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.
A novel encapsulated deep eutectic solvent (DES) was introduced for biodiesel production via a two-step process. The DES was encapsulated in medical capsules and were used to reduce the free fatty acid (FFA) content of acidic crude palm oil (ACPO) to the minimum acceptable level (< 1%). The DES was synthesized from methyltriphenylphosphonium bromide (MTPB) and p-toluenesulfonic acid (PTSA). The effects pertaining to different operating conditions such as capsule dosage, reaction time, molar ratio, and reaction temperature were optimized. The FFA content of ACPO was reduced from existing 9.61% to less than 1% under optimum operating conditions. This indicated that encapsulated MTPB-DES performed high catalytic activity in FFA esterificatio
... Show MoreThe aim of the research is to know the level of time management application and its impact on the performance of the job, a survey search in the general company for communication and information technology and provide recommendations that help employees to optimize the use of time and improve performance, which is an important element in controlling the various functions of the company. In order to achieve the objectives of the research, the questionnaire was based on two main variables and distributed to a random sample of (44) employees in the company out of (308) employees, thus the proportion of the sample (14%). After collecting the samples from the sample, there are (6) incomplete forms that have been retri
... Show MoreCollapsible soil has a metastable structure that experiences a large reduction in volume or collapse when wetting. The characteristics of collapsible soil contribute to different problems for infrastructures constructed on its such as cracks and excessive settlement found in buildings, railways channels, bridges, and roads. This paper aims to provide an art review on collapse soil behavior all over the world, type of collapse soil, identification of collapse potential, and factors that affect collapsibility soil. As urban grow in several parts of the world, the collapsible soil will have more get to the water. As a result, there will be an increase in the number of wetting collapse problems, so it's very important to com
... Show MoreRecovery of time-dependent thermal conductivity has been numerically investigated. The problem of identification in one-dimensional heat equation from Cauchy boundary data and mass/energy specification has been considered. The inverse problem recasted as a nonlinear optimization problem. The regularized least-squares functional is minimised through lsqnonlin routine from MATLAB to retrieve the unknown coefficient. We investigate the stability and accuracy for numerical solution for two examples with various noise level and regularization parameter.
The coefficient of charge transfer at heterogeneous devices of Au metal with a well-known dyeis investigations using quantum model.Four different solvent are used to estimation the effective transition energy. The potential barrier at interface of Au and dye has been determined using effective transition energy and difference between the Fermi energy of Au metal and ionization energy of dye. A possible transfer mechanism cross the potential barrier dyeand coupling strength interaction between the electronic levels in systems of Au and is discussed.Differentdata of effective transition energy and potential barrier calculations suggest that solvent is more suitable to binds Au with dye.
The aim of this research is to calculate mass transfer coefficient, kd, during cathodic protection of low carbon steel in neutral seawater (3.5% W/V NaCl in distilled water with pH = 7). Two types of cathodic protection were used:
First: Sacrificial anode cathodic protection (SACP) were a pipeline of steel carrying seawater using zinc as a sacrificial anode and with variable temperatures ranged (0 – 45oC) and volumetric flow rate ranged (5 – 900 lit/hr). It was found that the kd increases with increasing temperature and volumetric flow rate of seawater, where kd ranged (0.24×10-6 – 41.6×10-6 m/s).
Second: Impressed current cathodic pr
... Show MoreThe purpose of this paper to discriminate between the poetic poems of each poet depending on the characteristics and attribute of the Arabic letters. Four categories used for the Arabic letters, letters frequency have been included in a multidimensional contingency table and each dimension has two or more levels, then contingency coefficient calculated.
The paper sample consists of six poets from different historical ages, and each poet has five poems. The method was programmed using the MATLAB program, the efficiency of the proposed method is 53% for the whole sample, and between 90% and 95% for each poet's poems.
Correlation and path coefficient analysis were worked out for ten morphological traits in 30 three-way crosses of maize. Phenotypic and genotypic correlation analysis indicated that ear length; row numbers per ear, grain numbers per row, leaf area and leaves numbers had a positive significant correlation with grain yield per plant. Further partitioning of correlation coefficients into direct and indirect effects showed that traits days to silking, row numbers per row and leaves numbers had a positive direct effect on grain yield per plant. The traits ear length, grain numbers per row and leaf area had a maximum total effect on grain yield. Furthermore, PCA analysis has gave interested