Journal of Applied and Computational Mechanics
Volume:10 Issue: 1, Winter 2024

An exact solution is proposed for describing the steady-state and unsteady gradient Poiseuille shear flow of a viscous incompressible fluid in a horizontal infinite layer. This exact solution is described by a polynomial of degree N with respect to the variable y where the coefficients of the polynomial depend on the coordinate z and time t, a boundary value problem for a steady flow has been considered and the velocity field with a quadratic dependence on the horizontal longitudinal (horizontal) coordinate y is considered. The coefficients of the quadratic form depend on the transverse (vertical) coordinate z. Pressure is a linear form of the horizontal coordinates x and y. The exact solution of the constitutive system of equations for the boundary value problem is considered here to be polynomial. The boundary value problem is solved for a non-uniform distribution of velocities on the upper non-deformable boundary of an infinite horizontal liquid layer. The no-slip condition is set on the lower non-deformable boundary. The exact solution obtained is a polynomial of the tenth degree in the coordinates x, y and z. Stratification conditions are obtained for the velocity field, for the stress tensor components, and for the vorticity vector. The constructed exact solution describes the counterflows of a vertically swirling fluid outside the field of the Coriolis force. Shear stresses are tensile and compressive relative to the vertical (transverse) coordinates and relative to the horizontal (longitudinal) coordinates. The article presents formulas illustrating the existence of zones of differently directed vortices.

Today, the use of electricity sources is increasing as cities are growing. With the increasing use of mineral oils for transformers cooling in the distribution network, due to the problems encountered using these oils, an alternative fluid should be used inside the transformers instead of mineral oils. Therefore, mineral oils should be replaced with fluids that are more compatible with nature due to the environmental hazards and high costs. Hence, vegetable oils can be used as suitable alternatives for the mineral oils in transformers due to their low risk and the renewability. On the other hand, compared to the mineral oils that have a fire point of about 151 Celsius degrees, vegetable oils have fire points higher than 311 Celsius degrees. As a result, from this viewpoint, they are considered as harmless fluids. Vegetable oils are simply degraded in the nature, and due to their different chemical structures compared to the mineral oils, they can increase the life of the equipment. Besides, the most important point is that they improve the transformer cooling performance, in terms of thermal analysis. Thus, in this paper, the distribution transformer electromagnetic-thermal analysis and conjugate heat transfer, in presence of different types of vegetable oils, and different types of cores such as grain-oriented silicon steel, amorphous and vitroperm alloy are investigated. Afterwards, the obtained results, especially hot spot temperature, are compared with distribution transformer containing mineral oil. ANSYS software has also been used for simulations.

In the present work, a displacement-based high-order shear deformation theory is introduced for the static response of functionally graded plates. The present theory is variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. By dividing the transverse displacement into the bending and shear parts and making further assumptions, the number of unknowns and equations of motion of the present theory is reduced a and hence makes them simple to use. The material properties of the plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of volume fractions of material constituents. The equilibrium equations of a functionally graded plate are given based on the higher order shear deformation theory. The numerical results presented in the paper are demonstrated by comparing the results with solutions derived from other higher-order models found in the literature and the present numerical results of Finite Element Analysis (FEA). In the numerical results, the effects of the grading materials, lay-up scheme and aspect ratio on the normal stress, shear stress and static deflections of the functionally graded sandwich plates are presented and discussed. It can be concluded that the proposed theory is accurate, elegant and simple in solving the problem of the bending behavior of functionally graded plates.

The solar vortex engine (SVE) aims to replace the tall and expensive chimney structure in solar updraft power plants by a shorter less expensive structure named the vortex generator. In this study, the entire SVE system is simulated by CFD to determine the appropriate location for the turbine unit as well as prove the capability of the vortex generator in replacing the chimney. Three different cases for the SVE are considered and compared to corresponding cases of the solar chimney power plant (SCPP). Results revealed that the optimum turbine location is at the outlet hole of the vortex generator. An updraft air velocity of 1.82 m/s was achieved at the outlet hole, compared to 1.56 m/s at the base of a solar chimney with the same diameter as the upper hole. The consideration of the turbine pressure drop did not affect the formation and preservation of the air vortex. So, the 1 m high vortex generator successfully replaced the 8.6 m chimney component in solar updraft power plants, greatly reducing the cost and construction complexity of the plant. The vortex generator accelerated the air delivered from the solar collector, increasing its velocity by 14 times. The SVE’s power output is directly proportional to the static pressure drop across the turbine. The mean difference values along the air vortex field between the cases with and without a turbine are 0.67 Pa and 0.026 m/s for the static pressure drop and velocity magnitude, respectively.

