This paper deals with the continuous classical optimal control problem for triple partial differential equations of parabolic type with initial and boundary conditions; the Galerkin method is used to prove the existence and uniqueness theorem of the state vector solution for given continuous classical control vector. The proof of the existence theorem of a continuous classical optimal control vector associated with the triple linear partial differential equations of parabolic type is given. The derivation of the Fréchet derivative for the cost function is obtained. At the end, the theorem of the necessary conditions for optimality of this problem is stated and is proved.
The aim of this study is to investigate the sedimentation environments and diagenetic processes of the Ibrahim Formation (Oligocene-early Miocene) in Zurbatiya, eastern Iraq. The Ibrahim Formation is comprised mostly of clayey micrite and skeletal grains composed of planktonic foraminifera, calcispheres, radiolaria, and benthic foraminifera. Glauconite and pyrite were documented in some restricted zones of this formation; they reflect quiet and reducing conditions. Radiolaria were identified in Late-Oligocene which was not known previously at this age regionally in carbonate formations of the Arabian Plate (AP). Mudstone, wackestone, and planktonic foraminiferal wackepackstone are the main microfacies that are affected by dissolutio
... Show MoreThis study examines experimentally the performance of a horizontal triple concentric tube heat exchanger TCTHE made of copper metal using water as cooling fluid and oil-40 as hot fluid. Hot fluid enters the inner annular tube of the TCTHE in a direction at a temperature of 50, 60 and 70 oC and a flow rate of 20 l/hr. On the other hand, the cooling fluid enters the inner tube and the outer annular tube in the reverse direction (counter current flow) at a temperature of 25 oC and flow rates of 10, 15, 20, 25, 30 and 35 l/hr. The TCTHE is composed of three copper tubes with outer diameters of 34.925 mm, 22.25 mm, and 9.525 mm, and thicknesses of 1.27 mm, 1.143 mm, and 0.762 mm, respectively. TCTHE tube's length was 670
... Show MoreBuckling analysis of a laminated composite thin plate with different boundary conditions subjected to in-plane uniform load are studied depending on classical laminated plate theory; analytically using (Rayleigh-Ritz method). Equation of motion of the plates was derived using the principle of virtual work and solved using modified Fourier displacement function that satisfies general edge conditions. The eigenvalue problem generated by using Ritz method, the set of linear algebraic equations can be solved using MATLAB for symmetric and anti-symmetric, cross and angle-ply laminated plate considering some design parameters such as aspect ratios, number of layers, lamination type and orthotropic ratio. The results obtained g
... Show MoreThis study aims to assess the effect of adding twisted fins in a triple-tube heat exchanger used for latent heat storage compared with using straight fins and no fins. In the proposed heat exchanger, phase change material (PCM) is placed between the middle annulus while hot water is passed in the inner tube and outer annulus in a counter-current direction, as a superior method to melt the PCM and store the thermal energy. The behavior of the system was assessed regarding the liquid fraction and temperature distributions as well as charging time and energy storage rate. The results indicate the advantages of adding twisted fins compared with those of using straight fins. The effect of several twisted fins was also studied to discover
... Show Moreان الغرض من هذا البحث هو المزج بين القيود الضبابية والاحتمالية. كما يهدف الى مناقشة اكثر حالات مشكلات البرمجة الضبابية شيوعا وهي عندما تكون المشكلة الضبابية تتبع دالة الانتماء مرة دالة الاتنماء المثلثية مرة اخرى، من خلال التطبيق العملي والتجريبي. فضلا عن توظيف البرمجة الخطية الضبابية في معالجة مشكلات تخطيط وجدولة الإنتاج لشركة العراق لصناعة الأثاث، وكذلك تم استخدام الطرائق الكمية للتنبؤ بالطلب واعتماده
... Show MoreCritical buckling and natural frequencies behavior of laminated composite thin plates subjected to in-plane uniform load is obtained using classical laminated plate theory (CLPT). Analytical investigation is presented using Ritz- method for eigenvalue problems of buckling load solutions for laminated symmetric and anti-symmetric, angle and cross ply composite plate with different elastic supports along its edges. Equation of motion of the plate was derived using principle of virtual work and solved using modified Fourier displacement function that satisfies general edge conditions. Various numerical investigation were studied to exhibit a convergence and accuracy of the present solution for considering some design parameters such as edge
... Show MoreThe ability of four local fungal isolates for extracellular laccase production has been tested with five grams 1:1(w/v) humidified sawdust as substrate in mineral salt medium. After 21 day of incubation at 25±1 ? C and using one mycelial plug (5mm), higher level of laccase activity (0.15U/ml) and specific activity (15U/mg) were observed by Pleurotus ostreatus in comparison with other fungal isolates. The results of optimum conditions for laccase production from selected isolate showed that, the maximum laccase activity (0.55U/ml) and specific activity (55U/mg) were obtained at moisture ratio 1:3 (w/v), using 3 mycelial plugs (5 mm), after 15 days incubation period at 25±1 ? C. The results of phenol degradation by crud laccase revealed th
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