Question

Rectangular channel flow reactors are a useful basis for the development of electro chemical synthesis as part of a green and sustainable chemical manufacturing involving process electrification. A laboratory-scale electrochemical reactor, developed as a rectangular channel flow cell, had length (L) of 30 cm, a cross-sectional width (B) of3.0 cm and a cross-sectional height (s) of 5.0 mm, and was designed so that the flow would be well-developed before it reached the electrodes embedded in the sides of the reactor. Operation of the cell occurred isothermally at293 K, for a liquid electrolyte (of viscosity 1.002 mPa s and density998.2 kg m) for the electrochemical conversion of a reactant. The diffusion coefficient of the reactant in the liquid electrolyte is 2.67 x 10 cm? s at293 K. (a)Explaining all terms and symbols used, define the following. What are the units of kinematic viscosity (v)?kinematic viscosity of the liquid electrolyte at 293 K, providing your answer in the units you have previously given.(b)Calculate the If the equivalent diameter (de) of the laboratory reactor is given byequation (1),(c) \mathrm{d}_{\mathrm{e}}=4 \times \frac{\text { cross-sectional area }}{\text { cross-sectional perimeter }} calculate the value of the equivalent diameter of the reactor, andgive its units. (d)Noting that the Reynolds number (Re) of the reactor is given byequation (2), \mathrm{Re}=\frac{\mathrm{d}_{e} \mathrm{u}}{\mathrm{v}} in which u is the mean electrolyte velocity, use the data provided tocalculate, at 293 K, both the Reynolds number and the Schmidtnumber as a function of the volume flow rate. Comment on yourresults. (e)Use the data provided to calculate the Sherwood number (Sh) as a function of the volume flow rate at 293 K, and then plot Ig(Sh)against Ig(Re) and comment on your plot. For Re < 2000, the Sherwood number is predicted to be related tothe Reynolds number and the Schmidt number by equation (3)(f) \mathrm{Sh}=\mathrm{aRe}^{\mathrm{b}} \mathrm{Sc}^{/ / 3} where a and b are constants. Use your answers to parts (d) and (e)to calculate the values of a and b. Comment on your findings. For Re > 2000, the Sherwood number is predicted to be related tothe Reynolds number and the Schmidt number by equation (4) S h=c R e^{d} S c where c and d are constants. Use your answers to parts (d) and (e)to calculate the values of c and d. Comment on your findings.

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