Dynamic analysis of a simply supported beam resting on a nonlinear elastic foundation under compressive axial load using nonlinear normal modes techniques under three-to-one internal resonance condition

In this paper, the Nonlinear Normal Modes (NNMs) analysis for the case of three-to-one (3:1) internal resonance of a slender simply supported beam in presence of compressive axial load resting on a nonlinear elastic foundation is studied. Using the Euler?CBernoulli beam model, the governing nonlinear PDE of the beam??s transverse vibration and also its associated boundary conditions are extracted. These nonlinear motion equation and boundary condition relations are solved simultaneously using four different approximate-analytical solution techniques, namely the method of Multiple Time Scales, the method of Normal Forms, the method of Shaw and Pierre, and the method of King and Vakakis. The obtained results at this stage using four different methods which are all in time?Cspace domain are compared and it is concluded that all the methods result in a similar answer for the amplitude part of the transverse vibration. At the next step, the nonlinear normal modes are obtained. Furthermore, the effect of axial compressive force in the dynamic analysis of such a beam is studied. Finally, under three-to-one-internal resonance condition the NNMs of the beam and the steady-state stability analysis are performed. Then the effect of changing the values of different parameters on the beam??s dynamic response is also considered. Moreover, 3-D plots of stability analysis in the steady-state condition and the beam??s amplitude frequency response curves are presented.     

Analysis of Heat and Mass Transfer in a Vertical Annular Porous Cylinder Using FEM

The present study is intended to study heat and mass transfer in a vertical annular cylinder embedded with saturated porous medium. The inner surface of cylinder is maintained at uniform wall temperature and uniform wall concentration. The governing partial differential equations are non-dimensionalised and solved by using finite element method (FEM). The porous medium is discritised using triangular elements with uneven element size. Large number of smaller-sized elements are placed near the walls of the annulus to capture the smallest variation in solution parameters. The results are reported for both aiding and opposing flows. The effects of various non-dimensional numbers such as buoyancy ratio, Lewis number, Rayleigh number, aspect ratio, etc on heat and mass transfer are discussed. The temperature and concentration profiles are presented.     

Unique Outcomes of Internal Heat Generation and Thermal Deposition on Viscous Dissipative Transport of Viscoplastic Fluid over a Riga-Plate

Boundary layer stagnation point flow of Casson fluid over a Riga plate of variable thickness is investigated in present article. Riga plate is an electromagnetic actuator consists of enduring magnets and gyrated aligned array of alternating electrodes mounted on a plane surface. Physical problem is modeled and simplified under appropriate transformations. Effects of thermal radiation and viscous dissipation are incorporated. These differential equations are solved by Keller Box Scheme using MATLAB. Comparison is given with shooting techniques along with RangeKutta Fehlberg method of order 5. Graphical and tabulated analysis is drawn. The results reveal that Eckert number,radiation and fluid parameters enhance temperature whereas they contribute in lowering rate of heat transfer. The numerical outcomes of present analysis depicts that Keller Box Method is capable and consistent to solve proposed nonlinear problem with high accuracy.     

Step-wise laser excitation of the 4snf 3F Rydberg states of neutral zinc

The new experimental results on the effective quantum numbers and term energies of the highly excited odd-parity 4s4d ³D_1,2,3 →4snf ³F_2,3,4 Rydberg transitions of zinc have been presented. The experiment was performed using the three dye lasers simultaneously pumped by the second harmonic (532?nm) of the Q-switched Nd:YAG laser. The new observation includes the 4snf ³F₃ (12?≤n?≤?50) series excited from the 4s4d ³D₂ intermediate level. In addition, the 4snf ³F₂ (12?≤n?≤?28) and 4snf³F₄ (12?≤n?≤?33) series are observed from the thermally populated 4s4d ³D_1,3 fine structure components. The ionization potential of zinc has been determined from the unperturbed 4snf ³F₃ series as 75769.31?±?0.15?cm^?1, which is in excellent agreement with the previously reported value.     

Impact of Internal Heat Source on Mixed Convective Transverse Transport of Viscoplastic Material under Viscosity Variation

This communication addresses the impact of heat source/sink along with mixed convection on oblique flow of Casson fluid having variable viscosity. Similarity analysis has been utilized to model governing equations, which are simplified to set of nonlinear differential equations. Computational procedure of shooting algorithm along with 4th order Range-Kutta-Fehlberg scheme is opted to attain the velocity and temperature distributions. Impact of imperative parameters on Casson fluid flow, temperature, significant physical quantities such as skin friction, local heat flux and streamlines are displayed via graphs.     

