This paper is dealing with non-polynomial spline functions "generalized spline" to find the approximate solution of linear Volterra integro-differential equations of the second kind and extension of this work to solve system of linear Volterra integro-differential equations. The performance of generalized spline functions are illustrated in test examples

In this study the simple pullout concrete cylinder specimen reinforced by a single steel bar was analyzed for bond-slip behavior. Three-dimension nonlinear finite element model using ANSYS program was employed to study the behavior of bond between concrete and plain steel reinforcement. The ANSYS model includes eight-noded isoperimetric brick element (SOLID65) to model the concrete cylinder while the steel reinforcing bar was modeled as a truss member (LINK8). Interface element (CONTAC52) was used in this analysis to model the bond between concrete and steel bar. Material nonlinearity due to cracking and/or crushing of concrete, and yielding of the steel reinforcing bar were taken into consideration during the analysis. The accuracy of t

In this study, a new technique is considered for solving linear fractional Volterra-Fredholm integro-differential equations (LFVFIDE's) with fractional derivative qualified in the Caputo sense. The method is established in three types of Lagrange polynomials (LP’s), Original Lagrange polynomial (OLP), Barycentric Lagrange polynomial (BLP), and Modified Lagrange polynomial (MLP). General Algorithm is suggested and examples are included to get the best effectiveness, and implementation of these types. Also, as special case fractional differential equation is taken to evaluate the validity of the proposed method. Finally, a comparison between the proposed method and other methods are taken to present the effectiveness of the proposal meth

In this study, the flow and heat transfer characteristics of Al₂O₃-water nanofluids for a range of the Reynolds number of 3000, 4500, 6000 and 7500 with a range of volume concentration of 1%, 2%, 3% and 4% are studied numerically. The test rig consists of cold liquid loop, hot liquid loop and the test section which is counter flow double pipe heat exchanger with 1m length. The inner tube is made of smooth copper with diameter of 15mm. The outer tube is made of smooth copper with diameter of 50mm. The hot liquid flows through the outer tube and the cold liquid (or nanofluid) flow through the inner tube. The boundary condition of this study is thermally insulated the outer wall with uniform velocity a

This paper is concerned with the numerical solutions of the vorticity transport equation (VTE) in two-dimensional space with homogenous Dirichlet boundary conditions. Namely, for this problem, the Crank-Nicolson finite difference equation is derived.  In addition, the consistency and stability of the Crank-Nicolson method are studied. Moreover, a numerical experiment is considered to study the convergence of the Crank-Nicolson scheme and to visualize the discrete graphs for the vorticity and stream functions. The analytical result shows that the proposed scheme is consistent, whereas the numerical results show that the solutions are stable with small space-steps and at any time levels.

To evaluate and improve the efficiency of photovoltaic solar modules connected with linear pipes for water supply, a three-dimensional numerical simulation is created and simulated via commercial software (Ansys-Fluent). The optimization utilizes the principles of the 1st and 2nd laws of thermodynamics by employing the Response Surface Method (RSM). Various design parameters, including the coolant inlet velocity, tube diameter, panel dimensions, and solar radiation intensity, are systematically varied to investigate their impacts on energetic and exergitic efficiencies and destroyed exergy. The relationship between the design parameters and the system responses is validated through the development of a predictive model. Both single and mult

In this study the simple pullout concrete cylinder specimen reinforced by a single steel bar was analyzed for bond-slip behavior. Three-dimension nonlinear finite element model using ANSYS program was employed to study the behavior of bond between concrete and plain steel reinforcement. The ANSYS model includes eight-noded isoperimetric brick element (SOLID65) to model the concrete cylinder while the steel reinforcing bar was modeled as a truss member (LINK8). Interface element (CONTAC52) was used in this analysis to model the bond between concrete and steel bar. Material nonlinearity due to cracking and/or crushing of concrete, and yielding of the steel reinforcing bar were taken into consideration during the analysis. The accuracy of this

This research deals with the study of top soil electrical conductive regions located within Baghdad City. The research included measuring the dissolved soil material extraction Electrical Conductivity (EC) with an aqueous solution for the top (0-30 cm) soil layer of the study area. As the electrical conductivity values increase by increasing the amount of dissolved salts in principle, we can consider that the aim of this research is to predict the amount and distribution of (soil contamination with salts) which is represented by the (Salt Index), this factor calculated for each soil representative sample taken from the region with a depth of (30 cm). Laboratory (EC) test values measured by the use of solutions (EC) digital meter for the ex

Inherent fluctuations in the availability of energy from renewables, particularly solar, remain a substantial impediment to their widespread deployment worldwide. Employing phase-change materials (PCMs) as media, saving energy for later consumption, offers a promising solution for overcoming the problem. However, the heat conductivities of most PCMs are limited, which severely limits the energy storage potential of these materials. This study suggests employing circular fins with staggered distribution to achieve improved thermal response rates of PCM in a vertical triple-tube heat exchanger involving two opposite flow streams of the heat-transfer fluid (HTF). Since heat diffusion is not the same at various portions of the PCM unit,

The evolution of cryptography has been crucial to preservation subtle information in the digital age. From early cipher algorithms implemented in earliest societies to recent cryptography methods, cryptography has developed alongside developments in computing field. The growing in cyber threats and the increase of comprehensive digital communications have highlighted the significance of selecting effective and robust cryptographic techniques. This article reviews various cryptography algorithms, containing symmetric key and asymmetric key cryptography, via evaluating them according to security asset, complexity, and execution speed. The main outcomes demonstrate the growing trust on elliptic curve cryptography outstanding its capabi