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ON Numerical Blow-Up Solutions of Semilinear Heat Equations

This paper is concerned with the numerical blow-up solutions of semi-linear heat equations, where the nonlinear terms are of power type functions, with zero Dirichlet boundary conditions. We use explicit linear and implicit Euler finite difference schemes with a special time-steps formula to compute the blow-up solutions, and to estimate the blow-up times for three numerical experiments. Moreover, we calculate the error bounds and the numerical order of convergence arise from using these methods. Finally, we carry out the numerical simulations to the discrete graphs obtained from using these methods to support the numerical results and to confirm some known blow-up properties for the studied problems.

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Publication Date
Sun May 26 2019
Journal Name
Iraqi Journal Of Science
Hydraulic Characteristics of the Aquifer up Al-Khassa Dam Sub-Basin Kirkuk/NE Iraq

The aim of this study is to the evaluation of the general hydrogeology condition of the Al-Khassa sub-basin area. Pumping test has been done for five wells in the area. The hydrogeological characteristics (transmissivity, hydraulic conductivity and storage coefficient) were determined in the area by input data which obtained from the pumping test process into the (AquiferWin32, Version 5) software program. The data were analyzed using Copper-Jacob, Theis and Hantuosh methods for pumping, the values of hydraulic characteristics range from: transmissivity (0.98 to 19.57) m²/day in (W7-W9-W10-W12) sites and 416 m²/day in W1, hydraulic conductivity (0.051 to 0.305) m/day in (W7-W9-W10-W12) sites and 5.012 m/day in W1, storage coefficie

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Publication Date
Tue May 30 2023
Journal Name
Iraqi Journal Of Science
Reconstruction of Timewise Dependent Coefficient and Free Boundary in Nonlocal Diffusion Equation with Stefan and Heat Flux as Overdetermination Conditions

     The problem of reconstruction of a timewise dependent coefficient and free boundary at once in a nonlocal diffusion equation under Stefan and heat Flux as nonlocal overdetermination conditions have been considered. A Crank–Nicolson finite difference method (FDM) combined with the trapezoidal rule quadrature is used for the direct problem. While the inverse problem is reformulated as a nonlinear regularized least-square optimization problem with simple bound and solved efficiently by MATLAB subroutine lsqnonlin from the optimization toolbox. Since the problem under investigation is generally ill-posed, a small error in the input data leads to a huge error in the output, then Tikhonov’s regularization technique is app

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Publication Date
Mon Jul 20 2020
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Exact Solutions for Minimizing cost Function with Five Criteria and Release Dates on Single Machine

     In this paper, we present a Branch and Bound (B&B) algorithm of scheduling (n) jobs on a single machine to minimize the sum total completion time, total tardiness, total earliness, number of tardy jobs and total late work with unequal release dates. We proposed six heuristic methods for account upper bound. Also to obtain lower bound (LB) to this problem we modified a (LB) select from literature, with (Moore algorithm and Lawler's algorithm).  And some dominance rules were suggested. Also, two special cases were derived. Computational experience showed the proposed (B&B) algorithm was effective in solving problems with up to (16) jobs, also the upper bounds and the lower bound were effective in restr

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Publication Date
Wed Nov 20 2024
Journal Name
Journal Of Baghdad College Of Dentistry
Effect of silver nitrate incorporation into heat polymerized acrylic resin on some mechanical properties

Background: Polymers are very rarely used in their form. These modifications are carried out in order to improve the properties of polymers.Recently silver have been used successfully as antimicrobial (medical and dental) biomaterials that can prevent caries and infection of implants Purposes: The aim of the present in vitro study is to evaluate the effect of addition of silver nitrate to acrylic resin in different concentrationsthrough several tests part of these are: The effect of this additive on impact strength, transverse strength, and tensile strength of AgNO3 – loaded resin, and to assess any effect of addition of silver nitrate on coloration of acrylic resin. Materials and methods: Different concentrations of silver nitrate

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Publication Date
Mon Mar 08 2021
Journal Name
Baghdad Science Journal
The Effect of Heat Treatment on the Magnetic and Mechanical properties offe - Ni alloys.

