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Qwestrum Engineering360 · Chemical Engineering · Mass Transfer

Convective Mass Transfer

Convective mass transfer uses a coefficient k_c in direct analogy to heat convection; k_c comes from Sherwood-number correlations Sh = C·Re^m·Sc^n, and the Chilton-Colburn analogy links it to the heat-transfer coefficient.
Exam tip: keep SI units consistent end-to-end, write the governing relation symbolically before substituting, and sanity-check magnitude and sign.

Key formulas & points

Skim these first — then read the full notes below.

  • Sc=μ/Sc = \mu / (ρ D_AB) — mass-transfer analogue of Prandtl number
  • Chilton−ColburnjD=Sh(ReSc⅓)≈jHChilton-Colburn j_{D} = \frac{Sh}{(Re Sc^⅓)} \approx j_{H} (heat–mass analogy)
  • Gas-film vs liquid-film control in absorption

Topic details

Introduction

This topic mirrors convective heat transfer, replacing temperature with concentration, Nusselt with Sherwood and Prandtl with Schmidt. You compute k_c from correlations, exploit the heat–mass-transfer analogy to reuse familiar heat-transfer data, and identify whether the gas film or the liquid film controls the overall rate in a contacting device.

Key relations & formulas

NA=kc(CA,s−CA,∞)N_{A} = k_{c} (C_{A},s - C_{A},\infty )
(convective flux)
Sh=kcLDABSh = k_{c} \frac{L}{D_{AB}}
(Sherwood number)
Sh=0.023Re0.8Sc0.33Sh = 0.023 Re^0.8 Sc^0.33
(turbulent pipe, analogous to Dittus-Boelter)

Notation and sign conventions

Relation 1 —
NA=kcN_{A} = k_{c}
NA=kc(CA,s−CA,∞)N_{A} = k_{c} (C_{A},s - C_{A},\infty )
(convective flux)
Write this relation with symbols exactly as in Mass Transfer Operations — Treybal before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 2 —
Sh=kcLDABSh = k_{c} \frac{L}{D_{AB}}
Sh=kcLDABSh = k_{c} \frac{L}{D_{AB}}
(Sherwood number)
Write this relation with symbols exactly as in Mass Transfer Operations — Treybal before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 3 —
Sh=0.023Re0.8Sc0.33Sh = 0.023 Re^0.8 Sc^0.33
Sh=0.023Re0.8Sc0.33Sh = 0.023 Re^0.8 Sc^0.33
(turbulent pipe, analogous to Dittus-Boelter)
Write this relation with symbols exactly as in Mass Transfer Operations — Treybal before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Concept in depth

The similarity of the transport equations means mass transfer borrows the entire structure of heat transfer: the Sherwood number is the dimensionless coefficient, the Schmidt number plays the role of Prandtl, and the Chilton-Colburn j-factors let a measured heat-transfer correlation be converted into a mass-transfer one. Physically, k_c reflects how quickly turbulence renews the fluid at the interface. In a two-phase contactor the phase with the smaller coefficient offers the larger resistance, so recognising gas-film versus liquid-film control tells you which side to improve.

Assumptions and validity limits

State assumptions explicitly before using any relation for convective mass transfer — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.
Wrong assumptions invalidate the entire solution even when the formula is correct. In Mass Transfer viva and GATE descriptive questions, listing valid assumptions often earns separate marks.

Step-by-step problem approach

1. Read the question and list given data with SI units (common in Mass Transfer papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to convective mass transfer.
4. Use equation 1:
NA=kcN_{A} = k_{c}
.
5. Use equation 2:
Sh=kcLDABSh = k_{c} \frac{L}{D_{AB}}
.
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.

Applications & exam relevance

Convective Mass Transfer appears in distillation, absorption, and drying. In Indian chemical curricula this topic is tested because it connects theory to diffusion and interphase transfer.
GATE and semester exams often combine convective mass transfer with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use convective mass transfer?" — answer with a lab, mini-project, or plant visit example if possible.

Common mistakes in exams

Students confuse the Schmidt number with the Prandtl number, misuse the analogy by matching j_D to the wrong j_H, and forget that k_c has velocity units (m/s) whereas k_y or k_G use pressure or mole-fraction driving forces. Ignoring which film controls leads to wasted design effort.

Quick revision checklist

Before attempting convective mass transfer problems, confirm you can:
1.
Sc=μ/Sc = \mu /
(ρ D_AB) — mass-transfer analogue of Prandtl number
2.
Chilton−ColburnjD=Sh(ReSc⅓)≈jHChilton-Colburn j_{D} = \frac{Sh}{(Re Sc^⅓)} \approx j_{H}
(heat–mass analogy)
3. Gas-film vs liquid-film control in absorption
Revise the solved examples in Mass Transfer Operations — Treybal and one previous-year GATE or university paper for this unit.

Worked examples

Try the problem first — open the solution when you are ready to check.

k_c from Sherwood number

Problem

A correlation gives Sh = 150 for flow in a 20 mm duct with D_AB = 2.5×10⁻⁵ m²/s. Find k_c.

Solution

k_c = Sh·D_AB/L = 150 × 2.5×10⁻⁵/0.02 = 0.188 m/s. This coefficient multiplies the concentration difference to give the flux.

Conceptual check — Convective Mass Transfer

Problem

In a Mass Transfer semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of convective mass transfer." What should a complete answer include?

Exams & GATE

Treybal Ch. 3 — gas-phase vs liquid-phase controlled absorption.

📖 Standard books (India)

  • Mass Transfer Operations — Treybal

    Read: Syllabus unit

    Absorption, distillation, and extraction

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