Investigation of Nonlinear Problems of Heat Conduction in Tapered Cooling Fins Via Symbolic Programming

In this paper, symbolic programming is employed to handle a mathematical model representing conduction in heat dissipating fins with triangular profiles. As the first part of the analysis, the Modified Adomian Decomposition Method (MADM) is converted into a piece of computer code in MATLAB to seek solution for the mentioned problem with constant thermal conductivity (a linear problem). The results show that the proposed solution converges to the analytical solution rapidly. Afterwards, the code is extended to calculate Adomian polynomials and implemented to the similar, but more generalized, problem involving a power law dependence of thermal conductivity on temperature. The latter generalization imposes three different nonlinearities and extremely intensifies the complexity of the problem. The code successfully manages to provide parametric solution for this case. Finally, for the sake of exemplification, a relevant practical and real-world case study, about a silicon fin, for the complex nonlinear problem is given. It is shown that the numerical results are very close to those calculated by the classical Finite Difference Method (FDM)

On computation of real eigenvalues of matrices via the Adomian decomposition

AbstractThe problem of matrix eigenvalues is encountered in various fields of engineering endeavor. In this paper, a new approach based on the Adomian decomposition method and the Faddeev-Leverrier’s algorithm is presented for finding real eigenvalues of any desired real matrices. The method features accuracy and simplicity. In contrast to many previous techniques which merely afford one specific eigenvalue of a matrix, the method has the potential to provide all real eigenvalues. Also, the method does not require any initial guesses in its starting point unlike most of iterative techniques. For the sake of illustration, several numerical examples are included

Effect of dispersed hydrophilic silicon dioxide nanoparticles on batch adsorption of benzoic acid from aqueous solution using modified natural vermiculite: An equilibrium study

The equilibrium adsorption of benzoic acid from an aqueous medium on a natural vermiculite-based adsorbent was studied in the presence and absence of hydrophilic silicon dioxide nanoparticles in batchwise mode. The adsorbent was prepared through grinding natural vermiculite in a laboratory vibratory disk mill and the surfactant modification of ground vermiculite by cetyltrimethylammonium bromide, subsequently. The equilibrium isotherm in the presence and absence of nanoparticles was experimentally obtained and the equilibrium data were fitted to the Langmuir, Freundlich, Dubinin–Radushkevich and Temkin models. The results indicated that the dispersion of silicon dioxide nanoparticles at optimum concentration in the liquid phase remarkably increases the removal efficiency. Furthermore, it yields a more favorable equilibrium isotherm and changes the compatibility of equilibrium data from the Langmuir and Temkin equations to just the Langmuir equation. A quadratic polynomial model predicting the equilibrium adsorbent capacity in the presence of nanoparticles as a function of the adsorbate and initial nanoparticle concentrations was successfully developed using the response surface methodology based on the rotatable central composite design. A desirability function was used in order to optimize the values of all variables, independent and dependent ones, simultaneously

On Calculation of Adomian Polynomials by MATLAB

Adomian Decomposition Method (ADM) is an elegant technique to handle an extensive class of linear or nonlinear differential and integral equations. However, in case of nonlinear equations, ADM demands a special representation of each nonlinear term, namely, Adomian polynomials. The present paper introduces a novel MATLAB code which computes Adomian polynomials associated with several types of nonlinearities. The code exploits symbolic programming incorporated with a recently proposed alternative scheme to be straightforward and fast. For the sake of exemplification, Adomian polynomials of famous nonlinear operators, computed by the code, are given

Finding all real roots of a polynomial by matrix algebra and the Adomian decomposition method

In this paper, we put forth a combined method for calculation of all real zeroes of a polynomial equation through the Adomian decomposition method equipped with a number of developed theorems from matrix algebra. These auxiliary theorems are associated with eigenvalues of matrices and enable convergence of the Adomian decomposition method toward different real roots of the target polynomial equation. To further improve the computational speed of our technique, a nonlinear convergence accelerator known as the Shanks transform has optionally been employed. For the sake of illustration, a number of numerical examples are given

