De-icing by slot injection

We consider the removal of ice from a plate in a cold cross flow by injection of hot fluid through a slot in the plate. De-icing of this sort is required in a number of diverse industrial scenarios, and is particularly relevant to the aviation industry, where the presence of ice on aircraft wings is a major safety hazard. Thin aerofoil theory is used to determine the now above the injected fluid layer, and this is coupled to flow and energy equations in the injected layer and the ice. The key non-dimensional parameters and ratios in the problem are identified. The result is a nonlinear singular integro-differential equation which is coupled to a convection/diffusion equation and a Stefan condition. Some special cases are discussed and some asymptotic limits are identified. The problem is then solved numerically, and results for a number of different cases are presented.