An inverse method to estimate stem surface heat flux in wildland fires

Abstract

Models of wildland fire-induced stem heating and tissue necrosis require accurate estimates of inward heat flux at the bark surface. Thermocouple probes or heat flux sensors placed at a stem surface do not mimic the thermal response of tree bark to flames. We show that data from thin thermocouple probes inserted just below the bark can be used, by means of a one-dimensional inverse heat conduction method, to estimate net heat flux (inward minus outward heat flow) and temperature at the bark surface. Further, we estimate outward heat flux from emitted water vapor and bark surface re-radiation. Estimates of surface heat flux and temperature made by the inverse method confirm that surface-mounted heat flux sensors and thermocouple probes overestimate surface heat flux and temperature. As a demonstration of the utility of the method, we characterized uneven stem heating, due to leeward, flame-driven vortices, in a prescribed surface fire. Advantages of using an inverse method include lower cost, ease of multipoint measurements and negligible effects on the target stem. Drawbacks of the simple inverse model described herein include inability to estimate heat flux in very moist bark and uncertainty in estimates when extensive charring occurs.