Laminar Steady State Research Articles

Impact of the Thermophysical Properties of a Cuo-H<sub>2</sub>O-Based Nanofluid on the Performance of a Cylindrical Solar Concentrator

Sustainability in energy production, energy security, and global warming are major concerns facing the globe today. Cylindrical Solar Concentrator is extensively utilized for technologically advanced processes, heat, and power plant applications by utilizing daylight sunshine at no running cost. Numerous inputs and characteristics impact the concentrator's performance, with the type of heat transfer fluid and its mass flow rate being two of the most important. This paper gives a numerical investigation of the influence of thermo-physical attribute of CuO water-based nanofluids on the effectiveness of the Parabolic Trough Solar Concentrator in Ogbomosho weather condition (lat. 8o011, long. 4o111).The governing equations of nanofluids with laminar flow and steady state, using iterative relaxation techniques, as well as the efficiency of the concentrator, were solved. A C++ simulation program was developed to investigate the impacts of thermo physical parameters on concentrator efficiency, with nanoparticle sizes ranging from 1 to 10 percent and mass flow rates of 0.1 kg/s, 0.15 kg/s, and 0.2 kg/s, at a constant incident solar insolation flux of 186 W/m2. The results demonstrated that increasing the mass flow rate of the nanofluids improves the heat transmission properties. The thermo physical properties of CuO-based nanofluids and its effects on the performance of the solar parabolic trough collector are being examined. The impact of thermophysical attributes on thermal effectiveness results in improved thermal efficacy, heat transfer characteristics of nanofluids, and factors influencing its features in solar collectors, which determines its usability. The Parabolic Trough Collector system based on nanofluids is a promising technology with applications in green surroundings.

A traveling wave bifurcation analysis of turbulent pipe flow

Using various techniques from dynamical systems theory, we rigorously study an experimentally validated model by [Barkley et al 2015 Nature 526 550–3], which describes the rise of turbulent pipe flow via a PDE system of reduced complexity. The fast evolution of turbulence is governed by reaction-diffusion dynamics coupled to the centerline velocity, which evolves with advection of Burgers’ type and a slow relaminarization term. Applying to this model a spatial dynamics ansatz and geometric singular perturbation theory, we prove the existence of a heteroclinic loop between a turbulent and a laminar steady state and establish a cascade of bifurcations of various traveling waves mediating the transition to turbulence. The most complicated behaviour can be found in an intermediate Reynolds number regime, where the traveling waves exhibit arbitrarily long periodic-like dynamics indicating the onset of chaos. Our analysis provides a systematic mathematical approach to identifying the transition to spatio–temporal turbulent structures that may also be applicable to other models arising in fluid dynamics.

Experimental and numerical mass transfer study of carbon dioxide absorption using Al2O3/water nanofluid in wetted wall column

In this study, the CO2 absorption by Al2O3/water nanofluid was investigated in laboratory-scale wetted wall column. Effects of important operation parameters such as, nanoparticle volume fraction, fluid flow rate and temperature on the mass transfer coefficient have been studied under laminar conditions and steady state. According to the experimental results, the mass transfer coefficient of nanofluid is higher than base fluid water and the mass transfer coefficient increases with the increase of nanoparticle concentration, temperature, and fluid flow rate. The mass transfer coefficients Al2O3/water nanofluid were increased by 40.3% and 67.16% with addition of 0.0125 and 0.025 %v/v nanoparticle, respectively. Then, the mass transfer behavior of Al2O3/water nanofluid in an axi-symmetric two dimensional domains was simulated by applying computational fluid dynamics considering Brownian motion mass diffusion coefficient in nanofluid. The CFD results have a good agreement with experimental results. Also, results have shown that the dimensionless CO2 concentration in film layer clearly increases with an increase in nanoparticle volume fraction and the temperature; but when the fluid flow rate increases, the CO2 concentration decrease.

