An integral analysis for heat transfer in turbulent incompressible boundary layer flow

The integral approach is utilized in this paper to analyze incompressible turbulent thermal boundary layer flow over a flat plate for nonuniform wall heating. This approach involves the use of inner variables and laws for u+ and T+ that apply to the important wall region as well as to the remainder of the flow field. Predictions developed for Stanton number are found to be in excellent agreement with published experimental data for uniform, step, double-step, and linear wall temperature heating of air. The results of this integral analysis compare favorably with those of the traditional numerical approach. Because of its computational efficiency, this integral approach provides a useful supplementary tool for analyzing turbulent thermal boundary layers.