Develop an expression for Thiele modulus, the concentration profile and the catalyst

effectiveness factor when the reversible reaction A $=$ B occurs in a porous catalyst

whose half$-$length is L with a height H and width W$.$ The equilibrium constant is K

$=$ kf$/$kr$.$ Assume that diffusion mainly occurs in the x$-$coordinate, which is also

associated with the catalyst half$-$length L$.$ The effective diffusivity for specie A is

DAe and the local concentrations of species A and B are