A Numerical Solution of the Inverse Problem for Thermoforming Processes Using Finite Element Analysis

A nonstationary formulation of critical conditions for thermal explosion in the Thomas problem (asymmetric self-ignition) and the classical Frank-Kamenetskii problem (symmetric self-ignition) are numerically studied. By the example of the Thomas problem, it is shown that the thermal explosion limit depends on the form of the initial spatial temperature distribution of the medium. For the Frank-Kamenetskii problem, the effect of the initial spatial temperature distribution and the initial overheating of the reactant on the critical value of the Frank-Kamenetskii number is studied. The particular initial spatial temperature distribution is determined; the investigation of its evolution allows one to make a conservative estimate of the thermal explosion limit. The limitation of the classical criterion for thermal explosion is shown, and the limits of applicability of the stationary theory are numerically determined from the initial overheating. For engineering calculations, an analytical formula for conservatively estimating the critical conditions for thermal explosion as a function of the initial reactant overheating is obtained.

An inverse method for estimation of the initial temperature profile and its evolution in polymer processing

Homogeneous versus heterogeneous lunar mantle: Constraints from secondary crust production

Transient heating of a semitransparent spherical body

The identification of thermophysical properties of materials in dynamic experiments can be conveniently performed by the inverse solution of the associated heat conduction problem (IHCP). The inverse technique demands the knowledge of the initial temperature distribution within the material. As only a limited number of temperature sensors (or no sensor at all) are arranged inside the test specimen, the knowledge of the initial temperature distribution is affected by some uncertainty. This uncertainty, together with other possible sources of bias in the experimental procedure, will propagate in the estimation process and the accuracy of the reconstructed thermophysical property values could deteriorate. In this work the effect on the estimated thermophysical properties due to errors in the initial temperature distribution is investigated along with a practical method to quantify this effect. Furthermore, a technique for compensating this kind of bias is proposed. The method consists in including the initial temperature distribution among the unknown functions to be estimated. In this way the effect of the initial bias is removed and the accuracy of the identified thermophysical property values is highly improved.

The conventional boundary element method (BEM) needs a domain integral in heat conduction analysis with heat generation or initial temperature distribution. This paper shows that the three-dimensional heat conduction problem can be solved effectively by using the triple-reciprocity boundary element method without internal cells. In this method, the distribution of heat generation and initial temperature are interpolated by using integral equations. In this method, time-dependant fundamental solutions are used. A new computer program was developed and applied to solving several problems.

Thermal and geometrically non-linear stress analyses of an adhesively bonded composite tee joint

Diffusion-Controlled Bubble Growth

Tailored Forming provides an innovative process chain for manufacturing hybrid components. This study focuses on a process design of a hybrid bearing bushing consisting of aluminium alloy EN-AW-6082 and Titan-Grade-2 or -5 using numerical simulation. The manufacturing process used was a closed die forging process with pre-joined hybrid semi-finished products in a radial arrangement. Due to the simultaneous forming of two different materials, a fundamental knowledge about the flow properties of each material is necessary to achieve a stable forming process. For this, a material characterisation by means of uniaxial compression tests was carried out. The aim was to identify the temperature range in which the flow properties of aluminium and titanium converge. These results were used in a numerical study of the forming process of a hybrid bearing bushing. In a pre-step heating simulation, a suitable inhomogeneous temperature distribution of the hybrid semi-finished product was calculated to achieve the desired temperature field. Subsequently, a numerical study of a closed-die forging process for the manufacture of a hybrid bearing bushing was carried out. A comprehensive stress analysis was carried out to identify a suitable initial temperature distribution to avoid the occurrence of high tangential stresses, which can lead to cracks during the forming process. The results of the presented numerical study will be used in further experimental investigations to improve the presented forming process. KeywordsTailored formingFinite-element methodHybrid semi-finished product

Real-time reconstruction of the time-dependent heat flux and temperature distribution in participating media by using the Kalman filtering technique

Method for estimating change over time of the amount of heat stored in a semi-infinite phase-change material with a broad phase-change-temperature range

Regime classification of an exothermic reaction with nonuniform initial conditions

Liquid-phase temperature in the SpraySyn flame measured by two-color laser-induced fluorescence thermometry and simulated by LES

Analytic model for transient heat exchanger response

We investigate scavenging of gaseous pollutants in the atmosphere under the combined influence of rain and varying temperature distribution that affects the rate of soluble gas scavenging. We employ a one-dimensional model of precipitation scavenging of gaseous pollutants having arbitrary solubility that is valid for small gradients and for non-uniform initial vertical distributions of temperature and soluble trace gases concentration in the atmosphere. It is showed that transient altitudinal distributions of temperature and concentration under the influence of rain are determined by linear wave equations that describe propagation of temperature and scavenging wave fronts. Scavenging coefficient and the rates of precipitation scavenging are calculated for wet removal of methanol (\({\text{CH}}_{3} {\text{OH}}\)) using measured initial distribution of methanol and temperature in the atmosphere. Theoretical predictions of the dependence of the magnitude of the scavenging coefficient on rain intensity for tritium oxide and sulfur dioxide are in good agreement with the available atmospheric measurements.