The aim of this work is studying the binary system ??'??? Ni?)with two ratios (y=36,80) by using casting method for preparing the samples.Magnetic and Mechanical properties have been studidt different httrea^nttem^rature.All the alloys were found a ferromagnetic behavior and sensitive to the heat treatment. Best properties were found at the heat treatment 1100 C°.A significant different results were found above 1100C° for lower magnetic and mechanical values. This is possibly due to the change on the degree of magnetic moment orders, in which most of the moments are started to remove from coupled ferromagnetically.?

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Publication Date
Sun Mar 01 2020
Journal Name
Baghdad Science Journal
A Comparative Study on the Double Prior for Reliability Kumaraswamy Distribution with Numerical Solution

This work, deals with Kumaraswamy distribution. Kumaraswamy (1976, 1978) showed well known probability distribution functions such as the normal, beta and log-normal but in (1980) Kumaraswamy developed a more general probability density function for double bounded random processes, which is known as Kumaraswamy’s distribution. Classical maximum likelihood and Bayes methods estimator are used to estimate the unknown shape parameter (b). Reliability function are obtained using symmetric loss functions by using three types of informative priors two single priors and one double prior. In addition, a comparison is made for the performance of these estimators with respect to the numerical solution which are found using expansion method. The

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Publication Date
Wed Nov 28 2018
Journal Name
Al-khwarizmi Engineering Journal
Effect of Using Combined Square Nozzle & winglet with Helical Tape on Thermal Characteristics in Tube Heat Exchanger

Influence of combined square nozzle with helical tape inserted in a constant heat flux tube on heat transfer enhancement for turbulent airflow for Reynolds number ranging from 7000 to 14500 were investigated experimentally. Three different pitch ratios for square nozzle (PR = 5.8, 7.7 and 11.6) according to three different numbers of square nozzle (N = 3, 4 and 5) and constant pitch ratios for helical tape were used. The results observed that the Nusselt number and friction factor for combination with winglets were found to be up to 33.8 % and 21.4 %, respectively higher than nozzle alone for pitch ratio PR=5.8. The maximum value of thermal performance for using combination with winglets was about 1.351 for pitch ratio= 5.8. Nusselt numb

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Publication Date
Tue Sep 01 2020
Journal Name
Journal Of Engineering
Experimental Study on Heat Transfer and Flow Characteristics in Subcooled Flow Boiling in a Microchannel

The current study presents an experimental investigation of heat transfer and flow characteristic for subcooled flow boiling of deionized water in the microchannel heat sink. The test section consisted of a single microchannel having 300μm wide nominal dimensions and 300μm height (hydraulic diameter of 300μm). The test section formed of oxygen-free copper with 72mm length and 12mm width. Experimental operation conditions spanned the heat flux (78-800) kW/m2, mass flux (1700 and 2100) kg/m2.s at 31˚C subcooled inlet temperature. The boiling heat transfer coefficient is measured and compared with existing correlations. Also, the experimental pressure drop is measured and compared with microscale p

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Publication Date
Thu Mar 21 2019
Journal Name
Journal Of Legal Sciences
The crime of stirring up hatred "between the problematic interpretation of Quranic texts and the effectiveness of national legislation

            That the guarantee of respect for human rights and fundamental freedoms requires that all individuals within society be treated equally, and that the State, as the primary guarantor of the rights and freedoms of individuals, must provide adequate protection and combat any cause that would create discrimination or instigate a sense of hatred among the inhabitants of our beloved country, What we know is that the greatest factor that has lost lives is the hate factor throughout history, and the extremist groups have found no more effective reason than the creation of the hate factor. Hatred was the weapon for which many people were killed. The record of preparations for the

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Publication Date
Sun Dec 05 2010
Journal Name
Baghdad Science Journal
Stability of Nonlinear Systems of Fractional Order Differential Equations

In this paper, a sufficient condition for stability of a system of nonlinear multi-fractional order differential equations on a finite time interval with an illustrative example, has been presented to demonstrate our result. Also, an idea to extend our result on such system on an infinite time interval is suggested.

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