Analysis of Nonlinear Dynamic Behaviour of Nanobeam resting on Winkler and Pasternak Foundations

Dynamic modeling of nanobeam under stretching and two-parameter foundation effects result in nonlinear equations that are very difficult to find exact analytical solutions. In this study, variation iteration method is used to develop approximate analytical solutions to nonlinear vibration analysis of nanobeam under the effects of stretching and Winkler and Pasternak foundations. The governing equation of motion for the nanotube was derived based on Euler-Bernoulli beam theory. The developed approximate analytical solutions for the governing equation are validated the results of other methods of analysis, are also used to carry out effects of some model parameters on the dynamic behaviour of the nanobeam.  These analytical solutions can serve as a starting point for a better understanding of the relationship between the physical quantities in the problems as it provides clearer insights to understanding the problems in comparison with numerical methods

On Modeling for Prediction of the Effects of Carbon-Monoxide on Humans Operating under Continuous and Periodic Exposures

The advancements in technological innovations and the utilizations of some technological products or research outcomes have adversely affected the environment and in consequence, continuously pose serious threats to future survival of humans. To counter these assaults of the resultant environmental pollution and the threats of further degradation of the environment, the basic recommended approach for predicting the impact of the pollution and for the determination of the risk assessment strategies is through the use of mathematical models. In the list of various pollutants, carbon monoxide has been established as a major pollutant that seriously affects human health by converting the Oxyhemoglobin (O2Hb) in the blood to carboxyhemoglobin (COHb). Therefore, this paper presents mathematical models for the computations of carbon-monoxide and carboxyhemoglobin in the blood for the cases of humans under environmental and occupational exposures i.e. operating under continuous and periodic exposures to the pollutant. The developed models are solved analytically using Laplace transforms. The computed results show good agreement with the established experimental results. Using the percentage of COHb in the blood as a good index of health effects of carbon monoxide (CO) on humans, the computed COHb from the developed models is used to predict the effects of CO on human health. On the validation of the developed models, the computed results show good agreement with experimental results. Also, effects of the models parameters on the amount of COHb in the blood. This work will assist in evaluating the technological injuries, effectively controlling our pollutants emissions and also as a tool for designing and developing better equipment and engines with lower or zero emissions

Free Convection Flow and Heat Transfer of Nanofluids of Different Shapes of Nano-Sized Particles over a Vertical Plate at Low and High Prandtl Numbers

In this paper, free convection flow and heat transfer of nanofluids of differently-shaped nano-sized particles over a vertical plate at very low and high Prandtl numbers are analyzed.  The governing systems of nonlinear partial differential equations of the flow and heat transfer processes are converted to systems of nonlinear ordinary differential equation through similarity transformations. The resulting systems of fully-coupled nonlinear ordinary differential equations are solved using a differential transformation method - Padé approximant technique. The accuracy of the developed approximate analytical methods is verified by comparing the results of the differential transformation method - Padé approximant technique with those of previous works as presented in the literature. Thereafter, the analytical solutions are used to investigate the effects of the Prandtl number, the nanoparticles volume-fraction, the shape and the type on the flow and heat transfer behaviour of various nanofluids over the flat plate. It is observed that as the Prandtl number and volume-fraction of the nanoparticles in the basefluid increase, the velocity of the nanofluid decreases while the temperature increases.  Also, the maximum decrease in velocity and the maximum increase in temperature are recorded in lamina-shaped nanoparticles, followed by platelets, cylinders, bricks, and sphere-shaped nanoparticles, respectively. Using a common basefluid for all nanoparticle types, it is established that the maximum decrease in velocity and the maximum increase in temperature are recorded in TiO2 followed by CuO, Al2O3 and SWCNTs nanoparticles, respectively. It is hoped that the present study will enhance the understanding of free convection boundary-layer problems as applied in various industrial, biological and engineering processes

Thermal Performance and Optimum Design Analysis of Fin with Variable Thermal Conductivity Using Double Decomposition Method

In this paper, thermal performance and optimum design analysis of straight fin with variable thermal conductivity is carried out using double decomposition method. The developed heat transfer models are used to analyze the thermal performance, establish the optimum thermal design parameters and also, investigate the effects of thermo-geometric parameters and thermal conductivity (non-linear) parameters on the temperature distribution, heat transfer and thermal performance of the longitudinal rectangular fin. From the results, it shows that the fin temperature distribution, the total heat transfer, the fin effectiveness, and the fin efficiency are significantly affected by the thermo-geometric and thermal parameters of the fin. The analysis revealed that the operational parameters must be carefully chosen to ensure that the fin retains its primary purpose of removing heat from the primary surface.  The results obtained in this analysis provides platform for improvement in the design of fin in heat transfer equipment

INVESTIGATION OF THE DYNAMIC BEHAVIOUR OF NON-UNIFORM THICKNESS CIRCULAR PLATES RESTING ON WINKLER AND PASTERNAK FOUNDATIONS

