The temperature rise at the surface of a liquid layer subject to a concentrated heat source placed above the layer

A focused heat flux on the free surface of a liquid layer gives rise to combined thermocapillary and thermogravitational flow within the layer that dictates the magnitude of the temperature rise achieved at the surface. In the case of a high-boiling-point flammable liquid layer, this temperature rise determines the ignitability of the layer. An unconventional solution technique, which transforms the combined natural convection problem into a nonlinear conduction like problem, is introduced to derive a convenient relationship between the heater power and size and the maximum liquid surface temperature. This expression depends on the layer thickness and fluid properties, but does not contain any adjustable (empirical) parameters. Experimental data are reported for dodecane layers between 2 and 7 mm thick for heat fluxes up to 63 kW m(-2). The data are well correlated by our analytical result.