An exact integral method to evaluate wall heat flux in spatially developing two-dimensional wall-bounded flows

An integral method to evaluate wall heat flux in turbulent wall-bounded flows is presented. The method is mathematically exact and has the advantage of having no explicit streamwise gradient terms. Importantly, the mathematical exactness of the method allows for a direct measurement of the wall heat flux without any a priori assumptions regarding the flow or temperature field or invoking flow transport analogies. It is useful in cases when measurements at multiple streamwise locations are not available or feasible, for flows with ill-defined outer boundary conditions, or when the measurement grid does not extend over the whole boundary layer thickness. The method is applied to existing datasets for both forced and natural convection boundary layer flow for which independent estimates of wall heat flux were known, and the different results compare favorably. Complications owing to experimental limitations and measurement error in determining wall heat flux from the proposed method are presented, and mitigating strategies are described.