Search Results (5)

The aim of this study is to utilize a differential quadrature method with various kernels, such as Lagrange interpolation and discrete singular convolution, to tackle problems related to the Riesz fractional diffusion equation and the Riesz fractional advection–dispersion equation. The governing equation for convection and diffusion depends on both spatial and transient factors. By using the block marching technique, we transform these equations into an algebraic system using differential quadrature methods and the Caputo-type fractional operator. Next, we develop a MATLAB program that generates code capable of solving the fractional convection–diffusion equation in (1+2) dimensions for each shape function. Our goal is to ensure that our methods are reliable, accurate, efficient, and capable of convergence. To achieve this, we conduct two experiments, comparing the numerical and graphical results with both analytical and numerical solutions. Additionally, we evaluate the accuracy of our findings using the L_∞ error. Our tests show that the differential quadrature method, which relies mainly on the discrete singular convolution shape function, is a highly effective numerical approach for fractional convective diffusion problems. It offers superior accuracy, faster convergence, and greater reliability than other techniques. Furthermore, we study the impact of fractional order derivatives, velocity, and positive diffusion parameters on the results. Full article

The primary goal of this work is to solve the problem of drug diffusion through a thin membrane using a differential quadrature approach with drastically different shape functions, such as Lagrange interpolation and discrete singular convolution (the delta Lagrange kernel and the regularized Shannon kernel). A nonlinear partial differential equation with two time- and space-dependent variables governs the system. To reduce the two independent variables by one, the partial differential equation is transformed into an ordinary differential equation using a one-parameter group transformation. With the aid of the iterative technique, the differential quadrature methods change this equation into an algebraic equation. Then, using a MATLAB program, a code is created that solves this equation for each shape function. To ensure the validity, efficiency, and accuracy of the developed techniques, the computed results are compared to previous numerical and analytical solutions. In addition, the L∞ error is applied. As a consequence of the numerical outcomes, the differential quadrature method, which is primarily based on a discrete singular convolution shape function, is an effective numerical method that can be used to solve the problem of drug diffusion through a thin membrane, guaranteeing a higher accuracy, faster convergence, and greater reliability than other techniques. Full article

This paper introduces the generalized fractional differential quadrature method, which is based on the generalized Caputo type and is used for the first time to solve nonlinear fractional differential equations. One of the effective shape functions of this method is the Cardinal Sine shape function, which is used in combination with the fractional operator of the generalized Caputo kind to convert nonlinear fractional differential equations into a nonlinear algebraic system. The nonlinearity problem is then solved using an iterative approach. Numerical results for a variety of chaotic systems are introduced using the MATLAB program and compared with previous theoretical and numerical results to ensure their reliability, convergence, accuracy, and efficiency. The fractional parameters play an effective role in studying the proposed problems. The achieved solutions prove the viability of the presented method and demonstrate that this method is easy to implement, effective, highly accurate, and appropriate for studying fractional differential equations emerging in fields related to chaotic systems and generalized Caputo-type fractional problems in the future. Full article

Recently, the reverse osmosis (RO) process is widely used in the field of desalinating brackish water and seawater to produce freshwater, but the disadvantage of using this technology is the increase in the rates of electrical energy consumption necessary to manage these units. To reduce the rates of electrical energy consumption in RO desalination plants, geothermal energy and photovoltaic/thermal panels were used as preheating units to heat the feed water before entering RO desalination plants. The proposed system in this study consists of an RO desalination plant with an energy recovery device, photovoltaic/thermal panels, and a geothermal energy extraction unit. To evaluate the system performance, three incorporated models were studied and validated by previous experimental data. The results indicated that incorporating the geothermal energy and photovoltaic/thermal panels with the RO desalination plants has positive effects in terms of increasing productivity and reducing the rates of specific power consumption in RO desalination plants. The average saving in the specific power consumption for utilizing the thermal recovery system of PV panels and geothermal energy as preheating units reached 29.1% and 40.75% for the treatment of seawater and brackish water, respectively. Additionally, the economic feasibility showed the saving in the cost of freshwater produced from the RO desalination plants for incorporating both geothermal energy and photovoltaic panels with a thermal recovery system with reverse osmosis desalination plants of up to 39.6%. Full article

Recently, efficient decontamination of water and wastewater have attracted global attention due to the deficiency in the world’s water sources. Herein, activated carbon (AC) derived from willow catkins (WCs) was successfully synthesized using chemical modification techniques and then loaded with different weight percentages of nickel ferrite nanocomposites (10, 25, 45, and 65 wt.%) via a one-step hydrothermal method. The morphology, chemical structure, and surface composition of the nickel ferrite supported on AC (NFAC) were analyzed by XRD, TEM, SEM, EDX, and FTIR spectroscopy. Textural properties (surface area) of the nanocomposites (NC) were investigated by using Brunauer–Emmett–Teller (BET) analysis. The prepared nanocomposites were tested on different dyes to form a system for water remediation and make this photocatalyst convenient to recycle. The photodegradation of rhodamine B dye was investigated by adjusting a variety of factors such as the amount of nickel in nanocomposites, the weight of photocatalyst, reaction time, and photocatalyst reusability. The 45NFAC photocatalyst exhibits excellent degradation efficiency toward rhodamine B dye, reaching 99.7% in 90 min under a simulated source of sunlight. To summarize, NFAC nanocomposites are potential photocatalysts for water environmental remediation because they are effective, reliable, and reusable. Full article