Ibrahim Ozkol

Solution of boundary value problems for integro-differential equations by using differential transform method

In this study, we extended the differential transform method (DTM) to solve the integro-differential equations. New theorems for the transformation of integrals are introduced and prooved. The commonly encountered linear and nonlinear integro-differential equations that appear in literature are solved as an illustration for the efficiency of the method. Some numerical results are also given to demonstrate the superiority of the method to other common techniques. The results we obtained by using this technique is much more accurate compared to the existing ones.

Solution of differential–difference equations by using differential transform method

Abstract In this work, we successfully extended differential transform method (DTM), by presenting and proving new theorems, to the solution of differential–difference equations (DDEs). Theorems are presented in the most general form to cover a wide range of DDEs, being linear or nonlinear and constant or variable coefficient. In order to show the power and the robustness of the method and to illustrate the pertinent features of related theorems, examples are presented.

Solution of difference equations by using differential transform method

Abstract This work presents semi numerical–analytical solutions to both linear and nonlinear difference equations with variable coefficients by applying Differential Transform Method (DTM) and extending it with the related theorems and their proofs. To make clear and illustrate the features and capabilities of the presented method, examples are carried out and numerical results with comparison to exact solutions and other methods are given.

Solutions of integral and integro-differential equation systems by using differential transform method

In this study, differential transform method (DTM) is applied to both integro-differential and integral equation systems. The method is further expanded with a formulation to treat Fredholm integrals. If the system considered has a solution in terms of the series expansion of known functions, this powerful method catches the exact solution. So as to show this capability and robustness, some systems of integral and integro-differential equations are solved as numerical examples.

Free vibration analysis of circular plates by differential transformation method

This study analyses the free vibrations of circular thin plates for simply supported, clamped and free boundary conditions. The solution method used is differential transform method (DTM), which is a semi-numerical-analytical solution technique that can be applied to various types of differential equations. By using DTM, the governing differential equations are reduced to recurrence relations and its related boundary/regularity conditions are transformed into a set of algebraic equations. The frequency equations are obtained for the possible combinations of the outer edge boundary conditions and the regularity conditions at the center of the circular plate. Numerical results for the dimensionless natural frequencies are presented and then compared to the Bessel function solution and the numerical solutions that appear in literature. It is observed that DTM is a robust and powerful tool for eigenvalue analysis of circular thin plates.

Determination of the optimum geometry of the heat exchanger body via a genetic algorithm

ABSTRACT In the heat industry, design of the best-fitting heat exchanger in energy-converting systems has gained vital importance. In addition to fitness, the time needed to design an exchanger is also of great importance. In order to obtain the optimum heat exchanger, the geometry, the number of heat transfer units (NTU), and the pressure drop (ΔP) must be in harmony such that the requirements will be satisfied. The most important feature of this study, which makes it distinguishable from others, is the determination of optimum geometry, given performance limits, using a genetic algorithm. Therefore, this study offers an alternative way to calculate the needed geometry with a set of given initial values.

On the MHD and slip flow over a rotating disk with heat transfer

Purpose – To study the steady magnetohydrodynamic (MHD) flow of a viscous, Newtonian and electrically conducting fluid over a rotating infinite disk with slip boundary condition.Design/methodology/approach – The governing equations, which are partial and coupled, are transformed to ordinary ones by utilizing the similarity variables introduced by Karman and the resulting equation system is solved by using differential transform method.Findings – It is observed that both the slip factor and the magnetic flux decrease the velocity in all directions and thicken the thermal boundary layer.Originality/value – This paper studies the combined effects of slip and magnetic flux to the flow and thermal fields over a rotating single free disk in an ambient fluid, which were never studied together before.

Vibrational genetic algorithm as a new concept in airfoil design

We introduce the Vibration concept for real coded Genetic Algorithm and its implementation to inverse airfoil design, which decreases the number of CFD calculations. This concept assures efficient diversity in the population and consequently gives faster solution. We used the Vibration concept as vibrational mutation and vibrational crossover. For the mutational manner, a sinusoidal wave with random amplitude is introduced into population periodically from the beginning of the initial step of the genetic process. This operation spreads out the population over the design space and increases exploration performance of the genetic process. This makes passing over local optimums for genetic algorithm easy. In order to apply this new concept at the crossover stages, Double Directional Alpha (DDA) approximation in BLX‐α as a new crossover technique which was already presented in our earlier study is used. In the developed technique, the value of α oscillates systematically during the genetic process. Implementation of the Vibration concept to the inverse airfoil design makes the convergence faster.

Application of a magnetorheological damper modeled using the current–dependent Bouc–Wen model for shimmy suppression in a torsional nose landing gear with and without freeplay

In this study, shimmy of a nose landing gear model with torsional degree of freedom is analyzed. Equations governing the torsional nose landing gear model and the stretched string tire model are presented. Freeplay is incorporated into the model. A magnetorheological (MR) damper modeled using the current–dependent Bouc–Wen model is introduced to the torsional landing gear model with and without freeplay. Parameter identification of the Bouc–Wen model is accomplished using genetic algorithms. Incorporation of an MR damper into the landing gear model with and without freeplay is the advantage in this study. Implementation of the current–dependent Bouc–Wen model in such a landing gear model is another brand new concept.

Analytical-numerical analysis of entropy generation for gravity-driven inclined channel flow with initial transition and entrance effects

In this work, the entropy generation due to the flow of a gravity-driven laminar viscous incompressible fluid through an inclined channel is investigated. Fully developed flow field is solved for a Newtonian fluid. Then, temperature field is represented in a purely analytical expression and subject to isothermal boundary conditions on the walls and constant rectangular temperature profile at the inlet. This analytical solution is not similar to the already existing ones in the open literature. Also, the temperature field is numerically resolved by using the method of lines with the same inlet and boundary conditions. These two solutions overlap, which indicates the correctness of both solutions. In obtaining both analytical and numerical solutions, no assumption is made on the initial transition and entrance region. It is shown that the effect of this region, which has been omitted in previous studies, is highly dominant on the overall entropy generation. Therefore, the detailed thermal analysis of the entrance section is outlined.