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.
The 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 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 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
... Show MoreIn this paper, a least squares group finite element method for solving coupled Burgers' problem in 2-D is presented. A fully discrete formulation of least squares finite element method is analyzed, the backward-Euler scheme for the time variable is considered, the discretization with respect to space variable is applied as biquadratic quadrangular elements with nine nodes for each element. The continuity, ellipticity, stability condition and error estimate of least squares group finite element method are proved. The theoretical results show that the error estimate of this method is . The numerical results are compared with the exact solution and other available literature when the convection-dominated case to illustrate the effic
... Show MoreWitnessing the global arena many changes in the political, economic, social, scientific and technological have left their mark on the world as a whole, these changes require necessarily Advancement of the profession of auditing, and improve their performance, especially after the mixer skepticism the health of approach and the method followed by a check in the major audit firms global view as for the external audit of an active role in providing services to members of the community in various sectors, were to be provide these services to the highest level of quality.To ensure the quality of the audit process to be a proper planning is based on a scientific basis to be the substrate a strong underlying different audit works, and if planni
... Show MoreTrue random number generators are essential components for communications to be conconfidentially secured. In this paper a new method is proposed to generate random sequences of numbers based on the difference of the arrival times of photons detected in a coincidence window between two single-photon counting modules
Solvents are important components in the pharmaceutical and chemical industries, and they are increasingly being used in catalytic reactions. Solvents have a significant influence on the kinetics and thermodynamics of reactions, and they can significantly change product selectivity. Solvents can influence product selectivity, conversion rates, and reaction rates. However, solvents have received a lot of attention in the field of green chemistry. This is due to the large amount of solvent that is frequently used in a process or formulation, particularly during the purification steps. However, neither the solvent nor the active ingredient in a formulation is directly responsible for the reaction product's composition. Because these ch
... Show MoreThe annual performance of a hybrid system of a flat plate photovoltaic thermal system and a solar thermal collector (PVT/ST) is numerically analyzed from the energy, exergy, and environmental (CO2 reduction) viewpoints. This system can produce electricity and thermal power simultaneously, with higher thermal power and exergy compared to conventional photovoltaic thermal systems. For this purpose, a 3D transient numerical model is developed for investigating the system's performance in four main steps: (1) investigating the effects of the mass flow rate of the working fluid (20 to 50 kg/h) on the temperature behavior and thermodynamic performance of the system, (2) studying the impacts of using glass covers on the different parts of the s
... Show MoreThe Experiment was carried out to determine the level vibration transfer in three axes Horizontal X, Lateral Y and Vertical Z direction to seat driver tractor, Vector sum of vibration and Daily Vibration Exposure (8 hours) in seat driver tractor, and vibration in steering wheel tractor, Heart Rate, Systolic and Diastolic blood pressure and temperature were measure to all Drivers before and after used Chisel plow in operation tillage. Statistical analysis system was used, Split-Split Plot Design under Randomized Complete Block Design, Three factors were used in this experiment included Two types of Soil Moist and Dry soil which represented main plot, Three Velocity Tractor was second factor included 1.6,3.5 and 5.4 km/hr and Three Drivers Tr
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