Synthesis of some new triamide derivatives via Ugi five-component reaction in aqueous solution

Triamide derivatives have been synthesized in good yields in a novel, one-pot, five-component, and efficient process by the reaction of Z-oxazolone, water, primary amines, aldehydes, isocyanides, in the presence of catalytic amount of KAl(SO₄)₂·12H₂O (alum) as a non-toxic, reusable, inexpensive, and easily available reagent via Ugi reaction in aqueous solution.     

Thermal transport of rate-type fluid impinging obliquely over a heated sheet

The main objective of this study is to examine the two-dimensional (2D) oblique Oldroyd-B flow on a stretching heated sheet. The flow governing problem is converted into nonlinear ordinary differential equations through proper scaling transformations. The prevailing set of equations is solved computationally with a tolerance level of \({ 10}^{-5}\). The velocity and temperature of a fluid model under consideration are portrayed to discuss the influence of all associated parameters on momentum and thermal characteristics. Heat flux at the wall has been computed numerically and analysed in a physical manner. The results obtained depict a reversed flow region for non-positive values of shear flow components once a free parameter is varied. It is noticed that heat transfer at the wall drops due to a rise in Deborah number \(\beta _{1}\) as well as Biot number \(\hbox {Bi}\).     

Effects of inclined magnetic field on mixed convection in a nanofluid filled double lid-driven cavity with volumetric heat generation or absorption using finite element method

A computational analysis has been performed on mixed convection in a double sided lid-driven cavity in the presence of volumetric heat generation or absorption. Effects of inclined magnetic field are also studied. The governing parameters are solved via Galerkin weighted residual finite element method in space and the Crank–Nicolson in time. Governing parameters are nanoparticle volume fraction (0.0?≤???≤?0.04), Richardson number (0.01?≤?Ri?≤?10), internal heat generation or absorption parameter $(?10\le q\le 10),$ inclination angle of magnetic field (0°?≤?γ?≤?90°) and Hartmann number (0?≤?Ha?≤?100). It is observed that the highest heat transfer is obtained in case of the maximum value of heat absorption. As a further finding, heat transfer decreases with increasing of Hartmann number and increases with increasing of nanoparticle volume fraction.     

A Numerical Investigation of Nanocomposite of Copper and Titanium Dioxide in Water Based Fluid Influenced by Instigated Magnetic Region

Presence of external electrical field plays a vital role in heat transfer and fluid flow phenomena. Keeping this in view present article is a numerical investigation of stagnation point flow of water based nanoparticles suspended fluid under the influence of induced magnetic field. A detailed comparative analysis has been performed by considering Copper and Titanium dioxide nanoparticles. Utilization of similarity analysis leads to a simplified system of coupled nonlinear differential equations, which has been tackled numerically by means of shooting technique followed by Runge-Kutta of order 5. The solutions are computed correct up to 6 decimal places. Influence of pertinent parameters is examined for fluid flow, induced magnetic field, and temperature profile. One of the key findings includes that magnetic parameter plays a vital role in directing fluid flow and lowering temperature profile. Moreover, it is concluded that Cu-water based nanofluid high thermal conductivity contributes in enhancing heat transfer efficiently.     

Transverse Transport of Polymeric Nanofluid under Pure Internal Heating: Keller Box Algorithm

The present work aims to investigate transverse Oldroyd-B nanofluid flow on a stretched panel with consideration of internal heat generation. Buongiorno model is utilized to study influence of thermophoresis and Brownian motion effects. A numerical procedure known as Keller box algorithm is used to solve the governed physical model. Graphically velocity, temperature and concentration of nanoparticles are expressed. Also, concerned physical measures such as heat and mass transfer are investigated numerically. The simulations performed revealed that fluid parameters play a significant role in heat transfer under Brownian motion and thermophoresis effects. Local heat flux is elevated while local mass flux is suppressed with enhancing Brownian motion parameter. Streamlines pattern exhibits that flow is more inclined in the presence of Deborah number effects. To the best of our knowledge, transverse flow of an Oldroyd-B type fluid which incorporates the thermal relaxation effects has never been reported before in the presence of Brownian motion and internal heating phenomenon. Therefore we intend to discuss these features in detail. The obtained results are a novel contribution, which can be benchmark for further relevant academic research related to polymer industry.