The paper analyzes the influence of cutouts on the buckling of shallow shells with double curvature. Based on the Timoshenko-Reissner hypothesis, a mathematical model is presented that considers transverse shifts, material orthotropy, geometric nonlinearity and structural weakening by cutouts. Cutouts are specified discretely by single columnar functions. The computational algorithm is based on the Ritz method and the Newton method. The implementation of the algorithm is carried out in the Maple 2022 software package. To study the buckling, the Lyapunov criterion is adopted. Calculations of the buckling of flat shells of double curvature with square cuts, graphs of the dependence of deflections on loads and deflection fields are given. Accounting for the structural cutouts leads to a decrease in the critical load. At the same time, for the considered problems, it is found that the decrease in the critical load does not exceed 25 % for the cutout volume not exceeding 10 % of the shell volume.

We define a new class of linear canonical wavelet transform (LCWT) and study its properties like inner product relation, reconstruction formula and also characterize its range. We obtain Donoho-Stark’s uncertainty principle for the LCWT and give a lower bound for the measure of its essential support. We also give the Shapiro’s mean dispersion theorem for the proposed LCWT.

Multidirectional torsional hysteretic damper is a new type of damper that can be used to isolate and dissipate seismic effects on a structure. It can be designed to have a controllable post-elastic stiffness and exhibit high levels of damping as well as stable cyclic response. In this article, while offering a simplified numerical relationship for force-displacement response of the damper, the structure that is fitted with this innovative type of damper is optimized using the harmony search optimization procedure with discrete design variables. Numerical experiments show that the harmony search methodology can determine the damper parameters with high computational efficiency and outperform genetic algorithm and simulated annealing procedure in this regard.

Manual wheelchair users rely on their upper limbs for independence and daily activities. The high incidence of upper limb injuries can be attributed to the significant muscular demands imposed by propulsion as a repetitive movement. People with spinal cord injury are at high risk for upper limb injuries, including neuromusculoskeletal pathologies and nociceptive pain, as human upper limbs are poorly designed to facilitate chronic weight-bearing activities, such as manual wheelchair propulsion. Comprehending the underlying biomechanical mechanisms of motor control and developing appropriate rehabilitation tasks are essential to deal with the effects of poor motor control on the performance of manual wheelchair users and prevent long-term upper limb disability, which can interrupt electrical signals between the brain and muscles. Functional electrical stimulation utilizes low-intensity electrical signals to artificially generate body movements by stimulating the damaged peripheral nerves of patients with impaired motor control. Therefore, this study investigates the central nervous system strategy to control human movements, which can be used for task-specific functional electrical stimulation rehabilitation therapy. To this aim, two degrees of freedom musculoskeletal model of the upper limb, including six muscles, is developed, and an optimal controller consisting of two separate optimal parts is proposed to track the desired trajectories in the joint space and estimate the optimal muscle activations regarding physiological constraints. The simulation results are validated with electromyography datasets collected from twelve participants. This study's primary advantages are generating optimal joint torques, accurate trajectory tracking, and good similarities between estimated and measured muscle activations.

This study introduces a two-dimensional thermoelastic model for a homogeneous isotropic half-space with double porosity underlying an inviscid liquid half-space featuring temperature variations. The model incorporates the three-phase lag (TPL) heat equation and reveals that in the solid half-space, four coupled longitudinal waves intertwine with one uncoupled transverse wave, while one mechanical wave ripples through the liquid half-space. The investigation highlights dispersion, attenuation, and other effects affected by the thermal properties and the presence of voids. Using plane wave solutions and boundary conditions at the interface, a concise expression for the frequency equation of the model has been derived. Furthermore, the magnitudes of the displacements in the solid half-space and liquid half-spaces, the temperature change, and the volume fractional fields at the interface have been precisely determined. In the graphical section, computer-simulated results of various wave profiles for magnesium crystal material have been generated for different heat conduction thermoelastic models. The study's implications span various fields, such as hydrology, engineering, ultrasonics, navigation, and electronics.

