Wear-Model-Based Analysis of the State of Blast Furnace Hearth

The condition and state of the hearth of the blast furnace is of considerable importance since the life length of the refractories governs the campaign length of the furnace, but it is also of significance as it affects the drainage of iron and slag and the hot metal temperature and composition. The paper analyses the hearth of a blast furnace using a model of the lining wear based on the solution of an inverse heat conduction problem, studying the changes in the lining state throughout the campaign. Different operation states are detected, characterized by smooth and efficient hot metal production and by erratic behavior with large disturbances in the hearth state. During the periods of poor performance, the hearth exhibits a cycling state with stages of excessive skull growth on the unworn refractory, followed by periods of dissolution of the skull and lining erosion. An explanation of the transitions is sought by a stating and solving a force balance for the deadman with the aim to clarify whether it is floating or sitting. A connection between the thermal cycles in the hearth and the hot metal sulfur content is finally demonstrated.

Regularization of the backward stochastic heat conduction problem

In this paper, we study the backward problem for the stochastic parabolic heat equation driven by a Wiener process. We show that the problem is ill-posed by violating the continuous dependence on the input data. In order to restore stability, we apply a filter regularization method which is completely new in the stochastic setting. Convergence rates are established under different a priori assumptions on the sought solution.

An Extended Analytical Solution of the Non-Stationary Heat Conduction Problem in Multi-Track Thick-Walled Products during the Additive Manufacturing Process

An analytical model has been developed for calculating three-dimensional transient temperature fields arising in the direct deposition process to study the thermal behavior of multi-track walls with various configurations. The model allows the calculation of all characteristics of the temperature fields (thermal cycles, cooling rates, temperature gradients) in the wall during the direct deposition process at any time. The solution of the non-stationary heat conduction equation for a moving heat source is used to determine the temperature field in the deposited wall, taking into account heat transfer to the environment. The method considers the size of the wall and the substrate, the change in power from layer to layer, the change in the cladding speed, the interpass dwell time (pause time), and the heat source trajectory. Experiments on the deposition of multi-track block samples are carried out, as a result of which the values of the temperatures are obtained at fixed points. The proposed model makes it possible to reproduce temperature fields at various values of the technological process parameters. It is confirmed by comparisons with experimental thermocouple data. The relative difference in the interlayer temperature does not exceed 15%.

Convergence Analysis of Legendre wavelets in numerical solution of linear weakly singular Volterra integral equation for union of some intervals with application in heat conduction

In this paper we apply the Legendre wavelets basis to solve the linear weakly singular Volterra integral equation of the second kind. The basis is defined on [0,1) , and in this work we extend this interval to [0,n) for some positive integer n. For this aim we solve the problem on [0,1); then we apply the Legendre wavelets on [1,2) and use the lag solution on [0,1) to obtain the solution on [0,2) and continue this procedure. Convergence analysis of Legendre wavelets on [n,n+1), is considered in Section2. We give a convergence analysis for the proposed method, established on compactness of operators. In numerical results we give two sample problems from heat conduction. For this purpose, in Section 6 we give an equivalent theorem between the proposed heat conduction problem and an integral equation. Then we solve the equivalent integral equation by the proposed method on union of some interval and obtain the solution of the heat conduction problem. As Tables and Figures of two and three dimensional plots show, accuracy of the method is reasonable and there is not any propagation of error from lag intervals. The convergence analysis and these sample problems demonstrate the accuracy and applicability of the method.

Legendre spectral collocation technique for fractional inverse heat conduction problem

For fractional inverse heat conduction problem (FIHCP), this paper introduces a numerical study. For the proposed FIHCP, in addition to the unknown function of temperature, the boundary heat fluxes are also unknown. Related to the two independent variables, the proposed scheme uses a fully spectral collocation treatment. Our technique is determined to be more accurate, efficient and practicable. The obtained results confirmed the exponential convergence of the spectral scheme.

Experimental analysis of the evaporation of a thin liquid film deposited on a capillary heated tube: estimation of the local heat transfer coefficient

The aim of this work is to estimate the local heat flux and heat transfer coefficient for the case of evaporation of thin liquid film deposited on capillary heated channel: it plays a fundamental role in the two-phase heat transfer processes inside mini-channels. In the present analysis it is investigated a semi-infinite slug flow (one liquid slug followed by one single vapour bubble) in a heated capillary copper tube. The estimation procedure here adopted is based on the solution of the inverse heat conduction problem within the wall domain adopting, as input data, the temperature field on the external tube wall acquired by means of infrared thermography.