Consider the micro scale apparatus shown in the figure on the next page. This apparatus is designed to deliver a small, steady stream of methanol (MeOH) vapor to a separate device that reforms the methanol vapor into hydrogen gas needed for a miniature fuel cell. In the present system, liquid methanol is vaporized at a constant temperature. The methanol vapor passes through a tube, and then through a porous ceramic membrane. A steady flow of O₂gas over the membrane keeps the partial pressure of methanol vapor in the exit gas constant. Small amounts of liquid methanol are constantly added to the base of the apparatus to keep the liquid methanol level steady. The apparatus is heated to maintain a constant temperature of 20°C, and the total system pressure is kept constant at 1.0 atm. Let A = MeOH vapor and B = O₂gas. Consider the tube System 1 (z = 0 to z = L₁) the porous ceramic membrane (to z = L₁to z = L₂) System 2. 

a. The porous ceramic membrane in System 2 consists of a parallel array of cylindrical pores. Each pore has a uniform diameter of 5.0 microns (µm). Estimate the effective diffusion coefficient for MeOH vapor within the porous ceramic membrane. 

b. Based upon the nomenclature provided in the figure below, state boundary conditions for Systems I and 2 for MeOH in algebraic form. 

c. State relevant assumptions for the mass-transfer process for Systems 1 and 2. Based on these assumptions, develop the final, integrated mathematical expression for predicting the total MeOH transfer rate W_A through Systems 1 and 2. In this analysis, include the appropriate simplification of the general differential equation for mass transfer and Fick€™s flux equation. Leave all boundary conditions in algebraic form. Hint: To help link System 1 to System 2, consider the dilute UMD assumption. 

d. Using the dilute UMD assumption, estimate the total transfer rate of MeOH vapor from the apparatus in units of µ mole/h.

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Og gas + MEOH vapor O2 gas PA = 0.02 atm (well mixed) SYSTEM 2 in out cross section - z = L2 = 4.5 mm УА2 SYSTEM - z = L, = 3 mm A, = surface area occupied by pores = 0.5 mm? УА1 P = 1.0 atm SYSTEM T= 20°C dpore = 5.0 µm d=1.0 mm - z = 0 Liq МеОн: makeup Удо Heater (keeps liquid MeOH at 20°C as it vaporizes)