#### Analogy between momentum, heat and mass transfer
Because all three processes are carried by the same molecular and eddy motion in the boundary layer, their equations are similar. Reynolds analogy (for $Pr = Sc = 1$): $\dfrac{f}{2}=St=St_m$. For other fluids the Chilton-Colburn analogy applies ($0.6 < Pr < 60$, $0.6 < Sc < 3000$):

$$
j_H = St\,Pr^{2/3}= \frac{f}{2}= j_M = St_m\,Sc^{2/3}
$$

Hence, if $h$ is known, $h_m$ follows from

$$
\frac{h}{h_m} = \rho c_p\,Le^{2/3}
$$

Mass transfer can thus be predicted from heat transfer results by replacing $Nu \to Sh$ and $Pr \to Sc$.

#### Correlations
- Laminar flow over a flat plate: $Sh_L = 0.664\,Re_L^{1/2}\,Sc^{1/3}$.
- Turbulent flow in tubes (Gilliland-Sherwood): $Sh = 0.023\,Re^{0.83}\,Sc^{0.44}$. The Linton-Sherwood form $Sh = 0.023\,Re^{0.83}\,Sc^{1/3}$ is also used.
- Flow past a sphere (Frossling): $Sh = 2 + 0.552\,Re^{1/2}Sc^{1/3}$.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. The convective mass transfer coefficient is defined through
   A. N_A = -D dC/dx
   B. N_A = h_m (C_As - C_A_inf)
   C. N_A = h (Ts - T_inf)
   D. N_A = rho c_p h_m
   Answer: B. It is written like Newton's law of cooling; h_m has units of m/s. (Key point: Mass transfer coefficient)

2. The Schmidt number is
   A. alpha / D_AB, thermal over mass diffusivity
   B. h_m L / D_AB, convective over diffusive mass transfer
   C. nu / D_AB, the momentum over mass diffusivity ratio, the mass analogue of Pr
   D. h_m / V
   Answer: C. Sc = nu/D_AB; Sherwood is h_m L/D_AB and Lewis is alpha/D_AB = Sc/Pr. (Key point: Schmidt number)

3. The Chilton-Colburn analogy states
   A. St = St_m for any fluid
   B. Nu = Sh always
   C. f = Re/Pr
   D. St Pr^(2/3) = f/2 = St_m Sc^(2/3)
   Answer: D. j_H = j_M = f/2 extends the Reynolds analogy (valid for Pr = Sc = 1) to other fluids. (Key point: Chilton-Colburn analogy)

4. How can mass transfer be predicted from heat transfer results?
   A. Replace Nu with Sh and Pr with Sc in the heat transfer correlation
   B. Replace Nu with Re and Pr with Le
   C. It cannot be done
   D. Replace Sh with Pr only
   Answer: A. The similar boundary-layer equations let Nu correlations carry over with Nu to Sh and Pr to Sc. (Key point: Using the analogy)

## Related in Heat Transfer

- [Modes of heat transfer with rate equations](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Amodes-of-heat-transfer) — Heat Transfer, chapter 1
- [Factors affecting heat transfer and its applications](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Afactors-applications-heat-transfer) — Heat Transfer, chapter 1
- [Newton's law of cooling and convection coefficient](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Anewtons-law-cooling-convection-coefficient) — Heat Transfer, chapter 3
- [Dimensionless numbers in convection](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Asignificance-dimensionless-numbers-convection) — Heat Transfer, chapter 3
- [Composite furnace wall heat loss](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Acomposite-furnace-wall-interface-temperatures) — Heat Transfer, chapter 2
- [Plane wall with internal heat generation](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Aplane-wall-with-heat-generation) — Heat Transfer, chapter 2

## Related in other subjects

- [Velocity transfer function of two-mass system with analogies](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Atf-velocity-m2-fv-fi) — Control Systems, chapter 2
- [Overall heat transfer coefficient: two-layer plane wall](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Acomposite-plane-wall-two-layers-overall-u) — Fundamental of Thermodynamics & Heat Transfer, chapter 7, asked 2×
- [Two-mass system transfer function and F-V analogy](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Atf-two-mass-k1k2b1b2) — Control Systems, chapter 2
- [Two-mass system equations, X2/F, F-I and F-V analogies](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Ade-tf-fi-fv-m1-m2) — Control Systems, chapter 2