On the Control of the 2D Navier–Stokes Equations with Kolmogorov Forcing

This paper is devoted to the control problem of a nonlinear dynamical system obtained by a truncation of the two-dimensional (2D) Navier–Stokes (N-S) equations with periodic boundary conditions and with a sinusoidal external force along the x-direction. This special case of the 2D N-S equations is known as the 2D Kolmogorov flow. Firstly, the dynamics of the 2D Kolmogorov flow which is represented by a nonlinear dynamical system of seven ordinary differential equations (ODEs) of a laminar steady state flow regime and a periodic flow regime are analyzed; numerical simulations are given to illustrate the analysis. Secondly, an adaptive controller is designed for the system of seven ODEs representing the approximation of the dynamics of the 2D Kolmogorov flow to control its dynamics either to a steady-state regime or to a periodic regime; the value of the Reynolds number is determined using an update law. Then, a static sliding mode controller and a dynamic sliding mode controller are designed for the system of seven ODEs representing the approximation of the dynamics of the 2D Kolmogorov flow to control its dynamics either to a steady-state regime or to a periodic regime. Numerical simulations are presented to show the effectiveness of the proposed three control schemes. The simulation results clearly show that the proposed controllers work well.

Evaluation of thermal and fluid dynamic performance parameters in aluminum foam compact heat exchangers

This paper analyses the behavior of heat exchangers with metal foam. A numerical study in a laminar steady state two-dimensional model is provided to evaluate the thermal - fluid dynamic performance of the system. An aluminum foam block embedded with an array of five circular tubes and assigned uniform temperature, constitute the physical domain. The open-celled metal foam is considered as a porous medium in local thermal non equilibrium (LTNE) and the Darcy – Forchheimer – Brinkman model is assumed. The metal foam has a porosity equal to 0.9353 and a pore density equal to 20 pores per inch (PPI). The numerical simulations are carried out considering air as the cooling fluid with several mass flow rate for assigned temperature of the tube surface. The Reynolds number, Re, based on tube diameter, ranges from 56 to 1120, the ratios between the thickness of metal foam and tube diameter, Lmf/d, and between the tube pitch and tube diameter, 2H/d, are in the ranges from 1 to 20 and 1.5–25, respectively. The goal of this investigation is to find the compact heat exchanger size for an assigned metal foam that allows trade-off between the improvement of the heat transfer and the increment of pressure drop, and to study the fluid dynamics and thermal behavior of these configurations. The study focuses on thermal performances of a metal foam heat exchanger using several conventional parameters employed in the analysis of porous medium heat exchangers to find optimal geometrical configurations. Results are given in terms of Colburn factor, friction factor and area goodness factor as a function of Re, Lmf/d and 2H/d. It is shown that the compact heat exchanger, examined in the investigation, presents optimum Reynolds number values; where the ratio between the Colburn and the friction factor, AG, attains a maximum value for metal foam, with different thickness and distance between the tubes of the heat exchanger. Two correlations for AGmax are proposed for 56 ≤ Red ≤ 1120; one in terms of dimensionless thickness and another for the dimensionless pitch.

A complex evaluation of [C2mim][CH3SO3]– alumina nanoparticle enhanced ionic liquids internal laminar flow

This paper involves a numerical study of several water – ionic liquids mixtures and nanoparticle enhanced ionic liquids starting from a less studied ionic liquid: 1-Ethyl-3-methylimidazolium Methanesulfonate, [C2mim][CH3SO3]. The research start point was several previous published experimental results in regard to the water – ionic liquid mixtures and alumina based nanoparticle enhanced ionic liquids thermophysical properties. Consequently, all the considered fluids are completely described and can be successfully implemented in a numerical analysis using the single phase approach. The numerical analysis was performed in a cylindrical enclosure considering laminar steady state and results were collected in terms of Nusselt number, convective heat transfer coefficient, pressure drop and temperature on tube exit. Results were discussed in terms of heat transfer enhancement and pumping power requirement variation, as well as field synergy. Concluding, it can clearly say that mixing water with [C2mim][CH3SO3] ionic liquid it gets a decrease in laminar convective heat transfer coefficient, while adding nanoparticles the heat transfer is enhanced by maximum 50%, depending on the alumina mass concentration.

