For a chemical process, species A must be added to a stream of inert carrier gas...

 

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For a chemical process, species A must be added to a stream of inert carrier gas B. To do this in a controlled manner, liquid A is evaporated from a round pan into a flowing stream of B (see right figure below). Unfortunately, little is known about the mass transfer coefficients for the round pan and the diffusion coefficient of A in air, which prevents the process engineer from optimizing the conditions. In order to quantify the relative importance of convection and diffusion for the evaporation of A from the pan, two laboratory experiments are performed (see Figures below) under identical conditions (T = 293 K, P = 1 atm): 1/ Evaporation of liquid A from a narrow cylindrical tube with diameter Dtube = 2 cm (left figure on next page). Pure carrier gas B is blown over the top of the tube at velocity v = 1 m/s. The distance from the liquid surface to the top of the tube is L = 25 cm at the start of the experiment. pan 2/ Evaporation of liquid A from the actual process device, a flat circular pan with diameter Den = 10 cm. Pure carrier gas B is blown across the pan at velocity v = 1 m/s (right figure). gas B Dube L gas B liquid A Dpan liquid A An analytical balance is used to monitor evaporation in both experiments. When pseudo steady state is reached, the mass rate of evaporation (in kg/s) from the pan is 100 times larger than from the tube. The exact value of the vapor pressure of A, Pav is unknown, but PA < < 1 atm. A/ Derive an equation for the molar flux of A from the narrow tube as a function of PAv. Do not insert numerical values. B/ Calculate the Sherwood number for evaporation from the circular pan. For a chemical process, species A must be added to a stream of inert carrier gas B. To do this in a controlled manner, liquid A is evaporated from a round pan into a flowing stream of B (see right figure below). Unfortunately, little is known about the mass transfer coefficients for the round pan and the diffusion coefficient of A in air, which prevents the process engineer from optimizing the conditions. In order to quantify the relative importance of convection and diffusion for the evaporation of A from the pan, two laboratory experiments are performed (see Figures below) under identical conditions (T = 293 K, P = 1 atm): 1/ Evaporation of liquid A from a narrow cylindrical tube with diameter Dtube = 2 cm (left figure on next page). Pure carrier gas B is blown over the top of the tube at velocity v = 1 m/s. The distance from the liquid surface to the top of the tube is L = 25 cm at the start of the experiment. pan 2/ Evaporation of liquid A from the actual process device, a flat circular pan with diameter Den = 10 cm. Pure carrier gas B is blown across the pan at velocity v = 1 m/s (right figure). gas B Dube L gas B liquid A Dpan liquid A An analytical balance is used to monitor evaporation in both experiments. When pseudo steady state is reached, the mass rate of evaporation (in kg/s) from the pan is 100 times larger than from the tube. The exact value of the vapor pressure of A, Pav is unknown, but PA < < 1 atm. A/ Derive an equation for the molar flux of A from the narrow tube as a function of PAv. Do not insert numerical values. B/ Calculate the Sherwood number for evaporation from the circular pan.