Extension of a modified integral method to boundary conditions of prescribed surface heat flux

The paper presents a rationale whereby the double integral method (DIM) is applicable to problems in which the boundary derivative is a given known quantity. Attention is given to the application of the DIM to some representative problems, viz. a simple steady-state forced convection problem, an aerodynamic heating problem, and a transient forced convection problem. Also, one of the basic concepts of the DIM is extended to evaluate derivatives within the domain itself when they occur in the governing DIM equation.