Simple Diffusion Problem (after Chapra and Canale, Numerical Methods for Engineers) The figure shows a gas...

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Simple Diffusion Problem (after Chapra and Canale, Numerical Methods for Engineers) The figure shows a gas flowing over a series of reactors from left to right, and a liquid flowing from right to left in the reactors. The flow rates for the gas and liquid are QG and Q respectively. 1 2 3 4 5 Qo Co Caz Cas Cat Cas Qc CLG QL CU CLE CLS CLY CLS QL The exchange process from the gas to the liquid in each reactor is assumed to obey a simple diffusion law, m = d(cc), where m = mass transfer rate, d = diffusion coefficient and CA and CB are concentrations in each medium. At each reactor, the total mass absorbed per unit time by the fluid must match the mass lost by the gas. By treating this as a series of steady state reactions, one can write a pair of equations for each reactor that describes the conservation of mass. For example, the left-most reactor must satisfy the equations Q-Q+d(-)-0 where CLO = the concentration of the gas species of interest in the out-flowing liquid, CGO = the concentration of the gas species of interest in the in-flowing gas, CG1 and CL1 = the average concentrations in the liquid and gas in the first reactor. Write similar equations for each exchange and to obtain the equations for the 10 unknown concentrations in the reactors. Write the equation in a final form with the known quantities on the right. Simple Diffusion Problem (after Chapra and Canale, Numerical Methods for Engineers) The figure shows a gas flowing over a series of reactors from left to right, and a liquid flowing from right to left in the reactors. The flow rates for the gas and liquid are QG and Q respectively. 1 2 3 4 5 Qo Co Caz Cas Cat Cas Qc CLG QL CU CLE CLS CLY CLS QL The exchange process from the gas to the liquid in each reactor is assumed to obey a simple diffusion law, m = d(cc), where m = mass transfer rate, d = diffusion coefficient and CA and CB are concentrations in each medium. At each reactor, the total mass absorbed per unit time by the fluid must match the mass lost by the gas. By treating this as a series of steady state reactions, one can write a pair of equations for each reactor that describes the conservation of mass. For example, the left-most reactor must satisfy the equations Q-Q+d(-)-0 where CLO = the concentration of the gas species of interest in the out-flowing liquid, CGO = the concentration of the gas species of interest in the in-flowing gas, CG1 and CL1 = the average concentrations in the liquid and gas in the first reactor. Write similar equations for each exchange and to obtain the equations for the 10 unknown concentrations in the reactors. Write the equation in a final form with the known quantities on the right.