An Iterative Algorithm for the Estimation of Thermal Boundary Conditions Varying in Both Time and Space

Abstract

The presented survey of the up-to-date state of knowledge indicates that despite the great number of works devoted to the issue in question, there is no simple method that allows the use of commercial programs for the identification of the transient thermal state in elements with a simple or complex shape. This paper presents an inverse method developed to estimate the convective heat transfer coefficient varying both in time and space on a vertical plate during its cooling. Despite the smaller number of measurement points and larger disturbance of measured temperatures compared to the data presented in the available literature, comparable results are obtained. The developed iterative algorithm is also applied to estimate the time- and space-dependent heat flux and the convective heat transfer coefficient in the steam boiler membrane waterwall. The analysed component has the form of the non-simply connected and complex shape domain Ω. Temperature-dependent thermophysical properties are used. Calculations are performed for the unknown heat flux or heat transfer coefficient distribution on the domain boundary based on measured temperature transients disturbed with a random error of 0.5 °C. To reduce oscillations, the number of future time steps of NF = 20 is selected. The number of iterations in each time step ranges between 1 and 8. The estimated boundary conditions are close to the exact values. In this work, the ANSYS software using the FEM is applied.