Use of inverse modelling techniques for the estimation of heat transfer coefficients to fluids in cylindrical conduits

We propose a method for the estimation of the overall heat transfer coefficient to/from a fluid in a cylindrical pipe at high Peclet numbers from/to a medium with unknown temperature profile in the axial direction. The method uses an analytical solution of the heat equation in cylindrical coordinates subject to a Robin boundary condition and a parametrised, piecewise linear approximation of the external temperature profile. The velocity profiles of both viscous and turbulent flows are considered and compact solutions of the temperature profile of the fluid are evaluated in both cases as functions of the heat transfer coefficient and of the unknown external temperature profile. It is shown that these solutions provide an efficient method for the estimation of the heat transfer coefficient from fluid temperature data based on separable least squares. The overall procedure is illustrated by a numerical example using simulated data.