Number Of Undulations Research Articles

Effect of local thermal non-equilibrium model on natural convection in a nanofluid-filled wavy-walled porous cavity containing inner solid cylinder

In the current work, the impacts of local thermal non-equilibrium model and Al2O3-water nanofluid on natural convection heat transfer in a porous cavity consisting of a bottom heated wavy wall and an inner solid cylinder are investigated. The Galerkin weighted residual finite element method is utilized to simulate the dimensionless governing equations of the fluid flow and heat transfer. The effects of different parameters including Darcy number (10-6⩽Da⩽10-2), nanoparticle volume fraction (0⩽ϕ≤0.04), modified conductivity ratio (0.01⩽γ≤1000), number of undulations (1⩽N⩽4) and the porosity of the medium (0.2⩽ε⩽0.8) on the field of the flow and the heat transfer mechanisms are described. The Forchheimer-Brinkman-extended Darcy model along with the Boussinesq approximation are assumed to hold. A comprehensive validation of the present code is obtained by comparing the results with those of previous studies. The results show that all the mentioned parameters have significant impacts on the fluid flow and the temperature distributions. In addition, increasing the thermal conductivity of the nanoparticles leads to an increase in the rate of heat transfer for the nanofluid condition and reaches its maximum value at ϕ=0.04. Considering high values of ε, the average Nusselt number increases by the augmentation of ϕ, while at low values of the porosity, the average Nusselt number decreases after reaching a peak. The results of this study are very useful for designing a porous heat exchanger.

Free Convection in a Wavy Walled Cavity With a Magnetic Source Using Radial Basis Functions

In this study, free convection in a cavity with differentially heated wavy walls is numerically investigated in the presence of a magnetic source. Polyharmonic spline radial basis function (RBF) is utilized to discretize the governing dimensionless equations formulated by stream function-vorticity. The effects of dimensionless Hartmann number, Rayleigh number, the number of undulations, amplitude of wave, and the location of magnetic source are visualized in streamlines and isotherms as well as calculating average Nusselt number through the heated wall. Results show that primary vortex in streamlines is altered with the impact of magnetic source. The augmentation of undulations and amplitude causes convective heat transfer to decrease if Ra = 105. The impact of location of magnetic source is noted close to the top wall.

The Archaeology of Science in the Science of Archaeology

The Archaeology of Science in the Science of Archaeology ALEXY D. KARENOWSKA Revolution is a claim that can rarely be made without controversy, but as a description of the effect of science on the discipline of archeology over the last half century its justification is beyond dispute. Of the many scientific and technological developments that have contributed to the rapid evolution in the scope and capacity of archeological and historical research, among the most significant and visible have come from the area of imaging. Off-the-shelf tools now available for application to archeological research span a remarkable range of scales and capacities. We have, for example, techniques like reflectance transformation imaging (RTI) and multi-spectral imaging (MSI) that allow the recovery and discovery of minute textural and structural information about surfaces; magnetic resonance imaging (MRI) which gives us, non-invasively, spectroscopic information about the composition of three-dimensional objects, and satellite imaging technologies that enable geophysical surveying and mapping over kilometer scales with a speed and spatial resolution which, just twenty years ago, would have passed for science fiction. Though diverse in purpose and capability, these imaging instruments are united by a common basis: they all rely on the physics of electromagnetism. The part of the electromagnetic spectrum that is most faarion 27.3 winter 2020 A version of this paper was given verbally at the Annual Conference of the Institute for Digital Archaeology in Oxford in May of 2015. This meeting, dedicated to the theme of digital imaging in archaeology, served both as a timely celebration of recent progress in the field, and an opportunity to discuss different perspectives on this progress with colleagues from a range of specialisms. There, as here, I explore a magnetician’s eye view. 8 the archaeology of science miliar to us is visible light. Visible light is made up of a combination of travelling electric and magnetic fields: a wave of electrical energy (red, figure 1) together with wave of magnetic energy, propagating in the same direction, but inclined at ninety degrees to it (blue). The colour that visible light appears to the human eye is related to the distance between adjacent peaks of the waves, this length is called the wavelength and is inversely proportional to the number of undulations up and down per second, a quantity that we refer to as frequency. The term “frequency,” when applied to light is exactly analogous to that which we meet in the context of sound waves: the higher the frequency, or pitch, of a musical note, the shorter the acoustic wavelength, and vice versa. In the case of visible light, the longer the wavelength (that is, the lower the frequency) the redder it gets; the shorter it is, the bluer. If we change the wavelength significantly in one or Figure 1. Electromagnetic excitations are made up of a wave of electrical energy (red) together with wave of magnetic energy (blue). The two propagate in the same direction, but are perpendicular to each other. The wavelength, usually represented by the symtbol λ, is the distance between adjacent peaks of the two constituent waves and is inversely proportional to the frequency; that is, the number of undulations (or oscillations) up and down per second. Image by author. Alexy D. Karenowska 9 another direction, the light ceases to be visible to the human eye. When we extend beyond the visible part of the spectrum in the direction of longer wavelengths, we first encounter infrared light, and in the opposite direction—the one of shorter wavelengths—ultraviolet. If we increase or decrease the wavelength further still, the electromagnetic waves start to interact with matter rather differently from optical ones. In the direction of longer wavelengths, they first become microwaves —the kind of electromagnetic radiation that both your microwave oven and your mobile telephone use; then radio waves—the electromagnetic waves of short, medium, and long-wave radio transmission. In the opposite direction , when we increase the electromagnetic frequency above that of light, what we get are X-rays and, beyond that, their high-energy counterparts, gamma rays. It is only in the last one hundred and fifty years that a proper understanding of how electromagnetism works has been...