The study of the dynamic behaviour of non-uniform thickness circular plate resting on elastic foundations is very imperative in designing structural systems. This present research investigates the free vibration analysis of varying density and non-uniform thickness isotropic circular plates resting on Winkler and Pasternak foundations. The governing differential equation is analysed using the Galerkin method of weighted residuals. Linear and nonlinear case is considered, the surface radial and circumferential stresses are also determined. Thereafter, the accuracy and consistency of the analytical solutions obtained are ascertained by comparing the existing results available in pieces of literature and confirmed to be in a good harmony. Also, it is observed that very accurate results can be obtained with few computations. Issues relating to the singularity of circular plate governing equations are handled with ease. The analytical solutions obtained are used to determine the influence of elastic foundations, homogeneity and thickness variation on the dynamic behaviour of the circular plate, the effect of vibration on a free surface of the foundation as well as the influence of radial and circumferential stress on mode shapes of the circular plate considered. From the results, it is observed that a maximum of 8.1% percentage difference is obtained with the solutions obtained from other analytical methods. Furthermore, increasing the elastic foundation parameter increases the natural frequency. Extrema modal displacement occurs due to radial and circumferential stress. Natural frequency increases as the thickness of the circular plate increases, Conversely, a decrease in natural frequency is observed as the density varies. It is envisioned that; the present study will contribute to the existing knowledge of the classical theory of vibration

Perturbation Methods to Analysis of Thermal, Fluid Flow and Dynamics Behaviors of Engineering Systems

This chapter presents the applications of perturbation methods such as regular and homotopy perturbation methods to thermal, fluid flow and dynamic behaviors of engineering systems. The first example shows the utilization of regular perturbation method to thermal analysis of convective-radiative fin with end cooling and thermal contact resistance. The second example is concerned with the application of homotopy perturbation method to squeezing flow and heat transfer of Casson nanofluid between two parallel plates embedded in a porous medium under the influences of slip, Lorentz force, viscous dissipation and thermal radiation. Additionally, the dynamic behavior of piezoelectric nanobeam embedded in linear and nonlinear elastic foundations operating in a thermal-magnetic environment is analyzed using homotopy perturbation method which is presented in the third example. It is believed that the presentation in this chapter will enhance the understanding of these methods for the real world applications

Nonlinear Vibration Analysis of Thermo-Magneto-Mechanical Piezoelectric Nanobeam Embedded in Multi-Layer Elastic Media based on Nonlocal Elasticity Theory

The present article focuses on the investigations of electromechanical thermo-magnetic coupled effects on the nonlinear vibration of single-walled carbon nanobeam embedded in Winkler, Pasternak, quadratic and cubic nonlinear elastic media for simply supported and clamped boundary conditions are investigated. From the parametric studies, it is shown that the frequency of the nanobeam increases at low temperature but decreases at the high temperatures. The nonlocal parameter decreases the frequencies of the piezoelectric nanobeam. An increase in the quadratic nonlinear elastic medium stiffness causes a decrease in the first mode of the nanobeam with clamped-clamped supports and an increase in all modes of the simply supported nanobeam at both low and high temperature. When the magnetic force, cubic nonlinear elastic medium stiffness, and amplitude increase, there is an increase in all mode frequency of the nanobeam. A decrease in Winkler and Pasternak elastic media constants and increase in the nonlinear parameters of elastic medium results in an increase in the frequency ratio. The frequency ratio increases as the values of the dimensionless nonlocal, quadratic and cubic elastic medium stiffness parameters increase. However, the frequency ratio decreases as the values of the temperature change, magnetic force, Winkler and Pasternak layer stiffness parameters increase. An increase in the temperature change at high temperature reduces the frequency ratio but at low or room temperature, increase in temperature change, increases the frequency ratio of the structure nanotube. This work will greatly benefit in the design and applications of nanobeams in thermal and magnetic environments

Nonlinear Vibration Analysis of Thermo-Magneto-Mechanical Piezoelectric Nanobeam Embedded in Multi-Layer Elastic Media based on Nonlocal Elasticity Theory

The present article focuses on the investigations of electromechanical thermo-magnetic coupled effects on the nonlinear vibration of single-walled carbon nanobeam embedded in Winkler, Pasternak, quadratic and cubic nonlinear elastic media for simply supported and clamped boundary conditions are investigated. From the parametric studies, it is shown that the frequency of the nanobeam increases at low temperature but decreases at the high temperatures. The nonlocal parameter decreases the frequencies of the piezoelectric nanobeam. An increase in the quadratic nonlinear elastic medium stiffness causes a decrease in the first mode of the nanobeam with clamped-clamped supports and an increase in all modes of the simply supported nanobeam at both low and high temperature. When the magnetic force, cubic nonlinear elastic medium stiffness, and amplitude increase, there is an increase in all mode frequency of the nanobeam. A decrease in Winkler and Pasternak elastic media constants and increase in the nonlinear parameters of elastic medium results in an increase in the frequency ratio. The frequency ratio increases as the values of the dimensionless nonlocal, quadratic and cubic elastic medium stiffness parameters increase. However, the frequency ratio decreases as the values of the temperature change, magnetic force, Winkler and Pasternak layer stiffness parameters increase. An increase in the temperature change at high temperature reduces the frequency ratio but at low or room temperature, increase in temperature change, increases the frequency ratio of the structure nanotube. This work will greatly benefit in the design and applications of nanobeams in thermal and magnetic environments

Heat transfer study in a convective-radiative fin with temperature-dependent thermal conductivity and magnetic field using variation parameters method

In this work, a heat transfer study is carried out in a convective-radiative straight fin with temperature-dependent thermal conductivity and a magnetic field using the variation of parameters method. The developed heat transfer model is used to analyze the thermal performance, establish the optimum thermal design parameters and investigate the effects of thermo-geometric parameters and non-linear thermal conductivity parameters on the thermal performance of the fin. The results obtained are compared with the results in literature and good agreements are found. The analysis can serve as basis for comparison of any other method of analysis of the problem and it also provides a platform for improvement in the design of fin in heat transfer equipment