Batch removal of Pb (ΙΙ) ions from aqueous medium using gamma-Al2O3 nanoparticles/ethyl cellulose adsorbent fabricated via electrospinning method: An equilibrium isotherm and characterization study

The aim of the present work is to study the efficiency of a biocompatible polymer-based adsorbent for the removal of Pb (II) ions whose devastating effects on people’s health is a matter of great concern from aqueous solution. In this study, ethyl cellulose and gamma-Al2O3 nanoparticles/ethyl cellulose electrospun adsorbents were prepared for the batch removal of Pb (II) ions from aqueous solution. Both samples were characterized using contact angle analysis, N2 adsorption/desorption technique, FT-IR and SEM. The Freundlich model (R-square = 0.935 and RMSD (%) = 6.659) and the Dubinin-Radushkevich model (R-square = 0.944 and RMSD (%) = 6.145) were found to be more reliable in predicting the experimental data from the adsorption of Pb (II) ions onto the electrospun gamma-Al2O3 nanoparticles/ethyl cellulose than the Langmuir model (R-square = 0.685 and RMSD (%) = 14.61) and also the Temkin model (R-square = 0.695 and RMSD (%) = 14.38)

Modelling of photocatalytic CO2 reduction into value-added products in a packed bed photoreactor using the ray tracing method

This research suggests a comprehensive 3D model for modelling photocatalytic conversion of CO2 to methane, hydrogen and carbon monoxide in a packed bed reactor. This research includes two parts: designing the reactor's geometry using a new method in ''blender'' and using the computational fluid dynamics (CFD) technique to study and analyse the reaction, transport of phenomenon and light intensity through the reactor. Laminar flow, chemical reaction, mass transfer and optics physics were considered together to solve the equations. The surface reaction in the reactor follows a modified version of the Langmuir-Hinshelwood equation that evaluates the light profile in the reactor and the blockage of the catalyst's surface over time. Thus, a new method for 3D modelling light profiles in the reactor is introduced. The rate of reaction continues to increase with the pressure, and after 1 atm, the rate becomes steady. In the first 17 h, the methane rate is the highest, and then the carbon monoxide rate overcomes the methane rate. The rate of hydrogen is considerably lower than the other products. Changing pellets from spheres to Raschig rings causes growth in the probability density function (PDF) at the first moments. In methane's PDF, the amount of Raschig and sphere are 0.25 and 0.18, respectively, at the start of the reaction. Thus, the Raschig ring operates more effectively at the beginning moments of the process but eventually is outweighed after an hour by spherical particles. In the end, the validation of modelling and results were investigated with the aid of experimental data

Journal of Petroleum Science and Technology *Corresponding author EXPERIMENTAL STUDIES ON CONGO RED ADSORPTION BY TEA WASTE IN THE PRESENCE OF SILICA AND Fe 2 O 3 NANOPARTICLES

ABSTRACT In this work, the adsorption of the anionic dye, Congo red (CR), from aqueous solution by using tea waste (TW) has been carried out at 30 °C. The equilibrium sorption isotherms and kinetics were investigated. The equilibrium adsorption was studied by the Langmuir and Freundlich models of adsorption. The experimental results manifested that the Langmuir isotherm was the best model for the adsorption of CR by TW and implied the monolayer adsorption of CR on TW with the adsorption capacity of 40.6 mg/g at 30 °C. The kinetic data resulted from batch experiments were analyzed using pseudo-first-order and pseudo-second-order models. It was found that pseudosecond-order model provided the best fit for the experimental data (R 2 >0.99). The results illustrated that both silica and Fe 2 O 3 nanoparticles increased the adsorption of CR on TW by about 5% and 10% at 30 °C, respectively. The results suggested that TW should be a potential low-cost adsorbent for the removal of CR from aqueous solution