Journal of Applied and Computational Mechanics
Volume:5 Issue: 4, Spring 2019

This paper investigates the axial unsteady flow of a generalized Burgers’ fluid with fractional constitutive equation in a circular micro-tube, in presence of a time-dependent pressure gradient and an electric field parallel to flow direction and a magnetic field perpendicular on the flow direction. The mathematical model used in this work is based on a time-nonlocal constitutive equation for shear stress with time-fractional Caputo-Fabrizio derivatives; therefore, the histories of the velocity gradient will influence the shear stress and fluid motion. Thermal transport is considered in the hypothesis that the temperature of the cylindrical surface is constant. Analytical solutions for the fractional differential momentum equation and energy equation are obtained by employing the Laplace transform with respect to the time variable t and the finite Hankel transform with respect to the radial coordinate r. It is important to note that the analytical solutions for many particular models such as, ordinary/fractional Burgers fluids, ordinary/fractional Oldryd-B fluids, ordinary/fractional Maxwell fluids and Newtonian fluids, can be obtained from the solutions for the generalized fractional Burgers' fluid by particularizing the material coefficients and fractional parameters. By using the obtained analytical solutions and the Mathcad software, we have carried out numerical calculations in order to analyze the influence of the memory parameters and magnetic parameter on the fluid velocity and temperature. Numerical results are presented in graphical illustrations. It is found that ordinary generalized Burgers’ fluids flow faster than the fractional generalized Burgers’ fluids.

Effects of the uniform transverse magnetic field on the transient free convective flows of a nanofluid with generalized thermal transport between two vertical parallel plates have been analyzed. The fluid temperature is described by a time-fractional differential equation with Caputo derivatives. Closed form of the temperature field is obtained by using the Laplace transform and fractional derivatives of the Wright’s functions. A semi-analytical solution for the velocity field is obtained by using the Laplace transform coupled with the numerical algorithms for the inverse Laplace transform elaborated by Stehfest and Tzou. Effects of the derivative fractional order and physical parameters on the nanofluid flow and heat transfer are graphically investigated.

The primary aim of this manuscript is to present the approximate analytical solutions of the time fractional order α (1<α≤2) Vibration Equation (VE) of large membranes with the use of an iterative technique namely Residual Power Series Method (RPSM). The fractional derivative is defined in the Caputo sense. Example problems have been solved to demonstrate the efficacy of the present method and the results obtained are verified graphically. The convergence analysis of the proposed method has also been included in this article. It is seen that the present method is found to be reliable, very effective and easy to implement for various kinds of fractional differential equations used in science and engineering.

The problem under investigation contains a computational simulation of a specific heat exchanger with complex geometry fins. The problem solved is potentially interesting for researchers and engineers working on solar collectors and aerospace industry. It is known that heat transfer enhancement can be achieved by creating longitudinal vortices in the flow. These vortices can be generated by arc-shaped fins, and a computational analysis of such solar air channels is not a simple task. Therefore, we used a present-day commercial CFD code to solve the problem. The mathematical problem including the main equations and their explanation, as well as the numerical procedure was presented. The impact of arc-fins’ spacings on streamlines and temperature distributions was completely investigated, as well as the heat transfer rate, pressure drop and thermal enhancement factor. The Nusselt number (Nu) and friction loss (f) values of the solar air channel at AR = 1.321 (aspect ratio of channel width-to-height) and S = Pi/2 are found to be around 11.963% and 26.006%; 21.645% and 40.789%; 26.196% and 50.314%; and 30.322% and 58.355% higher than that with S = 3Pi/4, Pi, 5Pi/4 and 3Pi/2, respectively. Importantly, the arc-fins with Re = 12,000 at S = Pi/2 showed higher thermal enhancement performance than the one at S = 3Pi/4, Pi, 5Pi/4 and 3Pi/2 around 2.530%, 6.576%, 6.615% and 6.762%, respectively. This study contains the information which seems to be important for practical engineers.

