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.
Recovery 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 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.
This paper presents an application of a Higher Order Shear Deformation Theory (HOST 12) to problem
of free vibration of simply supported symmetric and antisymmetric angle-ply composite laminated plates.
The theoretical model HOST12 presented incorporates laminate deformations which account for the effects
of transverse shear deformation, transverse normal strain/stress and a nonlinear variation of in-plane
displacements with respect to the thickness coordinate – thus modeling the warping of transverse crosssections more accurately and eliminating the need for shear correction coefficients. Solutions are obtained in
closed-form using Navier’s technique by solving the eigenvalue equation. Plates with varying number of
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 purposes of this study are to measure masculine's identification among secondary school students, and to examine the significant differences among secondary school students in respect of students age (16-18) year. The researcher has prepared a questionnaire comprised (25) item to measure masculine identification among students: this scale was applied on (100) student who were selected as a sample from four different school at al-rusafa side in Baghdad. The scale then modified to (23) item to be more consistent. The results revealed that there were no significant differences among students based on the variable of age, and the mean of masculine identification showed a high level than the hypothesized mean.
In this research study the effect of fish on the properties optical films thickness 1200-1800 and calculated energy gap Basra direct transport permitted and forbidden to membranes and urged decreasing values ??of Optical Energy Gap increase fish included accounts optical also calculate the constants visual as factories winding down and the refractive index and reflectivity membranes also by real part and imaginarythe dielectric constant
Collapsible 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
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In this research we built a mathematical model of the transportation problem for data of General Company for Grain Under the environment of variable demand ,and situations of incapableness to determining the supply required quantities as a result of economic and commercial reasons, also restrict flow of grain amounts was specified to a known level by the decision makers to ensure that the stock of reserves for emergency situations that face the company from decrease, or non-arrival of the amount of grain to silos , also it took the capabilities of the tanker into consideration and the grain have been restricted to avoid shortages and lack of processing capability, Function has been adopted
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