As part of the manufacturing process for the fabrication of titanium-oxide-based solar panels, a…

As part of the manufacturing process for
the fabrication of titanium-oxide-based solar panels, a layer of nonporous
titanium oxide must be reduced to metallic titanium, Ti, by hydrogen gas as
shown in the following figure.

The reaction at the Ti/TiO2
boundary is given by

Pure H2 gas flows rapidly over
the surface of the nanoporous TiO2 slab. As TiO2(s) is
reduced to Ti (molecualr weight ), the path length
for mass transfer of H2 and H2O gas through the porous
slab from the surface to the Ti/TiO2 boundary increases with time.
You may assume that (1) the process operates at 1.0 atm and 9
»

As part of the manufacturing process for
the fabrication of titanium-oxide-based solar panels, a layer of nonporous
titanium oxide must be reduced to metallic titanium, Ti, by hydrogen gas as
shown in the following figure.

The reaction at the Ti/TiO2
boundary is given by

Pure H2 gas flows rapidly over
the surface of the nanoporous TiO2 slab. As TiO2(s) is
reduced to Ti (molecualr weight ), the path length
for mass transfer of H2 and H2O gas through the porous
slab from the surface to the Ti/TiO2 boundary increases with time.
You may assume that (1) the process operates at 1.0 atm and 900 K; (2) the
reaction is very fast so that the concentration of H2 gas at the
Ti/TiO2 boundary is zero and the reduction of TiO2(s) is
limited by the diffusion of TiO2(g) away from the Ti(s)/TiO2
boundary; (3) the diffusion process is pseudo-steady state along the diffusion
path; and (4) the effective gas-phase diffusion coefficient of H2
within the porous Ti(s) containing a mixture of H2(g) and H2O(g)
is 0.031 cm2/s at the temperature and pressure of the process,
whereas the effective diffusion coefficient of H2O(g) within the
nanoporous Ti(s) containing a mixture of H2(g) and H2O(g) is 0.01 cm2/s
at the temperature and pressure of the process. The density of the nanoporous
Ti(s) is 2.6 g/cm3.

a. Determine the flux of H2 to
the Ti/TiO2 boundary when , assuming

b. Determine the number of hours necessary
for all the TiO2 to be converted to Ti(s).

c. At , determine the
concentration profile for H2(g).

»

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