Consider a fuel cell operating at 800∘C, 1 atm. In the cathode, humidified air is supplied with the mole fraction of water vapor equal to 0.1. If the fuel cell employs circular flow channels with a diameter of 1 mm, find the maximum velocity of air that can be used while still maintaining laminar flow. Compare your result to Example 5.2.

To determine the maximum velocity of air that can be used while still maintaining laminar flow in the circular channels of the fuel cell, we need to calculate the Reynolds number (Re). Laminar flow is typically characterized by a Reynolds number less than 2,300 for flow within a pipe or tube.

The Reynolds number for flow in a pipe is given by:

Re = (ρ * u * D) / μ

where ρ is the density of air (kg/m³), u is the fluid velocity (m/s), D is the diameter of the pipe (m), and μ is the dynamic viscosity of air (Pa·s or N·s/m²).

However, we are not provided with the density and dynamic viscosity of air at 800°C. Those properties are temperature dependent and would need to be found in an engineering table or calculated using specialized software or empirical equations for gases as a function of temperature. These are not standard conditions, so we cannot use the room-temperature values for density and viscosity of air.

Assuming we have the appropriate values of ρ and μ at 800°C, we would proceed as follows:

1. Calculate the Reynolds number for laminar flow (assuming a maximum Re of 2,300). 2. Rearrange the Reynolds equation to solve for the maximum fluid velocity (u_max): u_max = (Re * μ) / (ρ * D)

3. Substitute the values for ρ, μ, and D along with Re=2300 into the equation to find the maximum velocity.

Since we're lacking specific data for ρ and μ at 800°C, you would need to locate these to complete the calculation.

As for comparing to Example 5.2, I don't have the specific example to reference. However, if you have the information from Example 5.2, you would compare the max velocity calculated with the velocity in the example to see how they differ. To make a valid comparison, ensure that the other conditions (like temperature and pressure) and assumptions are comparable between the two situations.