Numerical design and heat transfer analysis of a non-Newtonian fluid flow for annulus with helical fins

In this research, the flow and thermal characteristics of a non-Newtonian fluid flowing through a double pipe heat exchanger with helical fins around the inner tube were studied numerically. The non-Newtonian power law fluid is flowing in the laminar steady state through the annulus side. A 3D-CFD computational model has been conducted to determine the mean heat transfer coefficients and pressure lost in the annulus with constant temperature tube walls. A numerical analysis is performed for different values of Graetz number of (23 × 103 ≤ Gz ≤ 55 × 103) and fin pitch (25 mm ≤ p ≤ 100 mm). The model was validated for a smooth double pipe heat exchanger, and it's found a good agreement with empirical correlations. The use of helical fin established rotationally flow with vortex core, which enhances the heat transfer and pressure drop simultaneously. In addition, thermal performance was enhanced by the increase of fin pitch. By data reduction, valuable and applicable correlations for Nu and f are presented, which can be used in industrial designs of double pipe heat exchangers.

Double diffusive mixed convection study in a vertical annulus at different aspect ratio and Richardson number

The present study has been considered in heat, mass transfer and the reversal flow occurrence inside the annulus of concentric vertical cylinders numerically. Both the thermal buoyancy and the buoyancy due to different concentrations are of equal magnitude and direction. The forced flow direction effect is investigated. The problem is considered a laminar flow and steady state. The influencing parameters are identified for the problem are Richardson number, Lewis number, and length to gap ratio and Radius ratio. The dimensionless gap is kept constant at unity. The Richardson number is varied from 0.1 to 10, dimensionless length from 5 to 25, the dimensionless radius ratio from 1.5 to 11 and the lewis number from 0.1 to 10. The dimensionless temperature and concentration distributions are illustrated at various range of parameters. In addition, the average values concerning Nusselt as well as Sherwood numbers are correlated. The reverse flow is examined at both aiding and opposing flows. The reverse flow existence is affected by the Richardson number and the length to gap ratio. The value concerning thermal Grashof number is stable at 104.

Global Stability and Local Bifurcations in a Two-Fluid Model for Tokamak Plasma

We study a two-fluid description for high and low temperature components of the electron velocity distribution in an idealized tokamak plasma evolving on a cylindrical domain, taking into account nonlinear drift effects only. We refine previous results on the laminar steady state stability and include viscosity. Taking the temperature difference as the primary parameter, we show that linear instabilities and bifurcations occur within a finite interval and for small enough viscosity only, while the steady state is globally stable for parameters sufficiently far outside the interval. We find that primary instabilities always stem from the lowest spatial harmonics for aspect ratios of poloidal versus radial extent below some value larger than 2. Moreover, we show that any codimension-one bifurcation of the laminar state is supercritical, yielding spatio-temporal oscillations in the form of traveling waves, and hence locally stable for such bifurcations destabilizing the laminar state. In the degenerate case, where the instability region in the temperature difference is a point, these solutions form an arc connecting the bifurcation points. We also provide numerical simulations to illustrate and corroborate the analysis and find additional bifurcations of the traveling waves.

Numerical Investigation of Viscous Dissipation in Elliptic Microducts

In this work a numerical analysis of heat transfer in elliptical microchannels heated at constant and uniform heat flux is presented. A gaseous flow has been considered, in laminar steady state condition, in hydrodynamically and thermally fully developed forced convection, accounting for the rarefaction effects. The velocity and temperature distributions have been determined in the elliptic cross section, for different values of aspect ratio, Knudsen number and Brinkman number, solving the Navier-Stokes and energy equations within the Comsol Multiphysics® environment. The numerical procedure has been validated resorting to data available in literature for slip flow in elliptic cross sections with Br =0 and for slip flow in circular ducts with Br > 0. The comparison between numerical results and data available in literature shows a perfect agreement. The velocity and temperature distributions thus found have been used to calculate the average Nusselt number in the cross section. The numerical results for Nusselt number are presented in terms of rarefaction degree (Knudsen number), of viscous dissipation (Brinkman number), and of the aspect ratio. The results point out that the thermal fluid behavior is significantly affected by the viscous dissipation for low rarefaction degrees and for aspect ratios of the elliptic cross-section higher than 0.2.

