A direct method to calculate the heat transfer coefficient of steady similar boundary layer flows induced by continuous moving surfaces

The heat transfer coefficient mentioned in the title is calculated in this paper without to know the solution of the corresponding boundary value problem (neither in an explicit nor in an implicit form). This “direct method” makes use of a slightly modified form of the Merkin transformation which reverses the role of the dimensionless stream function f from that of an “old” dependent variable to one of a “new” independent variable and then gives the formal solution for the velocity and temperature profiles as a power series of 1−f/f∞ (where f∞ denotes the dimensionless entrainment velocity). The series solutions yield for f=0 explicit analytical expressions for the skin friction and the heat transfer coefficient of the flow. Owing to a formal mathematical analogy, the results also apply to the free convection boundary layer flows from vertical surfaces adjacent to fluid saturated porous media.