Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 7

Numerical Solution Related Abstracts

7 The Implementation of Secton Method for Finding the Root of Interpolation Function

Authors: Nur Rokhman


A mathematical function gives relationship between the variables composing the function. Interpolation can be viewed as a process of finding mathematical function which goes through some specified points. There are many interpolation methods, namely: Lagrange method, Newton method, Spline method etc. For some specific condition, such as, big amount of interpolation points, the interpolation function can not be written explicitly. This such function consist of computational steps. The solution of equations involving the interpolation function is a problem of solution of non linear equation. Newton method will not work on the interpolation function, for the derivative of the interpolation function cannot be written explicitly. This paper shows the use of Secton method to determine the numerical solution of the function involving the interpolation function. The experiment shows the fact that Secton method works better than Newton method in finding the root of Lagrange interpolation function.

Keywords: Numerical Solution, Interpolation, Secton method, non linear function

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6 Magnetohydrodynamic 3D Maxwell Fluid Flow Towards a Horizontal Stretched Surface with Convective Boundary Conditions

Authors: Abdul Rehman, M. Y. Malika, Farzana


The study deals with the steady, 3D MHD boundary layer flow of a non-Newtonian Maxwell fluid flow due to a horizontal surface stretched exponentially in two lateral directions. The temperature at the boundary is assumed to be distributed exponentially and possesses convective boundary conditions. The governing nonlinear system of partial differential equations along with associated boundary conditions is simplified using a suitable transformation and the obtained set of ordinary differential equations is solved through numerical techniques. The effects of important involved parameters associated with fluid flow and heat flux are shown through graphs.

Keywords: Numerical Solution, boundary layer flow, exponentially stretched surface, Maxwell fluid

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5 Numerical Investigation of Hygrothermal Behavior on Porous Building Materials

Authors: Faiza Mnasri, Kamilia Abahri, Mohammed El Ganaoui, Slimane Gabsi


Most of the building materials are considered porous, and composed of solid matrix and pores. In the pores, the moisture can be existed in two phases: liquid and vapor. Thus, the mass balance equation is comprised of various moisture driving potentials that translate the movement of the different existing phases occupying pores and the hygroscopic behavior of a porous construction material. This study suggests to resolve a hygrothermal mathematical model of heat and mass transfers in different porous building materials by a numerical investigation. Thereby, the evolution of temperature and moisture content fields has been processed. So, numerous series of hygrothermal calculation on several cases of wall are exposed. Firstly, a case of monolayer wall of massive wood has been treated. In this part, we have compared the numerical solution of the model on one and two dimensions and the effect of dimensional space has been evaluated. In the second case, three building materials (concrete, wood fiberboard and wooden insulation) are tested separately with the same boundary conditions and their hygrothermal behavior are compared. The evaluation of the exchange of heat and air at the interface between the wall and the interior ambiance is carried.

Keywords: Heat Transfer, Building materials, Numerical Solution, moisture diffusion

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4 Development of Extended Trapezoidal Method for Numerical Solution of Volterra Integro-Differential Equations

Authors: Fuziyah Ishak, Siti Norazura Ahmad


Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.

Keywords: Numerical Solution, Accuracy, extended trapezoidal method, Volterra integro-differential equations

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3 Heat Transfer and Trajectory Models for a Cloud of Spray over a Marine Vessel

Authors: S. R. Dehghani, Y. S. Muzychka, G. F. Naterer


Wave-impact sea spray creates many droplets which form a spray cloud traveling over marine objects same as marine vessels and offshore structures. In cold climates such as Arctic reigns, sea spray icing, which is ice accretion on cold substrates, is strongly dependent on the wave-impact sea spray. The rate of cooling of droplets affects the process of icing that can yield to dry or wet ice accretion. Trajectories of droplets determine the potential places for ice accretion. Combining two models of trajectories and heat transfer for droplets can predict the risk of ice accretion reasonably. The majority of the cooling of droplets is because of droplet evaporations. In this study, a combined model using trajectory and heat transfer evaluate the situation of a cloud of spray from the generation to impingement. The model uses some known geometry and initial information from the previous case studies. The 3D model is solved numerically using a standard numerical scheme. Droplets are generated in various size ranges from 7 mm to 0.07 mm which is a suggested range for sea spray icing. The initial temperature of droplets is considered to be the sea water temperature. Wind velocities are assumed same as that of the field observations. Evaluations are conducted using some important heading angles and wind velocities. The characteristic of size-velocity dependence is used to establish a relation between initial sizes and velocities of droplets. Time intervals are chosen properly to maintain a stable and fast numerical solution. A statistical process is conducted to evaluate the probability of expected occurrences. The medium size droplets can reach the highest heights. Very small and very large droplets are limited to lower heights. Results show that higher initial velocities create the most expanded cloud of spray. Wind velocities affect the extent of the spray cloud. The rate of droplet cooling at the start of spray formation is higher than the rest of the process. This is because of higher relative velocities and also higher temperature differences. The amount of water delivery and overall temperature for some sample surfaces over a marine vessel are calculated. Comparing results and some field observations show that the model works accurately. This model is suggested as a primary model for ice accretion on marine vessels.

Keywords: Numerical Solution, trajectory, evaporation, sea spray, marine icing

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2 Numerical and Analytical Approach for Film Condensation on Different Forms of Surfaces

Authors: A. Mirabdolah Lavasani, A. Kazemi Jouybari


This paper seeks to the solution of condensation around of a flat plate, circular and elliptical tube in way of numerical and analytical methods. Also, it calculates the entropy production rates. The first, problem was solved by using mesh dynamic and rational assumptions, next it was compared with the numerical solution that the result had acceptable errors. An additional supporting relation was applied based on a characteristic of condensation phenomenon for condensing elements. As it has been shown here, due to higher rates of heat transfer for elliptical tubes, they have more entropy production rates, in comparison to circular ones. Findings showed that two methods were efficient. Furthermore, analytical methods can be used to optimize the problem and reduce the entropy production rate.

Keywords: Numerical Solution, Condensation, analytical solution, entropy rate

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1 Numerical Study of Natural Convection in a Triangular Enclosure as an Attic for Different Geometries and Boundary Conditions

Authors: H. Golchoobian, M. H. Taheri, S. Saedodin, A. Sarafraz


In this paper, natural convection in an attic is numerically investigated. The geometry of the problem is considered to be a triangular enclosure. ANSYS Fluent software is used for modeling and numerical solution. This study is for steady state. Four right-angled triangles with height to base ratios of 2, 1, 0.5 and 0.25 are considered. The behavior of various parameters related to its performance, including temperature distribution and velocity vectors are evaluated, and graphs for the Nusselt number have been drawn. Also, in this study, the effect of geometric shape of enclosure with different height-to-base ratios has been evaluated for three types of boundary conditions of winter, summer day and one another state. It can be concluded that as the bottom side temperature and ratio of base to height of the enclosure increases, the convective effects become more prominent and circulation happened.

Keywords: Numerical Solution, natural convection, enclosure, nusselt number, triangular

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