The one-dimensional, spherical coordinate, non-linear partial differential equation of transient heat conduction through a hollow spherical thermal insulation material of a thermal conductivity temperature dependent property proposed by an available empirical function is solved analytically using Kirchhoff’s transformation. It is assumed that this insulating material is initially at a uniform temperature. Then, it is suddenly subjected at its inner radius with a step change in temperature. Four thermal insulation materials were selected. An identical analytical solution was achieved when comparing the results of temperature distribution with available analytical solution for the same four case studies that assume a constant thermal con

     The linear non-polynomial spline is used here to solve the fractional partial differential equation (FPDE). The fractional derivatives are described in the Caputo sense. The tensor products are given for extending the one-dimensional linear non-polynomial spline to a two-dimensional spline  to solve the heat equation. In this paper, the convergence theorem of the method used to the exact solution is proved and the numerical examples show the validity of the method. All computations are implemented by Mathcad15.

       In this paper we design a Simulink model which can be evaluate the concentration of Copper, Lead, Zinc, Cadmium, Cobalt, Nickel, Crum and Iron. So, this model would be a method to determine the contamination levels of these metals with the potential for this contamination sources with their impact. The aim of using Simulink environment is to solve differential equations individually and as given data in parallel with analytical mathematics trends. In general, mathematical models of the spread heavy metals in soil are modeled and solve to predict the behavior of the system under different conditions.

A non-polynomial spline (NPS) is an approximation method that relies on the triangular and polynomial parts, so the method has infinite derivatives of the triangular part of the NPS to compensate for the loss of smoothness inherited by the polynomial. In this paper, we propose polynomial-free linear and quadratic spline types to solve fuzzy Volterra integral equations (FVIE) of the 2nd kind with the weakly singular kernel (FVIEWSK) and Abel's type kernel. The linear type algorithm gives four parameters to form a linear spline. In comparison, the quadratic type algorithm gives five parameters to create a quadratic spline, which is more of a credit for the exact solution. These algorithms process kernel singularities with a simple techniqu

This paper presents a numerical solution to the inverse problem consisting of recovering time-dependent thermal conductivity and  heat source coefficients  in the one-dimensional  parabolic heat equation.   This  mathematical  formulation  ensures that the inverse problem  has a unique  solution.   However, the problem  is still  ill-posed since small errors  in the input data lead to a drastic  amount  of errors in the output coefficients.  The  finite  difference method  with  the Crank-Nicolson  scheme is adopted  as a direct  solver of the problem in a fixed domain.   The inverse problem is solved sub

An experimental study was conducted on pressure drop of water flow through vertical cylindrical packed beds in turbulent region and the influence of the operating parameters on its behavior. The bed packing was made of spherical and non-spherical particles (spheres, Rasching rings and intalox saddle) with aspect ratio range 3.46  D/dp  8.486 obtaining bed porosities 0.396 0.84 and Reynolds number 1217  21758. The system is consisted of 5 cm inside diameter Perspex column, 50 cm long; distilled water was pumped through the bed with flow rate 875, 1000, 1125, 1250,1375 and 1500 l/h and inlet water temperature 20, 30, 40 and 50 ˚C. The packed bed system was monitored by using LabVIEW program, were the result

we applied the direct product concept on the notation of intuitionistic fuzzy semi d-ideals of d-algebra with investigation some theorems, and also, we study the notation of direct product of intuitionistic fuzzy topological d-algebra.

In this paper we introduce new class of open sets called weak N-open sets and we study the relation between N-open sets , weak N-open sets and some other open sets. We prove several results about them. 

     The purpose of this paper is to introduce dual notions of two known concepts which are semi-essential submodules and semi-uniform modules. We call these concepts; cosemi-essential submodules and cosemi-uniform modules respectively. Also, we verify that these concepts form generalizations of two well-known classes; coessential submodules and couniform modules respectively. Some conditions are considered to obtain the equivalence between cosemi-uniform and couniform. Furthermore, the relationships of cosemi-uniform module with other related concepts are studied, and some conditional characterizations of cosemi-uniform modules are investigated.

The main purpose of this paper is to investigate some results. When h is  -( ,δ) – Derivation on prime Γ-near-ring G and K is a nonzero semi-group ideal of G, then G is commutative .