For planar vessel, there is an exact solution. Here , then
If the transformations  and , where  is the maximum temperature which occurs at  due to symmetry, are introduced
Integrating once and using the second boundary condition, the equation becomes
and integrating again
The above equation is the exact solution, but  maximum temperature is unknown, but we have not used the boundary condition of the wall yet. Thus using the wall boundary condition  at , the maximum temperature is obtained from an implicit expression,
Critical  is obtained by finding the maximum point of the equation (see figure), i.e.,  at .
So the critical Frank-Kamentskii parameter is . The system has no steady state (or explodes) for  and for , the system goes to a steady state with very slow reaction.