This paper is concerned with finding solutions to free-boundary inverse coefficient problems. Mathematically, we handle a one-dimensional non-homogeneous heat equation subject to initial and boundary conditions as well as non-localized integral observations of zeroth and first-order heat momentum. The direct problem is solved for the temperature distribution and the non-localized integral measurements using the Crank–Nicolson finite difference method. The inverse problem is solved by simultaneously finding the temperature distribution, the time-dependent free-boundary function indicating the location of the moving interface, and the time-wise thermal diffusivity or advection velocities. We reformulate the inverse problem as a non-linear optimization problem and use the lsqnonlin non-linear least-square solver from the MATLAB optimization toolbox. Through examples and discussions, we determine the optimal values of the regulation parameters to ensure accurate, convergent, and stable reconstructions. The direct problem is well-posed, and the Crank–Nicolson method provides accurate solutions with relative errors below 0.006% when the discretization elements are M=N=80. The accuracy of the forward solutions helps to obtain sensible solutions for the inverse problem. Although the inverse problem is ill-posed, we determine the optimal regularization parameter values to obtain satisfactory solutions. We also investigate the existence of inverse solutions to the considered problems and verify their uniqueness based on established definitions and theorems.
Many additives are used to improve the performance of cables in terms of increasing their flame retardancy, thermal stability, thermal conductivity, and other characteristics. Unfortunately, most of these additives contain heavy metals. Therefore, the main objective of this study is to introduce a material representing a new generation of environmentally friendly heavy metal-free stabilizers for cable grade poly(vinyl chloride) that can compete with traditional materials in terms of performance and distinctive properties. This unique additive is Oxydtron, a synthetic silicate or simply nanocement. The tests performed are rheological properties represented by a capillary rheometry analysis, limiting o
In the oil industry, the processing of vacuum residue has an important economic and environmental benefit. This work aims to produce industrial petroleum coke with light fuel fractions (gasoline, kerosene , gas oil) as the main product and de asphalted oil (DAO) as a side production from treatment secondary product matter of vacuum residue. Vacuum residue was produced from the bottom of vacuum distillation unit of the crude oil. Experimentally, the study investigated the effect of the thermal conversion process on (vacuum residue) as a raw material at temperature reaches to 500 °C, pressure 20 atm. and residence time for about 3 hours. The first step of this treatment is constructing a carbon steel batch re
... Show MoreThe purpose of this paper is to present an approach to compute accurately the distributions of the frictional heat generated, contact pressure and thermal stresses at any instant during the sliding period (heating phase) of the single-disc friction clutch system works in the dry condition and the complex interaction among them.
Numerical work was achieved using the developed elastic and thermal finite element models (axisymmetric models) to simulate the engagement of the single-disc friction clutch system.
The one-dimensional, spherical coordinate, non-linear partial differential equation of transient heat conduction through a hollow spherical thermal insulation material of a thermal conductivity temperature dependent property proposed by an available empirical function is solved analytically using Kirchhoff’s transformation. It is assumed that this insulating material is initially at a uniform temperature. Then, it is suddenly subjected at its inner radius with a step change in temperature. Four thermal insulation materials were selected. An identical analytical solution was achieved when comparing the results of temperature distribution with available analytical solution for the same four case studies that assume a constant thermal con
... Show MoreThe one-dimensional, cylindrical coordinate, non-linear partial differential equation of transient heat conduction through a hollow cylindrical thermal insulation material of a thermal conductivity temperature dependent property proposed by an available empirical
function is solved analytically using Kirchhoff’s transformation. It is assumed that this insulating material is initially at a uniform temperature. Then, it is suddenly subjected at its inner radius with a step change in temperature. Four thermal insulation materials were selected. An identical analytical solution was achieved when comparing the results of temperature distribution with available analytical solution for the same four case studies that assume a constant the
The purpose of this research is to demonstrate the effectiveness of a program to address the problem of mixing similar letters in the Arabic language for students in the second grade of primary and to achieve the goal of the research. The researcher followed the experimental method to suit the nature of this research and found that there are statistically significant differences between the tribal and remote tests, The effectiveness of the proposed educational program. At the end of the research, the researcher recommends several recommendations, the most important of which are: 1 - Training students to correct pronunciation of the outlets, especially in the first three stages of primary education (primary) and the use of direct training
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