MHD Natural Convection Ferrofluid Flow in Semi-Annulus Enclosures

This study examines the natural convection flow and the heat transfer of a water-based ferrofluid consisting Fe3O4 nanoparticles in a semi-annulus cavity with a circular outer and sinusoidal inner walls under the effect of a magnetic field produced by multiple nodal magnetic sources. The equations governing the ferrofluid flow are numerically solved using the dual reciprocity boundary element method. That is the equations are transformed into integral equations only on the boundary by using the fundamental solution of the Laplace equation and treating all other terms as nonhomegeneity through radial basis function approximation, which results in a discretized system of small size. The numerical computations are performed for several physical parameters namely, Hartmann, Rayleigh and magnetic numbers, solid volume fraction of nanoparticles, the number of undulation and the amplitude of sinusoidal wall. The obtained results show that increasing Rayleigh number, solid volume fraction and amplitude of sine waves enhance the average Nusselt number whereas it decreases with an increase in Hartmann number.

Enhancement of nanoparticle-phase change material melting performance using a sinusoidal heat pipe

Thermal energy storage with an assisted-heat pipe has several useful applications in engineering fields. Due to the large latent heat and nearly constant melting temperature, phase change materials become attractive for thermal energy storage applications. Unfortunately, the low thermal conductivities of phase change materials become a significant issue which should be overcome to achieve high energy storage efficiency. In the current work, a novel sinusoidal heat pipe is designed instead of a circular heat pipe in order to accelerate the melting rate of nanoparticle-enhanced phase change material without affecting the thermal energy storage capacity of system. By developing an enthalpy-based immersed boundary-lattice Boltzmann method for the solid-liquid phase change phenomenon, the melting process of nanoparticle-enhanced phase change material with a sinusoidal heat pipe is investigated with respect to different heat pipe temperature, heat pipe undulation number and sinusoidal amplitude, nanoparticle volume fraction, and eccentric location of heat pipe. The results indicate that the energy storage rate of nanoparticle-enhanced phase change material is highly improved by applying a sinusoidal heat pipe because of its enlarged heat transfer area between heat transfer fluid and nanoparticle-enhanced phase change material. Furthermore, through an optimization study, it is found that applying a sinusoidal heat pipe with larger radius is more effective than adding high thermal conductivity nanoparticles into phase change material to enhance the thermal energy storage rate. Besides, the sinusoidal heat pipe with an eccentric location near the bottom of thermal energy storage cavity is highly recommended to realize a faster phase change material melting rate due to the enhanced effect of natural convective heat transfer.

