This paper presents an alternative method for developing effective embedded optimized Runge-Kutta (RK) algorithms to solve oscillatory problems numerically.   The embedded scheme approach has algebraic orders of 5 and 4. By transforming second-order ordinary differential equations (ODEs) into their first-order counterpart, the suggested approach solves first-order ODEs. The amplification error, phase-lag, and first derivative of the phase-lag are all nil in the embedded pair. The alternative method’s absolute stability is demonstrated. The numerical tests are conducted to demonstrate the effectiveness of the developed approach in comparison to other RK approaches. The alternative approach outperforms the current RK methods

Numerical simulations have been carried out on the solar chimney power plant systems. This paper gives the flow field analysis for a solar chimney power generation project located in Baghdad. The continuity, Naver-stockes, energy and radiation transfer equations have been solved and carried out by Fluent software. The governing equations are solved for incompressible, 3-D, steady state, turbulent is approximated by a standard k -  model with Boussiuesq approximation to study and evaluate the performance of solar chimney power plant in Baghdad city of Iraq. The different geometric parameters of project are assumed such as collector diameter and chimney height at different working conditions of solar radiation intensity (300,450,600,750

This paper introduces a non-conventional approach with multi-dimensional random sampling to solve a cocaine abuse model with statistical probability. The mean Latin hypercube finite difference (MLHFD) method is proposed for the first time via hybrid integration of the classical numerical finite difference (FD) formula with Latin hypercube sampling (LHS) technique to create a random distribution for the model parameters which are dependent on time [Formula: see text]. The LHS technique gives advantage to MLHFD method to produce fast variation of the parameters’ values via number of multidimensional simulations (100, 1000 and 5000). The generated Latin hypercube sample which is random or non-deterministic in nature is further integ

This study numerically intends to evaluate the effects of arc-shaped fins on the melting capability of a triplex-tube confinement system filled with phase-change materials (PCMs). In contrast to situations with no fins, where PCM exhibits relatively poor heat response, in this study, the thermal performance is modified using novel arc-shaped fins with various circular angles and orientations compared with traditional rectangular fins. Several inline and staggered layouts are also assessed to maximize the fin’s efficacy. The effect of the nearby natural convection is further investigated by adding a fin to the bottom of the heat-storage domain. Additionally, the Reynolds number and temperature of the heat-transfer fluid (HTF) are e

This study proposes a mathematical approach and numerical experiment for a simple solution of cardiac blood flow to the heart's blood vessels. A mathematical model of human blood flow through arterial branches was studied and calculated using the Navier-Stokes partial differential equation with finite element analysis (FEA) approach. Furthermore, FEA is applied to the steady flow of two-dimensional viscous liquids through different geometries. The validity of the computational method is determined by comparing numerical experiments with the results of the analysis of different functions. Numerical analysis showed that the highest blood flow velocity of 1.22 cm/s occurred in the center of the vessel which tends to be laminar and is influe

In this study, the effect of intersecting ribs with inclined ribs on the heat transfer and flow characteristics of a high aspect ratio duct has been numerically investigated. The Relative roughness pitch (P/e) is 10 and the Reynolds number range from 35,700 to 72,800. ANSYS (Fluent-Workbench 18.0) software has been utilized to solve the Reynolds averaged Navier-Stokes (RANS) equations with the Standard k-ε turbulence model. Three ribbed models have been used in this study. Model 1 which is a just inclined ribs, Model 2 which has a single longitudinal rib at the center with inclined ribs and Model 3 which has two longitudinal ribs at the sides. The results showed that the heat transfer rate has been enhanced when the int

     This study is a numerical analysis of the transition process from the second to the third mode in transformer oil. In this study, it was determined how to change from the second to the third mode, which is thought to be a precursor to the process of electrical breakdown, which results in a significant loss of electrical energy and harm to electrical devices and equipment. The initiation time, length, rate of propagation velocity, and radius of the streamer discharge were determined. The transition from the second to the third mode during the electrical discharge process may lead to the occurrence of an electrical breakdown, which is one of the greatest challenges facing scientists and engineers who deal with the

This article deals with the approximate algorithm for two dimensional multi-space fractional bioheat equations (M-SFBHE). The application of the collection method will be expanding for presenting a numerical technique for solving M-SFBHE based on “shifted Jacobi-Gauss-Labatto polynomials” (SJ-GL-Ps) in the matrix form. The Caputo formula has been utilized to approximate the fractional derivative and to demonstrate its usefulness and accuracy, the proposed methodology was applied in two examples. The numerical results revealed that the used approach is very effective and gives high accuracy and good convergence.