Pergamon Int. Comm. Heat Mass Transfer, Vol.27, No. 7, pp. 945-954, 2000 Copyright© 2000Elsevier Science Ltd Printedin the USA.All rightsreserved 0735-1933/00IS-see frontmatter PIh S0735-1933(00)00174-3 ESTIMATION OF UNKNOWN WALL HEAT FLUX IN TURBULENT CIRCULAR PIPE FLOW Jian Su and Adriane B. Lopes Nuclear Engineering Department, COPPE/UFRJ CP 68509, Rio de Janeiro, 21945-970, Brazil sujian~lmn.con.ufrj.br AntSnio J. Silva Neto Instituto Polit~cnico, Universidade do Estado do Rio de Janeiro CP 97282, Nova Friburgo, Rio de Janeiro, 28601-970, Brazil Nuclear Engineering Department, COPPE/UFRJ ajsneto@iprj.uerj.br (Communicated by J.P. Hartnett and W.J. Minkowycz) ABSTRACT 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-Marquaxdt algorithm. The effects of sensor number and position are examined. © 2000ElsevierScience Ltd Introduction A wide variety of inverse heat conduction problems have been solved in the last two decades for the estimation of initial or boundary conditions, physical properties, geometric parameters, or heat source intensities. Beck et al. [1], Hensel [2], and Ozisik and Orlande [3], among others, present some of the methods developed for the solution of such problems. Despite many potential applications, inverse convection problems have only received some attention recently. Moutsoglou [4] apparently was the first to address an inverse convection problem that has utilized a sequential function specification algorithm for the estimation of the asymmetric heat flux in mixed convec- tion in a vertical channel. The same author [5] has also applied the whole domain regularization technique in a similar forced convection problem. Raghunath [6] has determined the inlet tern- 945