The one-dimensional, cylindrical coordinate, non-linear partial differential equation of transient heat conduction through a hollow cylindrical 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 the

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

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

In this paper, precision agriculture system is introduced based on Wireless Sensor Network (WSN). Soil moisture considered one of environment factors that effect on crop. The period of irrigation must be monitored. Neural network capable of learning the behavior of the agricultural soil in absence of mathematical model. This paper introduced modified type of neural network that is known as Spiking Neural Network (SNN). In this work, the precision agriculture system  is modeled, contains two SNNs which have been identified off-line based on logged data, one of these SNNs represents the monitor that located at sink where the period of irrigation is calculated and the other represents the soil. In addition, to reduce p

Water flow into unsaturated porous media is governed by the Richards’ partial differential equation expressing the mass conservation and Darcy’s laws. The Richards’ equation may be written in three forms,where the dependent variable is pressure head or moisture content, and the constitutive relationships between water content and pressure head allow for conversion of one form into the other. In the present paper, the “moisture-based" form of Richards’ equation is linearized by applying Kirchhoff’s transformation, which
combines the soil water diffusivity and soil water content. Then the similarity method is used to obtain the analytical solution of wetting front position. This exact solution is obtained by means of Lie’s

Cowpea is a very important legume in Nigeria that is being utilized to Substitute high-cost animal protein for low-income people. The knowledge of some physical properties of various moisture contents is of utmost importance in the design of its handling and processing equipment and machinery, which is the aim of this work, which studied the physical properties of IT99K-573-1-1 (SAMPEA14) variety of Cowpea within 8.77 to 21.58 % db moisture content. The properties studied include Major, Intermediate, and Minor diameters, Sphericity, Surface area, Specific gravity, Volume, Bulk density, 50-tap density, 100-tap density, 1250-tap density, seed mass, Angle of repose, Geometric mean diameter, and Arithmetic mean diameter. The