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.
This study found that one of the constructive, necessary, beneficial, most effective, and cost-effective ways to meet the great challenge of rising energy prices is to develop and improve energy quality and efficiency. The process of improving the quality of energy and its means has been carried out in many buildings and around the world. It was found that the thermal insulation process in buildings and educational facilities has become the primary tool for improving energy efficiency, enabling us to improve and develop the internal thermal environment quality processes recommended for users (student - teacher). An excellent and essential empirical study has been conducted to calculate the fundamental values of the
... Show MoreThis research is based on monitoring the local and environmental technologies in the design of the temporary hotel units (nomadic tents) in the desert in the south of Jordan in order to air condition them in summer and winter, maintaining the Jordanian identity, that they are presented with the form and technologies of the age in order to get to the universality.
The research adopted the descriptive analytical method and the researcher conducted the analysis of SWOT specified for the analysis of the positive and negative aspects in the design of the temporary hotel units and comparing them with the case studies available in the chosen research area "the Jordanian golden triangle", through the elements of the case under study. The res
The melting duration in the photovoltaic/phase-change material (PV/PCM) system is a crucial parameter for thermal energy management such that its improvement can realize better energy management in respect to thermal storage capabilities, thermal conditions, and the lifespan of PV modules. An innovative and efficient technique for improving the melting duration is the inclusion of an exterior metal foam layer in the PV/PCM system. For detailed investigations of utilizing different metal foam configurations in terms of their convective heat transfer coefficients, the present paper proposes a newly developed mathematical model for the PV/PCM–metal foam assembly that can readily be implemented with a wide range of operating condition
... Show MoreLet G be a graph with p vertices and q edges and be an injective function, where k is a positive integer. If the induced edge labeling defined by for each is a bijection, then the labeling f is called an odd Fibonacci edge irregular labeling of G. A graph which admits an odd Fibonacci edge irregular labeling is called an odd Fibonacci edge irregular graph. The odd Fibonacci edge irregularity strength ofes(G) is the minimum k for which G admits an odd Fibonacci edge irregular labeling. In this paper, the odd Fibonacci edge irregularity strength for some subdivision graphs and graphs obtained from vertex identification is determined.
The shortage in surface water quantities led to a shift in dependence on the groundwater as an alternative water source in southern parts of Iraq. The groundwater is decreasing in quantity and water quality is degrading due to different factors. Therefore, it is important to assess the groundwater quality of the Missan Governorate of the country by analyzing the physicochemical parameters and distinguishing the probable sources of contaminants in the area. The present study used water quality diagrams and statistical methods such as factor analysis and agglomerative cluster analysis to determine the sources of chemical ions in the forty-four groundwater samples collected from wells in the study area. In addition, the Water Quality Index (WQ
... Show MoreThe guava plant, Psidium guajava L., serves as proof of the abundant donations of nature, providing a delicious guava fruit; this plant is rich in groups of medicinal and nutritional benefits. Guava belonging to the Myrtaceae family, many previous studies reported many phytochemical constituents in its leaves that have many pharmacological activities and medicinal properties; this study focuses on the isolation, structural elucidation and calculation concentration of flavonoids, assessment of the cytotoxic activityof hyperin from Psidium guajava leaves newly cultivated in Iraq. The isolation process involved the use of thin-layer chromatography (TLC) and preparative high-performance liquid chromatography (PHPLC) and structural eluci
... Show MoreSchiff bases are versatile compounds synthesized from the condensation of primary amino compounds with aldehydes or ketones. The high thermal of many Schiff base and their complexes were useful attributes for their application as catalysts in reactions involving at high temperatures. This thermal behavior of Schiff bases and their complexes was evaluated by TGA/DTG and DTA curves with 10 mass losses related to dehydration and decomposition. This review summarizes the developments in the last decade for thermal analysis of Schiff bases. Therefore, synthesis of Schiff bases and their complexes are reviewe
A numerical study of the two-dimensional steady free convection flow in an inclined annulus between two concentric square cavities filled with a porous medium is presented in this paper for the case when the side outer walls are kept with differentially heated temperature while the horizontal outer walls and the inner walls are insulated. The heated wall is assumed to have spatial sinusoidal temperature variation about a constant mean value. The Darcy model is used and the fluid is assumed to be a standard Boussinesq fluid. For the Cartesian coordinate system, the governing equations which were used in stream function form are discretized by using the finite difference method with successive under – relaxation method (SUR) and are solv
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