Dilute gas flows through elliptic microchannels under H2 boundary conditions

This work presents a numerical investigation of slip flow inside microchannels characterized by an elliptic cross-section. A gaseous flow is considered, in laminar steady state condition, in hydrodynamically and thermally fully developed forced convection, accounting for the rarefaction effect. The momentum and energy equations are solved resorting to the finite element method; the numerical results are compared with analytical values available in the literature for slip flow in elliptic cross sections and in circular ducts, to validate the numerical procedure. The temperature field is determined by considering the H2 boundary condition for different combinations of heated walls among the four branches constituting the elliptic perimeter. Nusselt numbers and normalized wall temperatures in the case of two or four heated sides are presented and discussed.The influence of the cross section aspect ratio and of the rarefaction effects on the fluid behavior are investigated. The numerical results point out that the Nusselt number decreases with the Knudsen number, and increases with the aspect ratio of the elliptical channel.To evaluate the Nusselt numbers for different values of aspect ratio and Knudsen number (in all analyzed cases) a simple polynomial correlation is proposed.Finally a comparison between rectangular and elliptic microchannels has been performed, when the whole perimeter of the cross-section is heated, showing that for values of the aspect ratio greater than 0.33 the elliptic microducts are characterized by better thermal performances.

Numerical modeling of carrier gas flow in atomic layer deposition vacuum reactor: A comparative study of lattice Boltzmann models

This paper characterizes the carrier gas flow in the atomic layer deposition (ALD) vacuum reactor by introducing Lattice Boltzmann Method (LBM) to the ALD simulation through a comparative study of two LBM models. Numerical models of gas flow are constructed and implemented in two-dimensional geometry based on lattice Bhatnagar–Gross–Krook (LBGK)-D2Q9 model and two-relaxation-time (TRT) model. Both incompressible and compressible scenarios are simulated and the two models are compared in the aspects of flow features, stability, and efficiency. Our simulation outcome reveals that, for our specific ALD vacuum reactor, TRT model generates better steady laminar flow features all over the domain with better stability and reliability than LBGK-D2Q9 model especially when considering the compressible effects of the gas flow. The LBM-TRT is verified indirectly by comparing the numerical result with conventional continuum-based computational fluid dynamics solvers, and it shows very good agreement with these conventional methods. The velocity field of carrier gas flow through ALD vacuum reactor was characterized by LBM-TRT model finally. The flow in ALD is in a laminar steady state with velocity concentrated at the corners and around the wafer. The effects of flow fields on precursor distributions, surface absorptions, and surface reactions are discussed in detail. Steady and evenly distributed velocity field contribute to higher precursor concentration near the wafer and relatively lower particle velocities help to achieve better surface adsorption and deposition. The ALD reactor geometry needs to be considered carefully if a steady and laminar flow field around the wafer and better surface deposition are desired.

Double Diffusive Natural Convection in a Porous Rhombic Annulus

This article reports on an investigation performed to study laminar steady state double diffusive natural convection in a two-dimensional porous enclosure of rhombic cross-section. Solutions are obtained numerically using a finite volume method for the case when the inner wall is uniformly heated to a temperature T h while subjected to a high solute concentration S h , and the outer wall is evenly cooled to a temperature T c while exposed to a low solute concentration S c . Simulations are conducted for several values of Rayleigh number (Ra), Darcy number (Da), Prandtl number (Pr), porosity (ϵ), and enclosure gap (E g ) for fixed values of Lewis number (Le = 10) and buoyancy ratio (N = 10). The results are displayed in terms of streamlines, isotherms, isoconcentrations, mid-height velocity, temperature, concentration profiles, and local and average Nusselt and Sherwood number values. Predictions indicate that for the Lewis number and buoyancy ratio considered, the flow field is more affected by mass transfer than by heat transfer. Moreover, convection effects increase with an increase in Ra, Da, E g , and/or ϵ. The porosity of the porous matrix has no effect on the flow, temperature, and concentration fields at low values of Darcy number. Furthermore, the total heat and mass transfer increases as Pr increases and/or as the enclosure gap decreases due to an increase in the wall area over which heat and mass transfer occur. Values of and indicate dominant diffusion at low Ra number values with convection affecting the total heat and mass transfer at high Ra values.