Nonlinear vibration behavior of beam is an important issue of structural engineering. In this study, a mathematical modeling of a forced nonlinear vibration of Euler-Bernoulli beam resting on nonlinear elastic foundation is presented. The nonlinear vibration behavior of the beam is investigated by using a modified multi-level residue harmonic balance method. The main advantage of the method is that only one nonlinear algebraic equation is generated at each solution level. The computational time of using the new method is much less than that spent on solving the set nonlinear algebraic equations generated in the classical harmonic balance method. Besides the new method can generate higher-level nonlinear solutions neglected by previous multi-level residue harmonic balance methods. The results obtained from the proposed method compared with those obtained by a classical harmonic balance method to verify the accuracy of the method which shows good agreement between the proposed and classical harmonic balance method. Besides, the effect of various parameters such as excitation magnitude, linear and nonlinear foundation stiffness, shearing stiffness etc. on the nonlinear vibration behaviors are examined

Energy development of decaying isotropic turbulence in a 3-D periodic cube with non-rotating or rotating frames of reference is studied through direct numerical simulation using GPU accelerated lattice Boltzmann method. The initial turbulence is isotropic, generated in spectral space with prescribed energy spectrum E(κ)~κm in a range between κmin and κmax. The Taylor microscale Reynolds number Reλ and Rossby number Ro are introduced to characterize the inertial, viscous, and rotational attributes of the system. The focus of this study is on the scalings of early inverse energy transfer and late energy decay in the development of turbulent energy under various conditions through combinations of m, κmin, κmax, Reλ and Ro. First, we demonstrate the validity of the simulation by confirming the quantitative dependence of the decay exponent n on the initial energy spectrum exponent m, at Reλ =255 and Ro=∞, varying the values of m, κmin and κmax. Second, at relatively low Reλ, the decay exponent for different initial spectra statistically fall in respective ranges, all of which agree well with the corresponding analytical predictions. Third, we quantitatively investigate the 3-D inverse energy transfer. Our findings include (i) the exponent of inverse energy transfer spectrum E(κ)~κσ depends on the initial spectrum exponent E(κ) ~ κm: if m<4, σ=m while if m≥4, σ=4; (ii) rotation alters the inverse energy transfer rate when Reλ≤255 and Ro≥0.8; (iii) the energy increase in large scale during inverse energy transfer exhibits a bell shape, the peak of which varies with Reλ and Ro.

In this paper, we have used numerical simulation to study failure of adhesive joints in composite plates. To determine the failure load, adhesive joints are subjected to different types of loading and gradual failure of the joint is studied using the finite element method. The composite material failure theory is implemented into the FEM software. Also different geometries for the joint edge are considered and effect of these geometries and fillet chamfer angle on the failure load are investigated.

A numerical study is performed to analysis the buoyancy convection induced by the parallel heated baffles in an inclined square cavity. The two side walls of the cavity are maintained at a constant temperature. A uniformly thin heated plate is placed at the centre of the cavity. The horizontal top and bottom walls are adiabatic. Numerical solutions of governing equations are obtained using the finite volume method coupled with the upwind and central difference technique. Numerical results of the two-dimensional flow field governed by the Navier-Stokes equations are obtained over a wide range of physical parameters, namely the Rayleigh number, the Hartmann number, the inclined angle of the magnetic parameter and the vortex viscosity parameter. It is observed from the results, the heat transfer rate is reduced when increasing Hartmann number, inclination angle and vortex viscosity parameter. The higher heat transfer rate is obtained based on the Newtonian fluid compared to the micropolar fluid.

This paper presents the numerical elastic solution for a real problem, functionally graded chamber of hydraulic gear pumps under internal pressure. Because of the similarity and complexity for the considering geometry, a bipolar cylindrical coordinate system is used to extract the governing equations. The material properties are considered to vary along the two tangled circles with a power-law function. The two coupled governing equations solved by the differential quadrature method. The results are presented for various material index and show that the complexity in considering geometry and material inhomogeneity can change the stress and displacements value through the geometry efficiently. The results and presented method in this paper for extracting and solving the problem can be used for designing similar geometry more accurate. The results of this research are compared with those reported in the previous work.