Nanofluid is an innovative technology that is essential in biomedical applications. A nanofluid study of human blood flow mathematically is more favorable since it provides a hypothesis for complex systems faster and is cost-saving. Academic researchers have expressed interest in investigating the characteristics of Casson nanofluid flow within a cylindrical structure, which serves as a representative model for the flow of blood in constricted human arteries. However, slip velocity boundary conditions were considered by only a certain number of researchers. The goal of this study is to develop mathematical modelling of Casson fluid flow with gold nanoparticles in the slip cylinder. The impacts of convective heat transfer, magnetohydrodynamics (MHD), and porous medium are also investigated. The Tiwari-Das nanofluid model is utilized in the governing equations. Then, the governing equations with the related boundary conditions are transformed into dimensionless form. The analytical solutions were obtained through the use of the Laplace transform and the finite Hankel transform in combination. The results of nanofluid velocity, temperature, skin friction, and Nusselt number are analyzed through the use of graphs and tables containing relevant parameters. Slip velocity causes an increment in blood velocity and a decrement in skin friction. Blood velocity and temperature are enhanced as the nanoparticles' volume fraction is increased. It is significant in cancer treatment to increase the heat transfer rate at targeted cancerous cells.

This paper explores the incorporation of aramid fibers, recognized for their high mechanical flexibility and low thermal conductivity (TC), to serve as reinforcing agents within the highly porous aerogel matrix in order to overcome their fragility and weak mechanical structure that impose limitations on their practical utility especially in piping insulation. The thermal properties are determined using a micromechanical modeling approach that considers parameters such as temperature, fiber volume fraction, thermal conductivity, and porosity of the silica aerogel. For specific conditions, including an Aramid fiber radius of 6 microns, a silica aerogel thermal conductivity of 0.017 W.m-1</sup>.K-1</sup>, and a porosity of 95%, the resulting AFRA composite exhibits an Effective Thermal Conductivity (ETC) of 0.0234 W.m-1</sup>.K-1</sup>. Notably, this value is lower than the thermal conductivity of air at ambient temperature. The findings are further validated through experimental and analytical techniques. A response surface methodology (RSM) based on Box-Behnken design (BBD) is employed. This approach leads to the development of a quadratic equation intricately relating the key parameters to the ETC of the AFRA. The aim is optimization, identifying target optimal values for these parameters to further enhance the performance of AFRA composites.

In order to improve the design of the actuators of a Dragon Fly prototype, we study the loads applied to the actuators in operation. Both external and inertial forces are taken into account, as well as internal loads, for the purposes of evaluating the influence of the compliance of the arms on that of the "end-effector". We have shown many inadequacies of the arms regarding the stiffness needed to meet the initial design requirements. In order to reduce these inadequacies, a careful structural analysis of the stiffness of the actuators is carried out with a FEM technique, aimed at identifying the design methodology necessary to identify the mechanical elements of the arms to be stiffened. As an example, the design of the actuators is presented, with the aim of proposing an indirect calibration strategy. We have shown that the performances of the Dragon Fly prototype can be improved by developing and including in the control system a suitable module to compensate the incoming errors. By implementing our model in some practical simulations, with a maximum load on the actuators, and internal stresses, we have shown the efficiency of our model by collected experimental data. A FEM analysis is carried out on each actuator to identify the critical elements to be stiffened, and a calibration strategy is used to evaluate and compensate the expected kinematic errors due to gravity and external loads. The obtained results are used to assess the size of the actuators. The sensitivity analysis on the effects of global compliance within the structure enables us to identify and stiffen the critical elements (typically the extremities of the actuators). The worst loading conditions have been evaluated, by considering the internal loads in the critical points of the machine structure results in enabling us the sizing of the actuators. So that the Dragon fly prototype project has been set up, and the first optimal design of the arms has been performed by means of FEM analysis.

