Analytical expression for the non-isothermal effectiveness factor: the nth-order reaction in a slab geometry

The problem of calculating the effectiveness factor for a porous slab of catalyst pellet under non-isothermal conditions has been revisited. An exact formal analytical solution was obtained for a nth-order (integer n⩾0), exothermic and irreversible chemical reaction. Numerical calculations where performed, and an analytical formula was obtained for the very fast reaction limit. In addition, a fairly simple formula, which was called the low beta approximation, was developed and tested to be valid for low values of the thermicity group β⩽0.1.