Determination of the maximum temperature and its location is the matter of the greatest importance in many technological and scientific engineering applications. In terms of numerical calculations of the heat conduction equation by using uniform mesh increments in space, large computational cost is sometimes countered. However, adaptive grid refinement method could be computationally efficient both in terms of accuracy and execution time. In this work, the numerical solution of the heat conduction equation based on the slide modeling method (SMM) is introduced. This method is based on a pre-determined mesh density approach which divides each homogeneous region into different slides and then assigns higher mesh point densities to slides of interest regarding their relative importance by performing some mathematical calculations. The importance of each region is determined by some formulated weighting factors which rely on the estimation of temperature profiles in all regions and slides. To investigate the accuracy and efficiency of the proposed method, a number of different case studies have been considered. The results all revealed the strength of the proposed SMM in comparison with the conventional method (based on uniform mesh point distribution).

This paper introduces the optimization algorithm to improve search rate in urban path routing problems using viral infection and local search in urban environment. This algorithm operates based on two different approaches including wavelet transform and genetic algorithm. The variables proposed by driver such as degree of difficulty and difficulty traffic are of the essence in this technique. Wavelet transform as the first part of proposed algorithm derives edges risk. Finally, multistage genetic algorithm operates to find the optimal solution which is defined as the shortest path. The proposed algorithm is applied to the case study. The performances of the algorithm is investigated by comparing with other methods.

In recent years, the use of offshore wind turbines has been considered on the agenda of the countries which have a significant maritime boundary due to more speed and stability of wind at sea. The aim of this study is to investigate the effect of wind turbulence on the aero-hydrodynamic behavior of offshore wind turbines with a monopile platform. Since in the sea, the wind turbine structures are under water and structures interactions, the dynamic analysis has been conducted under combined wind and wave loadings. The offshore wind turbines have been investigated under two models of normal and severe wind turbulence, and the results of this study show that the amplitude of fluctuation of dynamic response is increased with increasing amount of wind turbulence, and this increase is not necessarily observed in the mean values of responses. Therefore, conducting the dynamic analysis is inevitable in order to observe the effect of wind turbulence on the structures response.

In this work, free convection of Cu-water nanofluid in an enclosure by considering internally heat generated in the porous circular cavity and the impacts of viscous dissipation are numerically evaluated by control volume finite element method (CVFEM). The outer and inner sides of the circular porous enclosure are maintained at a fixed temperature while insulating the other two walls. The impacts of diverse effective parameters including the Rayleigh number, viscous dissipation, and nanofluid concentration on features of heat transfer and fluid flow are examined. Moreover, a new correlation for the average Nusselt number is developed according to the study’s active parameters. It can be deduced by the results that the maximum value of the temperature is proportional to the viscous dissipation parameter.

In this study, the tensile strength, impact strength, and the hardness of the weld are determined. A criterion is proposed for describing the effect of residual stress on the weld mechanical properties. Dimensionless parameters such as Rya (the average of residual stress over the material yield strength), Rym (the maximum residual stress over the material yield strength), Ru2 (the difference in the residual stress over the material ultimate strength), and Ru3 (the difference ratio between the maximum and minimum of three-dimensional residual stresses over the material ultimate strength) are presented to describe the influence of residual stresses on the actual mechanical behavior of the welded pipe. Maximum Rya criterion and lowest strength are obtained at the weld gap center on the external surface of the pipe. The sharp decline in Ru2 criteria is consistent with the severe reduction in impact strength perpendicular to the weld gap.