Impact of nonhomogeneous nanofluid model on transient mixed convection in a double lid-driven wavy cavity involving solid circular cylinder

Heat transfer enhancement in engineering systems can be reached using nanofluids. Very often, technical devices are chambers with moving borders of a flat or a wavy shape having internal heat-conducting blocks. Therefore, the present study is devoted to study computationally the problem of time-dependent heat transfer of alumina-water nanoliquid within a differentially heated chamber with isothermal moving vertical walls and adiabatic horizontal ones under the impact of an inner solid cylinder. The upper wall of the chamber is assumed to have a wavy shape. Basic equations written in non-dimensional primitive variables using the two-component nonhomogeneous equilibrium model for transport phenomena in nanofluids incorporating the effects of Brownian diffusion and thermophoresis with Corcione empirical correlations for the viscosity and thermal conductivity combined with heat conduction equation for the centered solid cylinder has been resolved by the Galerkin finite-element method. The influences of the dimensionless time (0 ≤ τ ≤ 120), Reynolds number (Re=10 and 100), Richardson number (0.01 ≤ Ri ≤ 100), constant moving parameter [(λl=1,λr=−1), (λl=1,λr=1), (λl=−1,λr=1), (λl=−1,λr=−1)], nanoparticle volume fraction (0 ≤ ϕ ≤ 0.04), number of undulations (0 ≤ N ≤ 4) and the dimensionless radius of solid cylinder (0.05 ≤ S ≤ 0.25) on the isolines of stream function, temperature and nanoparticles concentrations, as well as the local and average Nusselt numbers have been investigated. It has been found that a rise of the average Nusselt number at the hot wall depends on the moving parameter and the thermal transmission intensity diminishes with the undulations number and the inner solid cylinder diameter. At the same time, the wavy shape of the border, the characteristics of internal cylinder and the properties of nanofluid are very good control parameters for the heat transfer rate and the fluid flow rate.

CFD analysis of mixed convection porous square cavity

The analysis of conventional flow and transfer of heat in a square cavity which is porous in nature is being done by the numerical study and research. There is insulation at the vertical walls of the cavity and bottom surface wavy in nature upholds uniform temperature which is little more than that at the upper lid. The non-dimensional governing equations are solved using the finite volume method. Several inclination angles are examined from 0° to 180°. The isotherm and streamline distribution, including varieties of local and average Nusselt numbers with the angle of inclination, are exposed. The outputs of the observations indicate that average Nusselt number has direct relationship with a number of undulations and also inclination angle.

Natural convection of an alumina-water nanofluid inside an inclined wavy-walled cavity with a non-uniform heating using Tiwari and Das’ nanofluid model

The present study is devoted to numerical analysis of natural convective heat transfer and fluid flow of alumina-water nanofluid in an inclined wavy-walled cavity under the effect of non-uniform heating. A single-phase nanofluid model with experimental correlations for the nanofluid viscosity and thermal conductivity has been included in the mathematical model. The considered governing equations formulated in dimensionless stream function, vorticity, and temperature have been solved by the finite difference method. The cavity inclination angle and irregular walls (wavy and undulation numbers) are very good control parameters for the heat transfer and fluid flow. Nowadays, optimal parameters are necessary for the heat transfer enhancement in different practical applications. The effects of the involved parameters on the streamlines and isotherms as well as on the average Nusselt number and nanofluid flow rate have been analyzed. It has been found that the heat transfer rate and fluid flow rate are non-monotonic functions of the cavity inclination angle and undulation number.

Numerical Investigation of Mixed Convection and Entropy Generation in a Wavy-Walled Cavity Filled with Nanofluid and Involving a Rotating Cylinder.

