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Joule heating is an important mechanism in electronic devices. It must be carefully controlled to avoid the possibility of thermal runaway, which can happen in a fraction of a second. In contrast, there are some applications in which reaching high temperatures in such short times would be desired, such as in biomass gasification systems. In this paper, a transient one-dimensional model based on the energy equation coupled with the charge conservation and voltage equations is used to analyze thermal runaway for various carbonaceous materials ranging from wood, which is an electrical insulator, to biochar, which is a moderate electrical conductor, to graphite which has high electrical conductivity. Numerical results are obtained for the temporal evolution of the temperature and charge distribution, as well as, Joule heating, heat losses, electric field, and voltage. It is found that for higher applied voltages the charges accumulate mostly near the boundaries, and due to the increase of the electrical conductivity with temperature, the dynamics of thermal runaway are observed. In addition, a nondimensional analysis is performed to determine the operating conditions that generate significant Joule heating in relation to heat losses. The dimensionless time, Fo, to reach a prescribed maximum lattice temperature is calculated given a set of bias conditions and dimensions in the form of a nondimensional parameter M2. |
