CONVECTIVE MASS TRANSFER
Overview: Mass transfer occurs when a substance is not uniformly distributed in another
substance. Fick’s law of diffusion is the mass transfer analog to Fourier’s law of heat conduction.
When fluid motion is present, heat conduction is enhanced and Newton’s law of convection results [ q = h A (Tw - T∞) ].
Similarly, mass diffusion is enhanced:
NA"= - D ΔCA
NA" = hm (CAw -CA∞)
In these expressions, NA" is the mass flux (kg/m2s) of component A, D is the diffusivity, and ΔC is the concentration gradient. The concentration at infinity is generally the density of the component in the free stream (kg/m3). If it is a gas, C is generally calculated from the ideal gas law (C = r = PA/RT, where P is the partial pressure of the component). If the component is vaporizing from the surface, the partial pressure is generally taken as the saturation pressure, although this is not a good assumption when the surface is curved and in other special cases. The mass convection coefficient, hm, has units of m/s in the SI system.
Just as there are equations which can be used to predict the thermal convection
coefficient, these same equations, with modifications, can be used to predict hm. If the flow is laminar, Equation 7.32 from Incropera and DeWitt is applicable. If the flow is turbulent, then 7.38, 7.42, or 7.45 may be chosen. A good example of the use of these equations is Example 7.3 in Incropera and DeWitt, which happens to be for turbulent flow following a transition.
Consider air at 20°C flowing at 3 km/hr over a water surface which is also 20°. The water surface is 6cm by 3cm and the air is moving parallel to the 6 cm direction. The relative humidity of the air is 30%. Find the Sherwood number, the mass convective heat transfer coefficient, and the evaporation rate of the water. Find the mass evaporated in 10 minutes. Take the properties of water in the correlation as the properties of air.
Equipment: Aluminum plate, fan, hot wire anemometer or pitot tube, electronic balance, and various other measurement devices, such as thermocouples and psychrometers.
Procedure: Measure the aluminum plate dimensions. Measure the air temperature and humidity.
Place fan at some distance from the balance and turn on. Measure the air velocity.
Turn off the fan and place aluminum plate on the balance. Turn on balance and zero.
Load plate with water until plate is covered. Measure the water temperature. Turn on
fan and record mass readings from balance every minute for up to 15 minutes.
Repeat for two more fan positions.
Analysis: For each airflow make a graph of mass versus time and use the slope to find the mass flux of water. Find the mass transfer coefficient from the experiment and also from the appropriate correlation. Compare the results.
Report: Assemble your results, including figures, tables, any graphs and calculations into a brief report. Compare the results from the experiment with those from the equation. Do they agree or not? How close is the agreement? Why might they not agree? What would you do differently if you had to do the experiment again? Would you suggest any changes to the experiment?