Electrothermal pumping is a recently trending method to force highly conductive fluids in a wide range of microfluidics applications with biological processes. Although most polymer fluids (biological and synthetic) are highly conductive exhibiting viscoelastic rheological properties that are relevant to biomedical applications, their behavior under the effect of electrothermal force has not yet been studied. To this aim, the PTT model (non-linear rheological constitutive equation) and electrothermal equations are implemented in the developed OpenFOAM solver. The effect of rheological characteristics of the fluids on the physical parameters such as velocity, elastic behavior, and vortices strength of electrothermal flow are investigated through the viscoelastic non-dimensional numbers. According to the results, electrothermal outlet velocity decreases by 726% as the retardation ratio (β number) increases from 0.2 to 0.9 and increases by 107% as the Weissenberg number </strong>raises from 0.001 to 10. Investigating all non-dimensional numbers simultaneously leads to the conclusion that higher electrothermal velocity is achieved by viscoelastic fluids with lower viscosity and higher relaxation time. This fact is useful for choosing the proper fluid for a particular application. As a practical example, 3000 ppm polyethylene oxide solution results in higher velocity in electrothermal flow compared to the 5% polyvinylpyrrolidone and 2000 ppm xanthan gum solution.

With recent advances in semiconductor technology, conventional cooling methods and standard coolants are no longer adequate to manage electronic chips’ enormous heat generation. Therefore, innovative cooling solutions are required to maintain these devices at optimum operating temperatures. Taylor flow in microchannels is an effective technique that allows excellent mixing of two fluids, which is crucial for heat transfer. A 3D numerical analysis of the heat transfer performance of liquid-liquid Taylor flow in a rectangular microchannel was carried out by ANYSY Fluent. Water droplets were dispersed in either ethylene or propylene glycol, with the interface between the two fluids captured using the Volume of Fluid method. For optimal computational time, two symmetries in the XY and XZ planes are considered. Furthermore, mesh size refinement was performed in the near-wall region to capture the liquid film. An analysis of the effect of plug/slug length and liquid film thickness is conducted with initially constant thermo-physical properties. This assumption was considered to analyse the heat transfer process and determine the most critical parameter affecting heat transfer performance. A user-defined function is then implemented in ANSYS Fluent to examine the effect of working fluids temperature-dependent viscosity change on the heat transfer rate. Conjugate heat transfer and axial conduction are also examined, as these two factors can significantly affect the thermal behaviour inside the microchannel and enable the achievement of realistic and accurate results. The results reveal that Taylor liquid-liquid flow can increase the heat transfer rate by up to 440% over single-phase flow. It was also found that the temperature-dependent viscosity of the working fluids significantly affects the plug/slug length and liquid film thickness, resulting in a 20.8% improvement in heat transfer rate compared with constant thermo-physical properties. This study will improve the state of knowledge on heat transfer by Taylor flow in microchannels and factors that can influence it, and highlight the significance of this flow pattern in enhancing heat transfer performance over single-phase flow.

Planetary gear trains (PGTs) with one or more degrees of freedom (DOFs) have numerous uses in PGT-based mechanisms. The majority of the currently available synthesis methods have focused on 1-DOF PGTs, with only a few investigations on multi-DOF PGT synthesis. The method for synthesizing 7-link 3-DOF PGMs is outlined. All possible link assortments are produced, labeled spanning trees are generated, and potential geared graphs are constructed. The guidelines for including geared edges and how to synthesize geared graphs are outlined. Vertex-degree arrays are generated to validate the geared graphs. Isomorphic geared graphs are identified by comparing the isomorphic identification numbers of geared graphs with the same spanning tree. Fractionated geared graphs are identified using the reachability matrix method. The new method has a straightforward algorithm. In contrast to what is reported in the literature, the results of the synthesis of 7-link 3-DOF PGMs show that there are seven non-fractionated mechanisms. MATLAB programs are used to acquire the vertex-degree arrays.