Reference ID: MET-3E56 | Process Engineering Reference Sheets Calculation Guide
Introduction & Context
The convective mass-transfer coefficient \(k_c\) quantifies how fast a species is transported between an interface and a moving fluid. In process engineering it is the key parameter that links the driving force (concentration or partial-pressure difference) to the evaporation or absorption rate. Typical applications include:
Design of cooling towers, humidifiers and de-humidifiers
Prediction of drying rates for solids and sprays
Sizing of gas-scrubbing and stripping columns
Estimation of volatile losses from storage tanks or spills
Because direct measurement of interfacial concentration is difficult, the coefficient is usually inferred from the measurable partial-pressure difference and the ideal-gas law. The sheet below shows the standard conversion route from partial pressures to mass flux.
Methodology & Formulas
Convert temperature to absolute scale
\[T(\text{K})=T(^\circ\text{C})+273.15\]
Evaluate the driving force
Partial-pressure difference:
\[\Delta p=p_{\text{sat}}-p_{\infty}\]
Ideal-gas concentration difference (mass basis):
\[\Delta C=\frac{\Delta p\cdot M}{R_u\,T}\]
where
\(M\) = molar mass of the evaporating species
\(R_u\) = universal gas constant (kPa m3 kmol-1 K-1)
Compute the mass flux
Instantaneous flux:
\[J=k_c\,\Delta C\]
Hourly flux (if required):
\[J_{\text{h}}=J\cdot 3600\]
The Sherwood number \(\text{Sh}=k_c\,L/\mathcal{D}_{AB}\) and the Schmidt number \(\text{Sc}=\nu/\mathcal{D}_{AB}\) link the coefficient to the diffusion coefficient \(\mathcal{D}_{AB}\) and kinematic viscosity \(\nu\). Once \(\text{Sh}\) is known, \(k_c\) follows directly.
Identify the continuous phase (gas or liquid) that is limiting mass transfer.
Record packing type, size, and surface area per volume ap.
Calculate the phase Reynolds number using superficial velocity and equivalent particle diameter.
Select a correlation validated for the same packing family and comparable Re range (e.g., Onda for Raschig rings, Bravo-Rocha for structured packings).
Check the Schmidt number exponent in the correlation; if your system exponent differs by >10 %, adjust the coefficient or use a more recent correlation.
Only if both the hydrodynamics (liquid holdup, gas velocity) and the physical properties (viscosity, diffusivity) remain nearly constant. In absorbers with large concentration changes, liquid viscosity can double, causing kc to drop 20–40 %. For rigorous design, divide the column into segments and recalculate kc for each segment.
Worked Example: Estimating Water Evaporation Rate from a Cooling-Tower Pan
A small natural-draft cooling tower uses an open pan of water at 25 °C to pre-cool the incoming air. To size the make-up water pump we need the mass flux of water vapour leaving the pan surface. The convective mass-transfer coefficient, \(k_c\), has been measured as 0.011 m s\(^{-1}\). Determine the evaporation rate in kg m\(^{-2}\) h\(^{-1}\) assuming the free-stream air is essentially dry.
Knowns
Temperature of water surface, \(T\) = 25 °C (298.15 K)
Vapour pressure of water at 25 °C, \(p_{\text{sat}}\) = 3.17 kPa
