On the determination of critical ambient temperatures and critical initial temperatures for thermal ignition

A new set of dimensionless parameters and variables is defined with a view to simplifying and clarifying the theoretical determination of the initial ambient and the critical initial temperatures in spatially uniform self-heating systems. With these new variables the determination of the critical ambient temperatures can be achieved without the iterative procedure necessary when using the traditional variables with the Arrhenius function. The determination of the critical initial temperature using the new variables highlights a significant new source of error which arises when the exponential approximation arises. There is neither necessity nor advantage in making this approximation with these new variables.