An investigation is made of a mathematical model of an idealised ablative material of finite thickness, which is mounted horizontally and exposed to a constant, uniform heat flux. The effect of a substrate or sample mounting is also investigated. Numerical and approximate solutions are developed for a perfectly conducting and a perfectly insulating substrate. These two extreme cases represent idealised upper and lower bounds for the mass loss rate of an ablative material mounted on a real substrate. Three ablation regimes (thermally thick, thermally non-thin and thermally thin) are identified and quantified in terms of the dimensionless parameter l/lc, where l is the initial thickness of the sample and lc is a critical thickness defined in terms of the difference in ablation temperature from ambient temperature, incident heat flux and thermal conductivity. The approximate solutions are valid for the thermally thin and non-thin regimes. It is observed in the numerical solutions that the substrate or sample homer has negligible effect on the mass loss rate in the thermally thick regime. However, the sample holder may have a large effect on the mass loss rate for the thermally thin and non-thin regimes. ~) 1997 Elsevier Science Ltd. Bi c h k L l NOTATION Biot number for convection from top surface Specific heat capacity (J kg-lK -1) Convective heat transfer coefficient (W m-2K -1) Thermal conductivity (W m-lK -1) Heat of vaporisation (J kg -~) Initial thickness of solid (m) Critical length for thermally thin behaviour (m) Constant heat flux (W m -2) Dimensionless parameter for radiation losses Location of top surface (m) Temperature (K) Initial temperature (K) Ambient temperature (K) Critical ablation temperature (K) Time (s) Time for top surface to reach ablation temperature (s) Dimensionless distance Distance from initial location of top surface (m) Greek symbols a Thermal diffusivity (m -2 s -~) /3 Ratio of ambient temperature to temperature range 3' Ratio ~/e Dimensionless thickness of solid e Ratio of sensible heat to heat of vaporisation parameter) eR Emissivity 0 Dimensionless temperature A Dimensionless constant heat flux p Density (kg m -a) o" Stefan-Boltzmann constant (W m-: K -4) ~-Dimensionless time Subscripts t, x, y, ~" Derivatives with respect to t etc.