On determining mean wall heat flux in turbulent thermal boundary layers

Reliable evaluation of wall heat flux in turbulent flows is of both fundamental and practical importance. In this study, we propose a new explicit integral method for predicting the mean wall heat flux in a spatially developing zero-pressure-gradient turbulent thermal boundary layer. The approach depends only on the wall-normal distributions of mean temperature and turbulent heat flux within the logarithmic layer and the lower outer region, substantially alleviating the dependence on near-wall data. This feature makes the method especially suitable in situations where measurements close to the wall are either inaccessible or contaminated by considerable uncertainty. Numerical and experimental datasets covering a range of Reynolds and Prandtl numbers are employed to evaluate the predictive capability of the approach, showing that the predicted wall heat flux agrees well with the reference values, typically within approximately ± 4 % . A general relation for wall heat flux is further derived by performing an n -fold repeated integration of the Reynolds-averaged energy equation, and the effect of the number of repeated integrations on the predictive accuracy of the method is investigated. Results indicate that the integral relation obtained from a tenfold integration typically yields more accurate wall heat flux predictions than that from a threefold integration, whereas the relation based on a twofold integration exhibits the worst performance.