Analysis and computation of the cross-flow past an oscillatiang cylinder with two degrees of freedom

The present thesis deals with analysis and numerical simulation of a new class of wake flows created by combined recti-linear (translational) and rotational oscillation of a cylinder placed in a steady uniform flow. The flow is incompressible and two-dimensional, and recti-linear and rotational oscillations are harmonic. The instantaneous translation and rotation start at the same moment and the development of the flow is studied in a coordinate frame which moves with the cylinder but does not rotate. The analysis is carried out for combined phase-locked translation and rotation with a single frequency. The results are presented for five set of the four dimensionless groups which characterize this flow. The resulting vortex formation modes and synchronization (lock-on) phenomena behind the cylinder (in the near-wake region) as well as the fluid forces acting on the cylinder are analyzed. In addition, a series of one-degree-of-freedom (1-DoF) forced vibration calculations are carried out to better understand what differences result from the addition of rotational oscillations to streamwise (in-line) or cross-stream (transverse) motion and to see which effects a transverse-only or in-line-only simulations miss. The numerical scheme is verified by applying it to the special cases of uniform flow past a stationary cylinder; a steadily rotating cylinder; a cylinder undergoing (1-DoF) forced (recti-linear or rotational) oscillations. Exceptionally good comparisons with previous experimental and numerical results are obtained. Furthermore, the simulations of the start-up flow for the case of combined (2-DoF) forced recti-linear and rotational cylinder oscillations at a moderate Reynolds number are consistent with the results of the analytical solution

Convergent Power Series of sech⁡(x) and Solutions to Nonlinear Differential Equations

It is known that power series expansion of certain functions such as sech⁡(x) diverges beyond a finite radius of convergence. We present here an iterative power series expansion (IPS) to obtain a power series representation of sech⁡(x) that is convergent for all x. The convergent series is a sum of the Taylor series of sech⁡(x) and a complementary series that cancels the divergence of the Taylor series for x≥π/2. The method is general and can be applied to other functions known to have finite radius of convergence, such as 1/(1+x2). A straightforward application of this method is to solve analytically nonlinear differential equations, which we also illustrate here. The method provides also a robust and very efficient numerical algorithm for solving nonlinear differential equations numerically. A detailed comparison with the fourth-order Runge-Kutta method and extensive analysis of the behavior of the error and CPU time are performed

A Numerical Algorithm for Solving Higher-Order Nonlinear BVPs with an Application on Fluid Flow over a Shrinking Permeable Infinite Long Cylinder

We present an efficient iterative power series method for nonlinear boundary-value problems that treats the typical divergence problem and increases arbitrarily the radius of convergence. This method is based on expanding the solution around an iterative initial point. We employ this method to study the unsteady, viscous, and incompressible laminar flow and heat transfer over a shrinking permeable cylinder. More precisely, we solve the unsteady nonlinear Navier–Stokes and energy equations after reducing them to a system of nonlinear boundary-value problems of ordinary differential equations. The present method successfully captures dual solutions for both the flow and heat transfer fields and a unique solution at a specific critical unsteadiness parameter. Comparisons with previous numerical methods and an exact solution verify the validity, accuracy, and efficiency of the present method

Numerical study of MHD effective Prandtl number boundary layer flow of γ Al2O3 nanofluids past a melting surface

This research article numerically studies the influences of an effective Prandtl number along with magnetic field on the melting heat transport characteristics of Ethylene glycol/Water with gamma Al2O3 nanoparticles over a stretching sheet. To analyse the impacts of effective Prandtl number, the non-dimensional melting heat transfer boundary conditions are derived for the first time with and without effective Prandtl number. A non-linear form of thermal radiation is used. The experimental based thermo-physical properties of gamma Al2O3 nanofluids are considered. The electric conductivities of Al2O3, water and ethylene glycol are used to calculate of effective electric conductivity to study the magnetic field effects. Mathematical models are developed and solved by numerical technique based on the Iterative Power Series (IPS) method with shooting strategy. The numerical outcomes are discussed through plots and tables. Keywords: Effective Prandtl number, Melting heat transfer, MHD, Nanofluids, Non-linear thermal radiatio

An epidemiological model for analysing pandemic trends of novel coronavirus transmission with optimal control

ABSTRACTSymptomatic and asymptomatic individuals play a significant role in the transmission dynamics of novel Coronaviruses. By considering the dynamical behaviour of symptomatic and asymptomatic individuals, this study examines the temporal dynamics and optimal control of Coronavirus disease propagation using an epidemiological model. Biologically and mathematically, the well-posed epidemic problem is examined, as well as the threshold quantity with parameter sensitivity. Model parameters are quantified and their relative impact on the disease is evaluated. Additionally, the steady states are investigated to determine the model's stability and bifurcation. Using the dynamics and parameters sensitivity, we then introduce optimal control strategies for the elimination of the disease. Using real disease data, numerical simulations and model validation are performed to support theoretical findings and show the effects of control strategies

MHD pulsatile flow of engine oil based carbon nanotubes between two concentric cylinders

In this article, thermal performance of engine oil in the presence of both single and multiple wall carbon nanotubes (SWCNTs and MWCNTs) between two concentric cylinders is presented. Flow is driven with oscillatory pressure gradient and magneto-hydrodynamics (MHDs) effects are also introduced to control the random motion of the nanoparticles. Arrived broad, it is perceived that the inclusion of nanoparticles increases the thermal conductivity of working fluid significantly for both turbulent and laminar regimes. Fundamental momentum and energy equations are based upon partial differential equations (PDEs) that contain thermos-physical properties of both SWCNTs and MWCNTs. The solution has been evaluated for each mixture, namely: SWCNT-engine oil and MWCNT-engine oil. Results are determined for each velocity, temperature, pressure and stress gradient. Graphical results for the numerical values of the emerging parameters, namely: Hartmann number (M), the solid volume fraction of the nanoparticles (ϕ), Reynolds number (Reω), and the pulsation parameter based on the periodic pressure gradient are analyzed for pressure difference, frictional forces, velocity profile, temperature profile, crux, streamlines and vorticity phenomena. In addition, the assets of various parameters on the flow quantities of observation are investigated. Keywords: MHD, Pulsating flow, Nanofluids, Carbon nanotubes, Concentric cylinder