This thesis examines two important physical phenomena that occur when solid fuels are exposed to external radiative heating: (1) the pyrolysis process in reaching ignition conditions and (2) the natural convection around one or more radiatively heated fuel samples. A vegetation fire (bushfire, wildfire, or forest fire) preheating the vegetation which is in its path is a particular example which occurs in nature. However there are many more applications where modelling the pyrolysis process and/or the natural convection is of practical use. For the pyrolysis phenomena, a one-dimensional time dependent pyrolysis model is proposed. The mathematical model is solved numerically and results are used to analyse the influence of the size of a wood-based fuel sample, the heating rate it is exposed to, and its initial moisture content in the process of the sample reaching the conditions where it can produce enough pyrolysate vapour to support a flame (flash point). In many pyrolysis models in the open literature it is assumed that the fuel samples are dry. In the present study it is found that the initial moisture content has a marked effect for a fuel sample reaching its flash point. For the convection phenomena, a two-dimensional steady model, which explores the natural convection around one or more solid fuels, is also presented. The flame front is represented by a radiating panel. This means that the solid fuels receive a non-uniform heating rate depending on their geometry and location in relation to the panel. Changes in temperature and velocity profiles are monitored for varying heating rates and sample sizes (or, equivalently, the Rayleigh number Ra). Additionally, in the case of multiple fuel samples, changes in the distance between the fuels is also taken into account. For multiple fuels in arbitrary locations it is possible that one sample will block some of the radiation from the panel from reaching another sample. This means that the fuel sample will receive a reduced heating rate. This reduction in heating is also incorporated in the natural convection model. Both the pyrolysis and natural convection models are solved numerically using the finite element software package COMSOL Multiphysics. A comparison of COMSOL is performed with benchmark solutions provided by the open literature. A good agreement in the numerical results is observed.