This paper reports on the analysis of the signals sent by accelerometers fixed on the axles of a vehicle which passes over a bridge. The length of the bridge is divided into some parts and the transmissibility measurement is applied to the signals recorded by two following instrumented axles. As the transmissibility procedure is performed on the divided signals, the method is called Short Time Transmissibility Measurement. Afterwards, a rescaling process is accomplished in order to estimate the bridge mode shapes. The numerical results indicate that the method can calculate the mode shapes of the bridge accurately. It is demonstrated that short time transmissibility method does not depend on the excitation characteristics contrary to the other related methods which assume that the excitation should be white noise. Generally, the bridge mode shapes may be invisible due to the excitation exerted by the road profile. This issue is also resolved by subtracting the signals from the successive axles. Finally, the signals are contaminated with noise and the robustness of the method is investigated.

There is a requirement to find accurate parameters to accomplish precise dimensional accuracy, excellent surface integrity and maximum MRR. This work studies the influence of various cutting parameters on output parameters like Cutting force, Surface roughness, Flatness, and Material removal rate while face milling. A detailed finite element model was developed to simulate the face milling process. The material constitutive behavior is described by Johnson-Cook material model and the damage criteria is established by Johnson-Cook damage model. The result indicate significant effects of all three cutting parameters on MRR and both feed rate and depth of cut have significant effect on cutting force. Also, feed rate has significant effect on PEEQ and none of the parameters have effect on flatness.

A semi-analytical investigation has been carried out to analyze unsteady MHD second-grade flow under the Dual-Phase-Lag (DPL) heat and mass transfer model in a vertical microchannel filled with porous material. Diffusion thermo (Dufour) effects and homogenous chemical reaction are considered as well. The governing partial differential equations are solved by using the Laplace transform method while its inversion is done numerically using INVLAP subroutine of MATLAB. The numerical values of fluid velocity, fluid temperature and species concentration are demonstrated through graphs while the numerical values of skin friction, heat transfer rate and mass transfer rate presented in tabular form for different values of parameters that govern the flow. For the first time, a comparison of heat transfer utilizing the classical Fourier’s heat conduction model, hyperbolic heat conduction Cattaneo-Vernotte (CV) model, and the DPL model is carried out for the flow of a second grade fluid. It is found that the differences between them vanish at dimensionless time t=0.4 (for temperature) and at t=0.5 (for velocity), i.e. at a time where the system reaches steady state. The influence of phase lag parameters in both thermal and solutal transport on the fluid flow characteristics have been deciphered and analyzed. The results conveyed through this article would help researchers to understand non-Fourier heat and mass transfer in the flow of second-grade fluids which may play a vital role in the design of systems in polymer industries.

In this article, the electro-osmotic flow of Oldroyd-B fluid in a circular micro-channel with slip boundary condition is considered. The corresponding fractional system is represented by using a newly defined time-fractional Caputo-Fabrizio derivative without singular kernel. Closed form solutions for the velocity field are acquired by means of Laplace and finite Hankel transforms. Additionally, Stehfest’s algorithm is used for inverse Laplace transform. The solutions for fractional Maxwell, ordinary Maxwell and ordinary Newtonian fluids are obtained as limiting cases of the obtained solution. Finally, the influence of fractional and some important physical parameters on the fluid flow are spotlighted graphically.

In the present work, a mathematical model is developed and analyzed to study the influence of nanoparticle concentration through Brownian motion and thermophoresis diffusion. The governing system of PDEs is transformed into a coupled non-linear ODEs by using suitable variables. The converted equations are then solved by using robust shooting method with the help of MATLAB (bvp4c). The impacts of dynamic parameters on the flow, energy and concentration are discussed graphically. It is noticed that the mass transfer rate in case of regular fluid is lower than that of nanofluid and the axial velocity converges to the boundary very fast in case of temperature dependent viscosity case than the regular viscous case.

In this paper, heat and mass transfer in the unsteady squeezing flow between parallel plates is analyzed using a perturbation-iteration algorithm. The similarity transformation is used to transform the governing partial differential equations into ordinary differential equations, before being solved. The solutions of the velocity, temperature and concentration are derived and sketched to explain the influence of various physical parameters. The convergence of these solutions is also discussed. The numerical results of skin friction coefficient, Nusselt number and Sherwood number are compared with previous works. The results show that the method which has been used, in this paper, gives convergent solutions with good accuracy.