Estimation of unknown wall heat flux in turbulent circular pipe flow

An inverse heat convection problem is solved for the estimation of a nonuniform wall heat flux in a thermally developing, hydrodynamically developed turbulent flow in a circular pipe based on temperature measurements obtained at several different locations in the stream. The direct problem of turbulent forced convection is solved with a finite difference method with appropriate algebraic turbulence modelling. The unknown wall heat flux is represented by a one-dimensional finite element interpolation. Nodal values at several chosen points are determined as unknown parameters by the Levenberg-Marquardt algorithm. The effects of sensor number and position are examined.