Heated falling films

We present new insights and results for the problem of a film falling down a heated wall: (i) treatment of a mixed heat flux boundary condition on the substrate; (ii) development of a long-wave theory for large Peclet numbers; (iii) refined treatment of the energy equation based on a high-order Galerkin projection in terms of polynomial test functions which satisfy all boundary conditions; (iv) time-dependent computations for the free-surface height and interfacial temperature; (v) numerical solution of the full energy equation; (vi) demonstration of the existence of a thermal boundary layer at the front stagnation point of a solitary pulse; (vii) development of models that prevent negative temperatures and are in good agreement with the numerical solution of the full energy equation.