Oscillatory Magnetohydrodynamic Natural Convection of Liquid Metal between Vertical Coaxial Cylinders

A numerical study of oscillatory magnetohydrodynamic (MHD) natural convection of liquid metal between vertical coaxial cylinders is carried out. The motivation of this study is to determine the value of the critical Rayleigh number, Racr for two orientations of the magnetic field and different values of the Hartmann number (Harand Haz) and aspect ratios A. The inner and outer cylinders are maintained at uniform temperatures, while the horizontal top and bottom walls are thermally insulated. The governing equations are numerically solved using a finite volume method. Comparisons with previous results were performed and found to be in excellent agreement. The numerical results for various governing parameters of the problem are discussed in terms of streamlines, isotherms and Nusselt number in the annuli. The time evolution of velocity, temperature, streamlines and Nusselt number with Racr, Har, Haz, and A is quite interesting. We can control the flow stability and heat transfer rate in varying the aspect ratio, intensity and direction of the magnetic field

Simulation and Analysis with Wavelet Transform Technique and the Vibration Characteristics for Early Revealing of Cracks in Structures

Implementation of improved instruments is used to detect damage in an accurate manner and fully analyze its characteristics. An aluminum beam has been used in this work to identify cracks by using a vibration technique. The simulation of frequency response feature was conducted using a finite element model to provide average measures of intensities of vibration. Two forms of wavelet packet transform (WPT) entropies Shannon and log energy were applied to identify the position, width, and size of the crack. The results showed that with an increase in crack depth, the amplitude also increased at certain crack sizes and for all crack positions. For two crack depths of 1.6 mm and 0.16 mm having the same crack size and position 12 mm and 60 mm, respectively, a 4.5% increase in amplitude was observed at a crack depth of 1.6 mm. Moreover, the amplitude varied inversely with the position. A 12.6% increase in amplitude was observed at a crack depth of 1.6 mm rather than 0.16 mm, while both depths occurred at the same crack position (75 mm) and size (20 mm). Experimental validation was performed on a cantilever beam with one crack. The maximum absolute error found was 7.5% for the crack position and 9.1% for the crack size. With the increase in crack depth, the obtained results decrease the stiffness of a beam in a single crack case

Mixed Convection inside a Duct with an Open Trapezoidal Cavity Equipped with Two Discrete Heat Sources and Moving Walls

The current research presents a numerical investigation of the mixed convection inside a horizontal rectangular duct combined with an open trapezoidal cavity. The region in the bottom wall of the cavity is heated by using two discrete heat sources. The cold airflow enters the duct horizontally at a fixed velocity and a constant temperature. All the other walls of the duct and the cavity are adiabatic. Throughout this study, four various cases were investigated depending on the driven walls. The effects of the Richardson number and Reynolds number ratio are studied under various cases related to the lid-driven sidewalls. The results are presented in terms of the flow and thermal fields and the average Nusselt number. The yielded data show that the average Nusselt number rises as the Richardson number and Reynolds number ratio increases. Furthermore, the Reynolds number ratio and the movement of the cavity sidewall(s) have a significant effect on the velocity and temperature contours. By the end of the study, it is shown that the maximum rates of heat transfer are related to Case 1 where the left sidewall moves downward and heater 2, which is placed near the left sidewall

Mixed Convection inside a Duct with an Open Trapezoidal Cavity Equipped with Two Discrete Heat Sources and Moving Walls

The current research presents a numerical investigation of the mixed convection inside a horizontal rectangular duct combined with an open trapezoidal cavity. The region in the bottom wall of the cavity is heated by using two discrete heat sources. The cold airflow enters the duct horizontally at a fixed velocity and a constant temperature. All the other walls of the duct and the cavity are adiabatic. Throughout this study, four various cases were investigated depending on the driven walls. The effects of the Richardson number and Reynolds number ratio are studied under various cases related to the lid-driven sidewalls. The results are presented in terms of the flow and thermal fields and the average Nusselt number. The yielded data show that the average Nusselt number rises as the Richardson number and Reynolds number ratio increases. Furthermore, the Reynolds number ratio and the movement of the cavity sidewall(s) have a significant effect on the velocity and temperature contours. By the end of the study, it is shown that the maximum rates of heat transfer are related to Case 1 where the left sidewall moves downward and heater 2, which is placed near the left sidewall

Hydrothermal and Entropy Investigation of Ag/MgO/H₂O Hybrid Nanofluid Natural Convection in a Novel Shape of Porous Cavity

In this study, a new cavity form filled under a constant magnetic field by Ag/MgO/H2O nanofluids and porous media consistent with natural convection and total entropy is examined. The nanofluid flow is considered to be laminar and incompressible, while the advection inertia effect in the porous layer is taken into account by adopting the Darcy–Forchheimer model. The problem is explained in the dimensionless form of the governing equations and solved by the finite element method. The results of the values of Darcy (Da), Hartmann (Ha) and Rayleigh (Ra) numbers, porosity (εp), and the properties of solid volume fraction (ϕ) and flow fields were studied. The findings show that with each improvement in the Ha number, the heat transfer rate becomes more limited, and thus the magnetic field can be used as an outstanding heat transfer controller

Galerkin Finite Element Analysis of Magneto-hydrodynamic Natural Convection of Cu-water Nanoliquid in a Baffled U-shaped Enclosure

Abstract In this paper, single-phase homogeneous nanofluid model is proposed to investigate the natural convection of magneto-hydrodynamic (MHD) flow of Newtonian Cu–H2O nanoliquid in a baffled U-shaped enclosure. The Brinkman model and Wasp model are considered to measure the effective dynamic viscosity and effective thermal conductivity of the nanoliquid correspondingly. Nanoliquid's effective properties such as specific heat, density and thermal expansion coefficient are modeled using mixture theory. The complicated PDS (partial differential system) is treated for numeric solutions via the Galerkin finite element method. The pertinent parameters Hartmann number (1 ≤ Ha ≤ 60), Rayleigh number (103 ≤ Ra ≤ 106) and nanoparticles volume fraction (0% ≤ ϕ ≤ 4%) are taken for the parametric analysis, and it is conducted via streamlines and isotherms. Excellent agreement between numerical results and open literature. It is ascertained that heat transfer rate enhances with Rayleigh number Ra and volume fraction ϕ, however it is diminished for larger Hartmann number Ha

Hydrothermal and Entropy Investigation of Ag/MgO/H2O Hybrid Nanofluid Natural Convection in a Novel Shape of Porous Cavity

In this study, a new cavity form filled under a constant magnetic field by Ag/MgO/H2O nanofluids and porous media consistent with natural convection and total entropy is examined. The nanofluid flow is considered to be laminar and incompressible, while the advection inertia effect in the porous layer is taken into account by adopting the Darcy–Forchheimer model. The problem is explained in the dimensionless form of the governing equations and solved by the finite element method. The results of the values of Darcy (Da), Hartmann (Ha) and Rayleigh (Ra) numbers, porosity (εp), and the properties of solid volume fraction (ϕ) and flow fields were studied. The findings show that with each improvement in the Ha number, the heat transfer rate becomes more limited, and thus the magnetic field can be used as an outstanding heat transfer controller