The Aim of this paper is to investigate numerically the simulation of ice melting in one and two dimension using the cell-centered finite volume method. The mathematical model is based on the heat conduction equation associated with a fixed grid, latent heat source approach. The fully implicit time scheme is selected to represent the time discretization. The ice conductivity is chosen
to be the value of the approximated conductivity at the interface between adjacent ice and water control volumes. The predicted temperature distribution, percentage melt fraction, interface location and its velocity is compared with those obtained from the exact analytical solution. A good agreement is obtained when comparing the numerical results of one

This research includes the study of dual data models with mixed random parameters, which contain two types of parameters, the first is random and the other is fixed. For the random parameter, it is obtained as a result of differences in the marginal tendencies of the cross sections, and for the fixed parameter, it is obtained as a result of differences in fixed limits, and random errors for each section. Accidental bearing the characteristic of heterogeneity of variance in addition to the presence of serial correlation of the first degree, and the main objective in this research is the use of efficient methods commensurate with the paired data in the case of small samples, and to achieve this goal, the feasible general least squa

A mixture of algae biomass (Chrysophyta, Cyanophyta, and Chlorophyte) has been investigated for its possible adsorption removal of cationic dyes (methylene blue, MB). Effect of pH (1-8), biosorbent dosage (0.2-2 g/100ml), agitated speed (100-300), particle size (1304-89μm), temperature (20-40˚C), initial dye concentration (20-300 mg/L), and sorption–desorption were investigated to assess the algal-dye sorption mechanism. Different pre-treatments, alkali, protonation, and CaCl2 have been experienced in order to enhance the adsorption capacity as well as the stability of the algal biomass. Equilibrium isotherm data were analyzed using Langmuir, Freundlich, and Temkin models. The maximum dye-sorption capacity was 26.65 mg/g at pH= 5, 25

       In this work, the fractional damped Burger's equation (FDBE) formula    = 0,

This paper introduces the Multistep Modified Reduced Differential Transform Method (MMRDTM). It is applied to approximate the solution for Nonlinear Schrodinger Equations (NLSEs) of power law nonlinearity. The proposed method has some advantages. An analytical approximation can be generated in a fast converging series by applying the proposed approach. On top of that, the number of computed terms is also significantly reduced. Compared to the RDTM, the nonlinear term in this method is replaced by related Adomian polynomials prior to the implementation of a multistep approach. As a consequence, only a smaller number of NLSE computed terms are required in the attained approximation. Moreover, the approximation also converges rapidly over a

          In this work, the modified Lyapunov-Schmidt reduction is used to find a nonlinear Ritz approximation of Fredholm functional defined by the nonhomogeneous Camassa-Holm equation and Benjamin-Bona-Mahony. We introduced the modified Lyapunov-Schmidt reduction for nonhomogeneous problems when the dimension of the null space is equal to two.  The nonlinear Ritz approximation for the nonhomogeneous Camassa-Holm equation has been found as a function of codimension twenty-four.

In this study, a brand-new double transform known as the double INEM transform is introduced. Combined with the definition and essential features of the proposed double transform, new findings on partial derivatives, Heaviside function, are also presented. Additionally, we solve several symmetric applications to show how effective the provided transform is at resolving partial differential equation.

In this work, a joint quadrature for numerical solution of the double integral is presented. This method is based on combining two rules of the same precision level to form a higher level of precision. Numerical results of the present method with a lower level of precision are presented and compared with those performed by the existing high-precision Gauss-Legendre five-point rule in two variables, which has the same functional evaluation. The efficiency of the proposed method is justified with numerical examples. From an application point of view, the determination of the center of gravity is a special consideration for the present scheme. Convergence analysis is demonstrated to validate the current method.