Before Frank-Kamenetskii, his doctoral advisor Nikolay Semyonov (or Semenov) proposed a thermal explosion theory with a simpler model with which he assumed a linear function for the heat conduction process instead of the Laplacian operator. Semenov's equation reads as
in which the exponential term  will tend to increase  as time proceeds whereas the linear term  will tend to decrease . The relevant importance between the two terms are determined by the Damköhler number . The numerical solution of the above equation for different values of  is shown in the figure.