Computational study of three-dimensional laminar and turbulent flows around electronic chip (heat source) located on a printed circuit board are presented. Computational field involves the solution of elliptic partial differential equations for conservation of mass, momentum, energy, turbulent energy, and its dissipation rate in finite volume form. The k-ε turbulent model was used with the wall function concept near the walls to treat of turbulence effects. The SIMPLE algorithm was selected in this work. The chip is cooled by an external flow of air. The goals of this investigation are to investigate the heat transfer phenomena of electronic chip located in enclosure and how we arrive to optimum level for cooling of this chip. These par

Conjugate heat transfer has significant implications on heat transfer characteristics, particularly in thick wall applications and small diameter pipes. In this study, a three-dimensional numerical investigation was carried out using commercial CFD software “ANSYS FLUENT” to study the influence of conjugate heat transfer of laminar flow in mini channels at constant heat flux wall conditions. Two parameters were studied and analyzed: the wall thickness and thermal conductivity and their effect on heat transfer characteristics such as temperature profile and Nusselt number. Thermal conductivity of (0.25, 10, 202, and 387) W/m²C and wall thickness of (1, 5, and 50) mm were used for a channel of (1*2) mm cross

      Numerical simulations have been investigated to study the external free convective heat transfer from a vertically rectangular interrupted fin arrays. The continuity, Naver-Stockes and energy equations have been solved for steady-state, incompressible, two dimensional, laminar with Boussiuesq approximation by Fluent 15 software. The performance of interrupted fins was evaluated to gain the optimum ratio of interrupted length to fin length (

This paper presents a linear fractional programming problem (LFPP) with rough interval coefficients (RICs) in the objective function. It shows that the LFPP with RICs in the objective function can be converted into a linear programming problem (LPP) with RICs by using the variable transformations. To solve this problem, we will make two LPP with interval coefficients (ICs). Next, those four LPPs can be constructed under these assumptions; the LPPs can be solved by the classical simplex method and used with MS Excel Solver. There is also argumentation about solving this type of linear fractional optimization programming problem. The derived theory can be applied to several numerical examples with its details, but we show only two examples

Never the less, banking compliance function became one of the most important functions in banking sector according to its characteristics that considered as an interior control tools to control (executive management, departments, subsidiaries…etc) in any bank; and their compliance towards applying rules, recommendations and legislations. In addition to, estimating the risks and limited them; and controlling the anti-money laundering. Thus, these functions that covered the main concept of (Banking Compliance) would avoid the bank to be under the control of any sanctions.

      In this paper we shall prepare an  sacrificial solution for fuzzy differential algebraic equations of fractional order (FFDAEs) based on the Adomian decomposition method (ADM) which is proposed to solve (FFDAEs) . The blurriness will appear in the boundary conditions, to be fuzzy numbers. The solution of the proposed pattern of  equations is studied in the form of a convergent series with readily computable components. Several examples are resolved as  clarifications, the numerical outcomes are obvious that the followed approach is simple to perform and precise when utilized to (FFDAEs).

This paper sheds the light on the vital role that fractional ordinary differential equations(FrODEs) play in the mathematical modeling and in real life, particularly in the physical conditions. Furthermore, if the problem is handled directly by using numerical method, it is a far more powerful and efficient numerical method in terms of computational time, number of function evaluations, and precision. In this paper, we concentrate on the derivation of the direct numerical methods for solving fifth-order FrODEs  in one, two, and three stages. Additionally, it is important to note that the RKM-numerical methods with two- and three-stages for solving fifth-order ODEs are convenient, for solving class's fifth-order FrODEs. Numerical exa

      In this paper we shall prepare an  sacrificial solution for fuzzy differential algebraic equations of fractional order (FFDAEs) based on the Adomian decomposition method (ADM) which is proposed to solve (FFDAEs) . The blurriness will appear in the boundary conditions, to be fuzzy numbers. The solution of the proposed pattern of  equations is studied in the form of a convergent series with readily computable components. Several examples are resolved as  clarifications, the numerical outcomes are obvious that the followed approach is simple to perform and precise when utilized to (FFDAEs).

The purpose of this paper is to introduce and study the concepts of fuzzy generalized open sets, fuzzy generalized closed sets, generalized continuous fuzzy proper functions and prove results about these concepts.