We take a model for steady-state plug-flow in a single channel of a catalytic monolith reactor and then solve the appropriate boundary value problem for a range of parameter values, using continuation methods adapted from dynamical systems theory. The problem is solved using either of two methods, shooting or relaxation. We show the effect of varying different parameters on the positions of the turning points in parameter space, and discuss the practical implications of these variations in qualitative behaviour for the design and operation of such a system.