The ignition of woody wildland fuel modeled as a one-dimensional slab subject to various modes of heating was investigated using a general pyrolysis code, Gpyro. The heating mode was varied by applying different convective and/or radiative, time-dependent heat flux boundary conditions on one end of the slab while keeping the other end insulated. Dry wood properties were used for the slab. Initially, wood was treated as chemically inactive and following this it is presumed to decompose via a single-stage kinetic model involving two solid phase species coupled with one gas phase species. This single-step model approximation for wood degradation was validated with experimental results. Critical time was defined as the time when the temperature of the heated side reached a critical value at which the ignition was assumed to take place. The chemically inactive assumption led to a significant underprediction of the critical time for a broad range of convective heat source temperatures at a fixed Biot number. When thermal decomposition was included, the critical time was quite sensitive to radiative and convective source temperatures and the Biot number during combined mode of heating. Time evolution of the mass loss and charring rates was weakly influenced by convective heating during the combined mode of heating. The variation of Biot number had little influence on this evolution when a combined mode of heating was applied.