A new approach to the electrostatic pull-in instability of nanocantilever actuators using the ADM–Padé technique

AbstractIn this paper, the Adomian decomposition method and Padé approximants are integrated to study the deflection and pull-in instability of nanocantilever electromechanical switches. In a distributed parameter model, intermolecular forces, including Casimir forces, are taken into account considering their range of application. A closed form power series solution based on Adomian polynomials is obtained. The obtained analytic results are compared with numerical solution. The Adomian method is accurate for small deflections, but the results of a pull-in instability study demonstrate that the accuracy of the Adomian solution is not as good for small deflections. Thus, to increase the accuracy of the Adomian solution for the pull-in instability, the Adomian power series is converted to Padé approximants. The results of the present method are compared with the numerical results as well as those of the Adomian decomposition method and other methods reported in the literature. The results obtained using the ADM–Padé are remarkably accurate compared with the numerical results. The proposed technique can be easily extended to solve a wide range of instability problems. Finally, the minimum initial gap and the detachment length of the actuator that does not stick to the substrate due to the intermolecular attractions, which is an important parameter for the pull-in instability of a nanocantilever actuator, are calculated using Adomian–Padé approximants

Free convection in a parallelogrammic porous cavity filled with a nanofluid using Tiwari and Das' nanofluid model

The free convection heat transfer of Cu-water nanofluids in a parallelogrammic enclosure filled with porous media is numerically analyzed. The bottom and top of the enclosure are insulated while the sidewalls are subject to limited temperature difference. The Darcy flow and the Tiwari and Das’ nanofluid models are considered. The governing dimensionless partial differential equations are numerically solved using a finite difference code. The results are reported for isotherms and streamlines as well as Nusselt number as a function of the volume fraction of nanoparticles, porosity, types of the porous matrix, inclination angle, aspect ratio and different Rayleigh numbers. It is found that the presence of the nanoparticles inside the enclosure deteriorates the heat transfer rate, which is caused due to the increase of dynamic viscosity by the presence of nanoparticles. Therefore, in applications in which the nanofluids are used for their advantages, such as enhanced dielectric properties or antibacterial properties, more caution for the heat transfer design of the enclosure is necessary

CONVECTIVE FLOW AND HEAT TRANSFER OF NANO-ENCAPSULATED PHASE CHANGE MATERIAL (NEPCM) DISPERSIONS ALONG A VERTICAL SURFACE

Nano-encapsulated phase change suspension is a novel type of functional fluid in which the nanoparticles undergo phase change that contribute to heat transfer. Thus, the working fluid carries heat not only by sensible heat but also in the form of latent heat stored in the particles. The natural convection and heat transfer of Nano-Encapsulated Phase Change Materials (NEPCMs) suspensions within a boundary layer along a heated flat surface are theoretically investigated in this work. The nanoparticles are core-shell structured with the core fabricated from PCMs covered by a solid shell. A similarity solution approach along with the finite element method is employed to address the phenomena. The outcomes indicate that a decisive factor in boosting the heat transfer is the temperature at which NEPCM particles undergo the phase transition. The heat transfer parameter can be enhanced by about 25% by just adding 5% of NEPCM particles, compared to the case with no NEPCM particles

Fluid–structure interaction of free convection in a square cavity divided by a flexible membrane and subjected to sinusoidal temperature heating

Purpose: The purpose of the present paper is to model a cavity, which is equally divided vertically by a thin, flexible membrane. The membranes are inevitable components of many engineering devices such as distillation systems and fuel cells. In the present study, a cavity which is equally divided vertically by a thin, flexible membrane is model using the fluid–structure interaction (FSI) associated with a moving grid approach. Design/methodology/approach: The cavity is differentially heated by a sinusoidal time-varying temperature on the left vertical wall, while the right vertical wall is cooled isothermally. There is no thermal diffusion from the upper and lower boundaries. The finite-element Galerkin technique with the aid of an arbitrary Lagrangian–Eulerian procedure is followed in the numerical procedure. The governing equations are transformed into non-dimensional forms to generalize the solution. Findings: The effects of four pertinent parameters are investigated, i.e., Rayleigh number (104 = Ra = 107), elasticity modulus (5 × 1012 = ET = 1016), Prandtl number (0.7 = Pr = 200) and temperature oscillation frequency (2p = f = 240p). The outcomes show that the temperature frequency does not induce a notable effect on the mean values of the Nusselt number and the deformation of the flexible membrane. The convective heat transfer and the stretching of the thin, flexible membrane become higher with a fluid of a higher Prandtl number or with a partition of a lower elasticity modulus. Originality/value: The authors believe that the modeling of natural convection and heat transfer in a cavity with the deformable membrane and oscillating wall heating is a new subject and the results have not been published elsewhere

Free convection heat transfer and entropy generation in an odd-shaped cavity filled with a Cu-Al2O3 hybrid nanofluid

