In this paper the description of the simplest variant of conservative averaging method for partial differential (or integro-differential) equations in cylinder type domain is given. Different types of boundary conditions (both linear and non-linear) are considered. As application of the method the process of intensive steel quenching as the time inverse ill-posed problem for the hyperbolic heat...

This paper demonstrates the deterministic errors in thermocouple measurements, or bias, through numerical simulation and illustrates the impact of these erroneous measurements on inverse heat conduction problem solutions. The case of molten metal solidifying through cooling in a sand mold is considered. Artificial data for the sand surface temperature and at two different locations below the sa...

An adjoint based functional optimization technique in conjunction with the spectral stochastic finite element method is proposed for the solution of an inverse heat conduction problem in the presence of uncertainties in material data, process conditions and measurement noise. The ill-posed stochastic inverse problem is restated as a conditionally well-posed L2 optimization problem. The gradient...

In the present work, an inverse analysis of combined radiation and laminar forced convection heat transfer in a two-dimensional channel with variable cross sections is performed. The conjugate gradient method is used to find the temperature distribution over the heater surface to satisfy the prescribed temperature and heat flux distributions over the design surface. The fluid is considered to b...

A Bayesian inference approach is presented for the solution of the inverse heat conduction problem. The posterior probability density function (PPDF) of the boundary heat flux is computed given temperature measurements within a conducting solid. Uncertainty in temperature measurements is modeled as stationary zero-mean white noise. The inverse solution is obtained by computing the expectation o...

The local time-dependent surface heat transfer coefficients for plate finned-tube heat exchangers are estimated in a three-dimensional inverse heat conduction problem. The inverse algorithm utilizing the Steepest Descent Method (SDM) and a general purpose commercial code CFX4.4 is applied successfully in this study in accordance with the simulated measured temperature distributions on the fin s...

In this paper, a boundary integral method is used to solve an inverse linear heat conduction problem in two-dimensional bounded domain. An inverse problem of measuring the heat flux from partial (on part of the boundary) dynamic boundary measurements is considered. An algorithm is given by using the fundamental solution.

Mathematical model of direct and inverse problems is developed for the flat plate probe which is subjected to timedependent heat flux at one end, while the other end is kept insulated. The direct solution, which is concerned with determination of the temperature distribution in the probe, is developed using an approach based on the method of variation of parameters. The direct solution is used ...