This numerical study considers the mixed convection and the inherent entropy generated in AlO–water nanofluid filling a cavity containing a rotating conductive cylinder. The vertical walls of the cavity are wavy and are cooled isothermally. The horizontal walls are thermally insulated, except for a heat source segment located at the bottom wall. The dimensionless governing equations subject to the selected boundary conditions are solved numerically using the Galerkin finite-element method. The study is accomplished by inspecting different ranges of the physical and geometrical parameters, namely, the Rayleigh number (), angular rotational velocity (), number of undulations (), volume fraction of AlO nanoparticles (), and the length of the heat source . The results show that the rotation of the cylinder boosts the rate of heat exchange when the Rayleigh number is less than . The number of undulations affects the average Nusselt number for a still cylinder. The rate of heat exchange increases with the volume fraction of the AlO nanoparticles and the length of the heater segment.

Unsteady MHD mixed convection flow in a lid-driven cavity with a heated wavy wall

The unsteady mixed convection flow under the effect of an externally applied uniform magnetic field is investigated numerically in a lid-driven cavity with a sinusoidal wavy wall. The governing equations given in terms of stream function, vorticity and temperature are discretized by using the dual reciprocity boundary element method (DRBEM) in space and a two-level time integration scheme is employed in time discretization. The simulations focus on the effects of several physical parameters, namely Hartmann and Rayleigh numbers, Joule heating parameter, the inclination angle of magnetic field and number of undulation of wavy wall on the flow and temperature distribution. Moreover, the stability analysis of the numerical method is performed in terms of time increment and time relaxation parameters for various combinations of the problem controlling parameters.

Numerical study of the effect of magnetic field on Fe3O4 –water ferrofluid convection with thermal radiation

PurposeThe purpose of this paper is to examine the effect of magnetic field on ferrofluid convective mode with radiation.Design/methodology/approachViscosity of Fe3O4 ferrofluid is considered as a function of magnetic field. Solutions of the governing equations are obtained by a powerful numerical method, namely, control volume finite element method (CVFEM). Roles of radiation parameter (Rd), number of undulations (N), Fe3O4–water volume fraction (ϕ), Hartmann (Ha) and Rayleigh numbers are illustrated graphically. A correlation for Nuave is extracted.FindingsThe inner wall temperature decreases with increasing buoyancy forces, but increases with increasing Rd and Ha. Also increasing Rd results in increasing nanofluid motion. This influence is more evident when convection flow is dominant. As nanofluid temperature increases, the nanofluid begins moving from the warm surface to the outer one and dropping along the circular cylinder. At low Rayleigh number, conduction is more significant than convection. |Ψmax| increases as buoyancy force increases and it decreases as the Lorentz force increases. As Hartmann number increases, the center of the vortices moves to x = 0. As Ra increases, convection becomes stronger. Thus, |Ψmax| and temperature gradient increase with increasing Ra. As N increases, the distortion of isotherms reduces and vortices become weaker. Increasing Hartmann number results in a reduction in the thermal plume and the heat transfer mechanism changes from convection to conduction. Nusselt number decreases with increasing N ⋅ Nu decreases with increasing Lorentz force. At N = 5 , increasing the Lorentz force causes the main vortices to convert into three smaller ones. As the Lorentz force increases, the two upper vortices merge together and the thermal plume vanishes. The number of extrema in the Nuloc profile matches the existence of the thermal plume and the number of undulations. Nuave increases with increasing Rd. As buoyancy forces increase, the temperature decreases and in turn Nuave increases with increasing Ra.Originality/valueNanofluids are an innovative way to enhance radiation heat. In this paper, MHD Fe3O4–water nanofluid natural convection with radiation source term is examined. Magnetic field-dependent (MFD) viscosity is considered. Using the CVFEM, numerical simulations are carried out for various values of the radiation parameter (Rd = 0 to 0.8), volume fraction of Fe3O4–water (ϕ = 0 to 0.04), Rayleigh number (Ra = 103, 104 and 105), number of undulations (N = 3,4 and 5) and Hartmann number (Ha = 0 to 40).

