Excessive heat generation within a body can cause unbounded temperature or thermal instability. In this work, a stability criterion is established for one-dimensional composite solids with internal heat generation at a rate proportional to their temperature. In the development, a spatial state formulation is used to derive a characteristic equation for system eigenvalues. A root locus analysis of the characteristic equation yields a stability criterion, by which an upper bound of heat source for thermal stability is obtained, and the gain of heat source is related to the number of unstable (positive) eigenvalues. The proposed stability test requires minimum numerical effort, does not require the information about system eigenvalues, and is applicable to various spatial distributions of heat source.

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