In this work, the pseudoparabolic problem of the fourth order is investigated to identify the time -dependent potential term under periodic conditions, namely, the integral condition and overdetermination condition. The existence and uniqueness of the solution to the inverse problem are provided. The proposed method involves discretizing the pseudoparabolic equation by using a finite difference scheme, and an iterative optimization algorithm to resolve the inverse problem which views as a nonlinear least-square minimization. The optimization algorithm aims to minimize the difference between the numerical computing solution and the measured data. Tikhonov’s regularization method is also applied to gain stable results. Two

An experimental and theoretical works were carried out to model the wire condenser in the domestic refrigerator by calculating the heat transfer coefficient and pressure drop and finding the optimum performance. The two methods were used for calculation, zone method, and an integral method. The work was conducted by using two wire condensers with equal length but different in tube diameters, two refrigerants, R-134a and R-600a, and two different compressors matching the refrigerant type. In the experimental work, the optimum charge was found for the refrigerator according to ASHRAE recommendation. Then, the tests were done at 32˚C ambient temperature in a closed room with dimension (2m*2m*3m). The results showed that th

This paper proposes a new structure for a Fractional Order Sliding Mode Controller (FOSMC) to control a Twin Rotor Aerodynamic System (TRAS). The new structure is composed by defining two 3-dimensional sliding mode surfaces for the TRAS model and introducing fractional order derivative integral in the state variables as well as in the control action. The parameters of the controller are determined so as to minimize the Integral of Time multiplied by Absolute Error (ITAE) performance index. Through comparison, this controller outperforms its integer counterpart in many specifications, such as reducing the delay time, rise time, percentage overshoot, settling time, time to reach the sliding surface, and amplitude of chattering in control inpu

For many problems in Physics and Computational Fluid Dynamics (CFD), providing an accurate approximation of derivatives is a challenging task. This paper presents a class of high order numerical schemes for approximating the first derivative. These approximations are derived based on solving a special system of equations with some unknown coefficients. The construction method provides numerous types of schemes with different orders of accuracy. The accuracy of each scheme is analyzed by using Fourier analysis, which illustrates the dispersion and dissipation of the scheme. The polynomial technique is used to verify the order of accuracy of the proposed schemes by obtaining the error terms. Dispersion and dissipation errors are calculated

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

In this paper, the Reliability Analysis with utilizing a Monte Carlo simulation (MCS) process was conducted on the equation of the collapse potential predicted by ANN to study its reliability when utilized in a situation of soil that has uncertainty in its properties. The prediction equation utilized in this study was developed previously by the authors. The probabilities of failure were then plotted against a range of uncertainties expressed in terms of coefficient of variation. As a result of reliability analysis, it was found that the collapse potential equation showed a high degree of reliability in case of uncertainty in gypseous sandy soil properties within the specified coefficient of variation (COV) for each property. When t