A numerical investigation of magneto-hydrodynamic natural convection of Cu–water nanofluid in a wavy cavity using CVFEM

In this work, magneto-hydrodynamic natural convection of a nanofluid in a wavy cavity considering Brownian motion is studied numerically using the control volume finite element method. The effective viscosity and thermal conductivity of the nanofluid are defined by the correlation in which the impact of Brownian motion on the thermal conductivity is considered. The considered wavy cavity is heated from the left side and it cooled from the right side. Also, the top and bottom walls of the considered wavy cavity are assumed adiabatic. The impacts of various controlling parameters such as the Rayleigh number, wavy contraction ratio, Hartmann number and undulation number are examined on the contour maps of the streamlines and the isotherms. Further, the average and local Nusselt numbers are calculated and presented graphically and discussed. The findings narrate that the strength of the convective flow has a direct relationship with the Rayleigh number and also it has a reverse relationship with the wavy contraction ratio.

Nanofluid MHD natural convection through a porous complex shaped cavity considering thermal radiation

Control volume based finite element method (CVFEM) is applied to simulate H2O based nanofluid radiative and convective heat transfer inside a porous medium. Non-Darcy model is employed for porous media. Influences of Hartmann number, nanofluid volume fraction, radiation parameter, Darcy number, number of undulations and Rayleigh number on nanofluid behavior were demonstrated. Thermal conductivity of nanofluid is estimated by means of previous experimental correlation. Results show that Nusselt number enhances with augment of permeability of porous media. Effect of Hartmann number on rate of heat transfer is opposite of radiation parameter.

Subcritical vibrations of a large flexible rotor efficiently reduced by modifying the bearing inner ring roundness profile

Abstract Undesired vibration of a rotor is harmful for industrial processes and decreases the machine lifetime. In industrial processes, large rotors are commonly operated below the critical speed. In the subcritical speed range, the bearings are an important excitation source of vibration. The bearing inner ring based excitation is observed at a frequency, which is the rotor rotating frequency multiplied by the number of undulations in the roundness profile of the roller race of the bearing inner ring. Subcritical resonance occurs, when the bearing excitation frequency equals the natural frequency of the rotor system. The present study investigates the effect of the bearing inner ring roundness profile on the subcritical vibrations of a flexible rotor. The roundness profile of the bearing inner ring was measured, while installed on the rotor shaft. The roundness profile was modified to five different geometries to investigate different excitation cases. Finally, the roundness error of the inner ring was minimized. The rotor subcritical vibration was measured with each bearing inner ring geometry in the horizontal and vertical directions. The analysis was focused on the 2nd, 3rd and 4th harmonic vibration components, occurring at 1/2, 1/3 and 1/4 of the critical rotational speed. The results clearly suggest that the roundness profile of the roller race of the bearing inner ring affects the rotor subcritical vibration significantly. The increased waviness components of the bearing inner ring roundness profile increased the corresponding subcritical vibration amplitude. Minimizing the roundness error decreased the subcritical vibration substantially.

Numerical Investigation of Laminar Natural Convection in a Square Cavity With Wavy Wall and Horizontal Fin Attached to the Hot Wall

Laminar natural convection in differentially heated square cavity with right cold wavy wall and horizontal conducting fin attached to its left hot wall has been investigated numerically. The vertical walls are maintained at different isothermal temperatures, while the horizontal walls are insulated. The fluid that filled the cavity is air with Prandtl number of 0.71. The investigation has been performed for Rayleigh number in the range of 103–106, the thermal conductivity ratio was varied from 10 to 105, three fin lengths and positions have been examined (0.25, 0.5, and 0.75), and three numbers of undulation were tested (one, two, and three undulations). The wave amplitude and the fin thickness were kept constant at 0.05 and 0.04, respectively. The results obtained show that increasing the fin thermal conductivity or the Rayleigh number increases the average Nusselt number especially when the fin length increases. It was also found that the fin position enhances the heat transfer when the fin is placed opposite to the crest of the wavy wall. The trend of the local Nusselt number is wavy. The effect of undulations number appears when the fin length is greater than 0.5. The average Nusselt number enhanced when a conducting fin is added to the cavity with wavy wall and without fin by 51.23% and 56.85% for one and three undulations, respectively, when the Rayleigh number is 105 and the fin length is 0.75.

