Chapter 9, Problem 9.120P

Fuel cells similar to the PEM cell of Example 1.5 operate with a mixture of liquid water and methanol instead of hydrogen: the anode is placed in direct contact with the liquid fuel. Oxygen (species A) is delivered to the exposed cathode by free convection. Hence, no fans or pumps are needed to operate the device. The power output of passive, direct methanol fuel cells (DMFCs) can become mass transfer limited, since the electric current produced by the DMFC is related to the rate at which oxygen is consumed at the cathode by the expression $I=4n_{\text{A}}f{m}_{\text{A}}$ , where $f$ is Faraday’s constant, $f=96,489\text{coulombs/mol}$ . Consider a passive DMFC with a $120\text{mm}\text{×}\text{120}\text{mm}$ membrane. Determine the maximum possible electric current produced by the DMFC when the oxygen mass fraction at the cathode is $m_{A,s}=0.10$ for cases where the cathode is facing up or is vertical. As a first approximation and to illustrate the sensitivity of the device to its orientation relative to the vertical direction, assume buoyancy forces are dominated by the difference in density associated with the change in the oxygen mass fraction between the cathode surface and the quiescent environment, which is atmospheric air at $T_{\infty }=25°C$ . Assume the quiescent air is composed of nitrogen and oxygen, with an oxygen mass traction $m_{A,\infty }=0.233$ .