Hemodynamics of the aortic valve and root: implications for surgery.

Hemodynamics of the aortic valve and root: implications for surgery.

Numerical study of the effects of heat transfer methods on CH4/(CH4 + H2)-AIR pre-mixed flames in a micro-stepped tube

In this study, an approach to modification and improvement of CH4/air pre-mixed flame in a micro-stepped tube is numerically studied. The effects of added hydrogen to methane as an additive, entrance mixture velocity and some physical properties such as the micro-stepped tube wall thermal conductivity and the outer wall convective and radiative heat transfer coefficients on temperature distribution and combustion progress in a micro-stepped tube are calculated using a high order, high accuracy 2D numerical laminar steady state code. The results show that adding hydrogen to methane in a micro-stepped tube can play a pivotal role in modification processes of combustion phenomena in a micro combustor. Also, it is found that adding hydrogen to CH4 can assure the flame presence in some certain conditions in comparison to the simple backward facing step method. Moreover, adding hydrogen can improve the concentration of the combustion vital radicals and also temperature distribution along the micro combustor, impressively. In this regard, adding hydrogen to methane as an additive sustains the combustion vital radicals against the variation of the heat transfer conditions in or around a micro-combustor.

Effects of Natural Convection from an Open Square Cavity Containing a Heated Circular Cylinder

The problem of natural convection heat transfer in a square open cavity containing a heated and conducting circular cylinder at the centre is analyzed in this paper. As boundary conditions of the cavity, the left vertical wall is kept at a constant heat flux, bottom and top wall are kept at different high and low temperature respectively. The remaining side is open. Two dimensional laminar steady state natural convection is considered. This configuration is related in the design of electronic devices, solar energy receivers, uncovered flat plate solar collectors geothermal reservoirs etc. The fluid is concerned with different Prandtl numbers, Grashof numbers and the properties of the fluid are assumed to be constant. The development of Mathematical model is governed by the coupled equations of continuity, momentum and energy and is solved by employing Galerkin weighted finite element method. Flow field and heat transfer were predicted for fluid with Pr = 0.72 , 1.0 ,7.0; Gr = 103, 104, 105 ,106; inclination angles of the cavity are ? = 0°, 15°, 30°, 45° and diameter ratio dr = 0.2.The average Nusselt number increases as the increases of inclination angle of the cavity for lower Pr and lower temperature at bottom wall. The average Nu increases mainly for higher inclinations and for higher Gr. Various vortices and recirculations are formed into the flow field for higher Pr and higher temperature at the bottom wall. DOI: http://dx.doi.org/10.3329/bjsir.v47i1.10718Bangladesh J. Sci. Ind. Res. 47(1), 19-28, 2012

Slip Flow in Elliptic Microducts with Constant Heat Flux

This paper outlines a numerical model for determining the dynamic and thermal performances of a rarefied fluid flowing in a microduct with elliptical cross-section. A slip flow is considered, in laminar steady state condition, in fully developed forced convection, with Knudsen number in the range 0.001−0.1, in H1 boundary conditions. The velocity and temperature distributions are determined in the elliptic cross-section, for different values of both aspect ratio γ and Knudsen number, resorting to the Comsol Multiphysics software, to solve the momentum and energy equations. The friction factors (or Poiseuille numbers) and the convective heat transfer coefficients (or Nusselt numbers) are calculated and presented in graphs and tables. The numerical solution is validated resorting to data available in literature for continuum flow in elliptic cross-sections (Kn = 0) and for slip flow in circular ducts ([Formula: see text]). A further benchmark is carried out for the velocity profile for slip flow in ellipticalcross-sections, thanks to a recent analytical solution obtained using elliptic cylinder coordinates and the separation of variables method. The Poiseuille and Nusselt numbers for elliptic cross-sections are discussed. The results may be used to predict pressure drop and heat transfer performance in metallic microducts with elliptic cross-section, produced by microfabrication for microelectromechanical systems (MEMS).