Numerical simulation for solidification in a LHTESS by means of nano-enhanced PCM

Abstract In order to saving thermal energy, latent heat thermal energy storage systems (LHTESS) can be utilized. Common phase change material (PCM) has low thermal conductivity. In this paper, CuO nanoparticles have been used to enhance the performance of LHTESS. CuO–water nanofluid properties are estimated by means of KKL. This unsteady process has been simulated by Finite element method. Results prove that solidification process is accelerated by adding CuO nanoparticles in to pure PCM. As number of undulations increases average temperature and total energy profiles reduce while solid fraction profile increases. Also, it can be concluded that highest rate of solidification is obtained for dp = 40 nm.

Mixed Convection in a Cavity Saturated with Wavy Layer Porous Medium: Entropy Generation

In this paper, the effects of the wavy nanofluid/porous interface on the mixed convection and entropy generations of Cu–water nanofluid in a horizontally partitioned non-Darcy porous double lid-driven cavity are investigated. The bottom cavity wall is heated, and the top wall is cooled. Both of the left and right walls are adiabatic. The upper and the lower parts of the square cavity are filled with the nanofluid. The wavy middle part of the cavity is filled with the non-Darcy porous medium. The effects of the fundamental parameters were studied, including Reynolds number, Richardson parameter (), and Darcy parameter () as well as nanofluid/porous interface parameters including the porous media height (), nanofluid heights, the amplitude of wavy interface (), and the number of interface undulations (). It is found that the decrease of the Darcy parameter brings a big resistance force for the fluid flow, an increase in the heat transfer by conduction, and a significant decrease in the irreversibility due to the heat transfer. And the effects of the nanoparticle concentrations depend on the convection mode. The average Bejan number is close to unity at forced convection mode.

Effect of Aspect Ratio on Natural Convection in a Porous Wavy Cavity

The present study analyzes natural convective flow and heat transfer in a wavy cavity saturated with porous medium. The sidewalls of the cavity are maintained at constant temperatures where higher temperature is applied on the vertical left wall while the wavy right wall is cooled at a lower temperature. The remaining top and bottom walls are taken to be adiabatic. The Darcy model is adopted for the fluid flow through the porous medium. The governing equations and boundary conditions are solved using the finite difference method over a range of cavity aspect ratios, wavy wall amplitudes, number of undulations and Darcy–Rayleigh numbers. The waviness of the cavity enhances the heat transfer inside the cavity, and the heat transfer rate is more enhanced when the aspect ratio of the cavity is close to 1. The study is applicable to the design of solar heating systems and geothermal reservoirs.

Effect of a wavy interface on the natural convection of a nanofluid in a cavity with a partially layered porous medium using the ISPH method

ABSTRACTThe effect of a wavy nanofluid/porous-medium interface on the natural convection of a Cu–water nanofluid in a differentially heated non-Darcy porous cavity was investigated using the ISPH method. Wall boundary conditions were applied by improved scheme using the analytical kernel renormalization function and its gradient based on the quintic kernel function. The effect of the Rayleigh number and the Darcy number on the heat transfer of Cu–water nanofluid with a various solid volume fraction were studied. Results showed that higher amplitude, height, and the undulation number of the sinusoidal interface between the nanofluid and porous medium layer lead to a decrease in the average Nusselt number.

Convective heat transfer of micropolar fluid in a horizontal wavy channel under the local heating

A numerical analysis of laminar mixed convection of micropolar fluid in a horizontal wavy channel with a local heater has been carried out. Governing equations formulated in dimensionless stream function, vorticity and temperature have been solved by finite difference method. Effects of Rayleigh number, Reynolds number, Prandtl number, vortex viscosity parameter and undulation number on streamlines, isotherms, vorticity isolines as well as horizontal velocity and temperature profiles with average Nusselt number at the heater have been studied. It has been found that the average Nusselt number is an increasing function of Rayleigh, Reynolds and Prandtl numbers and a decreasing function of undulation number while an influence of vortex viscosity parameter is non-monotonic.