The present paper aims to analyze the thermal convective heat transport and generated irreversibility of water-Cu-Al2O3 hybrid nanosuspension in an odd-shaped cavity. The side walls are adiabatic, and the internal and external borders of the enclosure are isothermally kept at high and low temperatures of Thand Tc, respectively. The control equations based on conservation laws are formulated in dimensionless form and worked out employing the Galerkin finite element technique. The outcomes are demonstrated using streamlines, isothermal lines, heatlines, isolines of Bejan number, as well as the rate of generated entropy and the Nusselt number. Impacts of the Rayleigh number, the hybrid nanoparticles concentration (ϕhnf), the volume fraction of the Cu nanoparticles to ϕhnf ratio (ϕr), width ratio (WR) have been surveyed and discussed. The results show that, for all magnitudes of Rayleigh numbers, increasing nanoparticles concentration intensifies the rate of entropy generation. Moreover, for high Rayleigh numbers, increasing WR enhances the rate of heat transport

Latent heat thermal storage of nano-enhanced phase change material filled by copper foam with linear porosity variation in vertical direction

The melting flow and heat transfer of copper-oxide coconut oil in thermal energy storage filled with a nonlinear copper metal foam are addressed. The porosity of the copper foam changes linearly from bottom to top. The phase change material (PCM) is filled into the metal foam pores, which form a composite PCM. The natural convection effect is also taken into account. The effect of average porosity; porosity distribution; pore size density; the inclination angle of enclosure; and nanoparticles’ concentration on the isotherms, melting maps, and the melting rate are investigated. The results show that the average porosity is the most important parameter on the melting behavior. The variation in porosity from 0.825 to 0.9 changes the melting time by about 116%. The natural convection flows are weak in the metal foam, and hence, the impact of each of the other parameters on the melting time is insignificant (less than 5%)

Competition of natural convection and thermal creep in a square enclosure

Although natural convection and thermal creep have been well recognized in the continuum and rarefied regimes, respectively, the study of the competition of them in a wide flow regime is very scarce. From a theoretical point of view, natural convection can be described by Navier–Stokes–Fourier (NSF) equations at the macroscopic level, while thermal creep needs descriptions at the molecular level. Therefore, it is quite challenging to capture these two effects simultaneously. In this work, we employ the unified stochastic particle Bhatnagar–Gross–Krook (USP-BGK) method to investigate thermally driven gas flow in a square enclosure. The simulation results obtained by the USP-BGK method are validated by comparing to those from NSF solutions and direct simulation Monte Carlo method for the continuum and transitional regimes, respectively. We find that the flow patterns in the whole flow regime cannot be determined by just one nondimensional parameter, i.e., the Rayleigh number (Ra), but needs two nondimensional parameters, i.e., the Knudsen number (Kn) and the Froude number (Fr), or Kn and Ra. Specifically, small Knudsen and Froude numbers tend to generate natural convection, while large Knudsen and Froude numbers tend to cause thermal creep. Moreover, our simulation results and analyses demonstrate that when Kn 0.28, or equivalently, L/L* > 1.0, where L is the characteristic length of the system and L* is the equivalent characteristic length of molecules. These findings provide useful guidance for better understanding of the complex gas flows resulting from the competition of natural convection and thermal creep under microscale or low-density conditions such as on Mars

Consecutive charging and discharging of a PCM-based plate heat exchanger with zigzag configuration

Due to the remarkable energy savings, isothermal nature of the operation and low costs, energy storage with phase-change materials (PCMs) is a reliable technology for filling the gap between energy supply and demand. In this paper, an attempt has been made to modify the storage functionality of PCM in a plate type heat exchanger with zigzag configuration. A two-dimensional, time-dependent simulation model for the PCM phase transition during the charging and discharging modes has been developed and validated via earlier related findings. The effects of zigzag angle orientation, inlet flowrate and mean temperature of the heat transfer fluid (HTF) are thoroughly studied and revealed. Results show that increasing the angle of zigzag orientation has no noticeable impact on the development of phase transition during the early stages of operation. However, this effect becomes more noticeable and almost leads to faster storage/retrieval rates as time further elapses. It is found that the system with the zigzag angle of 60° augments the storage rate by 32.6% compared with the system of 30° zigzag angle. Also, higher HTF temperature and/or higher Reynold number result in faster phase-transition rates during both parts of the energy charging-discharging cycle

Latent heat thermal storage of nano-enhanced phase change material filled by copper foam with linear porosity variation in vertical direction

Data Availability Statement: Data is contained within the article.Copyright: © 2021 by the authors. The melting flow and heat transfer of copper-oxide coconut oil in thermal energy storage filled with a nonlinear copper metal foam are addressed. The porosity of the copper foam changes linearly from bottom to top. The phase change material (PCM) is filled into the metal foam pores, which form a composite PCM. The natural convection effect is also taken into account. The effect of average porosity; porosity distribution; pore size density; the inclination angle of enclosure; and nanoparticles’ concentration on the isotherms, melting maps, and the melting rate are investigated. The results show that the average porosity is the most important parameter on the melting behavior. The variation in porosity from 0.825 to 0.9 changes the melting time by about 116%. The natural convection flows are weak in the metal foam, and hence, the impact of each of the other parameters on the melting time is insignificant (less than 5%).Funding: This research received no external funding