Analytical and numerical investigations of laminar and turbulent Poiseuille–Ekman flow at different rotation rates

Laminar and turbulent Poiseuille–Ekman flows at different rotation rates have been investigated by means of analytical and numerical approaches. A series of direct numerical simulations (DNSs) with various rotation rates (Ro2=0–1.82) for Reynolds number Reτ0=180 based on the friction velocity in the nonrotating case has been conducted. Both (laminar and turbulent) flow states are highly sensitive to the rotation. Even a small rotation rate can reduce the mean streamwise velocity and induce a very strong flow in the spanwise direction, which, after attaining a maximum, decreases by further increasing the rotation rate. It has been further observed that turbulence is damped by increasing the rotation rate and at about Ro2=0.145 a transition from the fully turbulent to a quasilaminar state occurs. In this region Reynolds number is only large enough to sustain some perturbations and the mean velocity profiles have inflection points. The instability of the turbulent shear stress is probably the main reason for the formation of the elongated coherent structures (roll-like vortices) in this region. In the fully turbulent parameter domain all six components of Reynolds stress tensor are nonzero due to the existence of the spanwise mean velocity. The Poiseuille–Ekman flow in this region can be regarded as a turbulent two-dimensional channel flow with a mean flow direction inclining toward the spanwise direction. Finally, due to the further increase in the rotation rate, at about Ro2=0.546 turbulence is completely damped and the flow reaches a fully laminar steady state, for which an analytical solution of the Navier–Stokes equations exists. The DNS results reproduce this analytical solution for the laminar state.

An improved unsteady, unstructured, artificial compressibility, finite volume scheme for viscous incompressible flows: Part I. Theory and implementation

AbstractA robust, artificial compressibility scheme has been developed for modelling laminar steady state and transient, incompressible flows over a wide range of Reynolds and Rayleigh numbers. Artificial compressibility is applied in a consistant manner resulting in a system of preconditioned governing equations. A locally generalized preconditioner is introduced, designed to be robust and offer good convergence rates. Free artificial compressibility parameters in the equations are automated to allow ease of use while facilitating improved or comparable convergence rates as compared with the standard artificial compressibility scheme. Memory efficiency is achieved through a multistage, pseudo‐time‐explicit time‐marching solution procedure. A node‐centred dual‐cell edge‐based finite volume discretization technique, suitable for unstructured grids, is used due to its computational efficiency and high‐resolution spatial accuracy. In the interest of computational efficiency and ease of implementation, stabilization is achieved via a scalar‐valued artificial dissipation scheme. Temporal accuracy is facilitated by employing a second‐order accurate, dual‐time‐stepping method. In this part of the paper the theory and implementation details are discussed. In Part II, the scheme will be applied to a number of example problems to solve flows over a wide range of Reynolds and Rayleigh numbers. Copyright © 2002 John Wiley & Sons, Ltd.

Laminar natural convection in inclined open shallow cavities

Laminar steady state natural convection in inclined shallow cavities has been numerically studied. The side facing the opening is heated by a constant heat flux, sides perpendicular to the heated side are insulated and the opening is in contact with a fluid at constant temperature and pressure. Equations of mass, momentum and energy are solved using constant properties and Boussinesq approximation and assuming an approximate boundary conditions at the opening. Isotherms and streamlines are produced, heat and mass transfer is calculated for Rayleigh numbers from 10 3 to 10 10, cavity aspect ratio A= H/ L from 1 to 0.125. The results show that flow and heat transfer are governed by Rayleigh number, aspect ratio and the inclination. Heat transfer approaches asymptotic values at Rayleigh numbers independent of the aspect ratio. The asymptotic values are close to that for a flat plate with constant heat flux. The effect of elongation of open cavities is to delay this asymptotic behavior. It is also found that the inclination angle of the heated plate is an important parameter affecting volumetric flow rate and the heat transfer.