Abstract

The present article investigates the squeezing flow of two types of nanofluids such as Cu-water and Cu-kerosene between two parallel plates in the presence of magnetic field. The governing non-linear partial differential equations are transformed into ordinary differential equations by applying suitable similarity transformation and then solved numerically using RK-4 method with shooting technique and analytically using differential transformation method (DTM). The influence of arising relevant parameters on flow characteristics has been discussed through graphs and tables. A comparative study has been taken into account between existing results and present work and it is found to be in excellent harmony.

Abstract

In this study, a simple and high accurate series-based method called Differential Transformation Method (DTM) is used for solving the coupled nonlinear differential equations in fluids mechanic problems. The concept of the DTM is briefly introduced, and its application on two different cases, natural convection of a non-Newtonian nanofluid between two vertical plates and Newtonian nanofluid flow between two horizontal plates, has been studied. DTM results are compared with those obtained by a numerical solution (Fourth-order Runge–Kutta) to show the accuracy of the proposed method. Results reveal that DTM is very effective and convenient which can achieve more reliable results compared to other analytical methods in solving some engineering and sciences problems.

Abstract

This paper focuses on the dynamic behavior of variable-span morphing wings (VSMW) oscillating in pitch and plunge motions under subsonic flight conditions. The unswept cantilevered wing is modeled as three-stepped Euler-Bernoulli beam. The aerodynamic loads acting on the wing are represented by Theodorsen's unsteady aerodynamic theory. The differential equations of motion that describe the behavior of the dynamics of Euler-Bernoulli beam are derived through the Hamilton's principle. The differential transformation method (DTM) is implemented to equations of motion and boundary conditions. The solution of the aeroelastic system is obtained by the classical frequency domain solution, k-method. Goland wing and High-Altitude Long-Endurance (HALE) wing are used as the basis for this study. Prior to analyzing flutter characteristics of VSMW, validation cases are conducted to ensure that the developed algorithm works well. Furthermore, flutter speed and flutter frequency are analyzed for different elongation ratios of wing. There is a significant difference in flutter values of fully retracted and fully extended wing configurations. It can be concluded that both flutter speed and flutter frequency decrease dramatically as wing span extends. Another important finding is that the flutter speed and flutter frequency reductions are relatively high at the initial stages of wing span extension.