Presence Of Natural Convection Research Articles

Numerical Study of Solidification in Cavity with the Presence of Natural Convection

Numerical Study of Solidification in Cavity with the Presence of Natural Convection

Experimental and Theoretical Study of Ventilation and Heat Loss From Isothermally Heated Clothed Vertical Cylinder in Uniform Flow Field

The flow characteristics and heat transfer are studied in a vertical annulus of a heated cylinder surrounded by a permeable cylinder, subject to cross uniform wind with open end to the environment and in the presence of natural convection. The objective here is to develop a computationally efficient model capable of capturing the physics of the flow and heat transport to predict air renewal rates in the vertical annulus. The small quantities of air infiltrating/exfiltrating through the porous cylinder over its upstream/downstream regions do not substantially affect the external flow pattern around the clothed cylinder. The air annulus flow and heat transport model predicted the radial and vertical mass fluxes and the mass flow rate at the opening as a function of environment conditions, porous cylinder thermal properties, wind speed, and annulus geometry. Experiments were performed in a low speed wind tunnel (0.5–5 m/s), in which an isothermally heated vertical cylinder surrounded by a clothed outer cylinder was placed in uniform cross wind. The tracer gas method is used to predict total ventilation flow rates through the fabric and the opening. Good agreement was found between the model and experimental measurements of air renewal rate and predicted heat loss from the inner cylinder at steady conditions. A parametric study is performed to study the effect of wind speed and temperature difference between the wind and skin temperature on induced ventilation through the clothing and the opening. It is found that natural convection enhances ventilation of the annulus air at wind speed, less than 3 m/s, while at higher speeds, natural convection effect is negligible. As the temperature difference between external wind and inner cylinder surface increases, the vertical air temperature gradient and total upward airflow through the opening increase.

Heat flow analysis for natural convection within trapezoidal enclosures based on heatline concept

Heat flow patterns in the presence of natural convection within trapezoidal enclosures have been analyzed with heatlines concept. In the present study, natural convection within a trapezoidal enclosure for uniformly and non-uniformly heated bottom wall, insulated top wall and isothermal side walls with inclination angle φ have been investigated. Momentum and energy transfer are characterized by streamfunctions and heatfunctions, respectively, such that streamfunctions and heatfunctions satisfy the dimensionless forms of momentum and energy balance equations, respectively. Finite element method has been used to solve the velocity and thermal fields and the method has also been found robust to obtain the streamfunction and heatfunction accurately. The unique solution of heatfunctions for situations in differential heating is a strong function of Dirichlet boundary condition which has been obtained from average Nusselt numbers for hot or cold regimes. Parametric study for the wide range of Rayleigh number ( Ra ) , 10 3 ⩽ Ra ⩽ 10 5 and Prandtl number ( Pr ) , 0.026 ⩽ Pr ⩽ 1000 with various tilt angles φ = 45 ° , 30 ° and 0 ° (square) have been carried out. Heatlines are found to be continuous lines connecting the cold and hot walls and the lines are perpendicular to the isothermal wall for the conduction dominant heat transfer. The enhanced thermal mixing near the core for larger Ra is explained with dense heatlines and convective loop of heatlines. The formation of boundary layer on the walls has a direct consequence based on heatlines. The local Nusselt numbers have also been shown for side and bottom walls and variation of local Nusselt numbers with distance have also been explained based on heatlines. It is found that average heat transfer rate does not vary significantly with φ for non-uniform heating of bottom wall.

Oscillatory and nonoscillatory behavior of a simple model for cool flames, Sal'nikov's reaction, P → A → B, occurring in a spherical batch reactor with varying intensities of natural convection

When cool flames, or indeed any exothermic chemical reaction, occur in a fluid inside an unstirred vessel, the heat from the reaction often induces temperature gradients and consequently motion, i.e., natural convection. The intensity of the resulting flow is governed by the Rayleigh number (Ra). This work simulates numerically the behavior of Sal'nikov's reaction, P → A → B, under the influence of natural convection in an unstirred spherical reactor. This reaction is the simplest to exhibit the thermokinetic oscillations characterizing cool flames. The behavior of this system can be represented on a three-dimensional regime diagram, whose axes are ratios of the characteristic timescales ( τ) for chemical reaction, diffusion (of both heat and mass), and natural convection. Previous work has identified a region of oscillations on this diagram in the purely diffusive limit, when Ra = 0. This work extends this analysis to the general 3D space, where diffusion and natural convection are both important. A region in which oscillations are observed has been found for fixed values of the first-order rate constants for Sal'nikov's reaction. There is a distinct change in the shape of the region of oscillations around the critical value of Ra ∼ 500, when natural convection becomes important. When diffusion dominates transport (Ra < 500), the boundaries between oscillatory and nonoscillatory solutions are largely independent of the ratio of timescales τ step 2 / τ convection and agree well with the values found previously in the purely diffusive limit. When natural convection is important (Ra > 500), the oscillations occur over a wider range of parameters than is the case for a diffusive system. The presence of natural convection also leads to various, more complex behaviors than are seen in the diffusive or well-mixed limits. A region in the regime diagram was found where the oscillations in temperature and the concentration of A have small amplitudes and a frequency that is quite different from those generated in a well-mixed system. It is possible that these oscillations are caused by natural convection, i.e., are not thermokinetic oscillations produced by the chemical reaction. It was also found that sometimes the oscillations in the temperature and the concentration of A are in phase; more generally they are in anti-phase. The evolution of nonoscillatory behavior with relatively small increases in temperature was found to be always fairly similar, regardless of the intensity of natural convection. The shape of the temperature profile along the vertical axis of the reactor did, however, change with the intensity of natural convection. Finally, the nonoscillatory solutions with a large rise in temperature in the presence of natural convection were found to be very much like those seen in the purely diffusive limit for small times, due to the relatively long induction time (∼3.5 s in a vessel with diameter 0.1 m) for the onset of natural convection.

Role of ‘Bejan’s heatlines’ in heat flow visualization and optimal thermal mixing for differentially heated square enclosures

Heat flow patterns in the presence of natural convection have been analyzed with Bejan’s heatlines concept. Momentum and energy transfer are characterized by streamfunctions and heatfunctions, respectively such that streamfunctions and heatfunctions satisfy the dimensionless forms of momentum and energy balance equations, respectively. Finite element method has been used to solve the velocity and thermal fields and the method has also been found robust to obtain the streamfunction and heatfunction accurately. The unique solution of heatfunctions for situations in differential heating is a strong function of Dirichlet boundary condition which has been obtained from average Nusselt numbers for hot or cold regimes. The physical significance of heatlines have been demonstrated for a comprehensive understanding of energy distribution and optimal thermal management via analyzing three cases. Case 1 involves the uniform and non-uniform heating of bottom wall with cooled side walls. The studies illustrate that the heat flow primarily occurs from the central regime of the bottom wall to a very small regime of the top portion of side walls. A large portion of central regime of cold side walls do not receive significant amount of heat. In order to maximize the thermal energy distribution, the distributed heating at the middle portions of the bottom and side walls have been considered in case 2 and heatlines clearly depict the distributions of heat from the hot walls to the large regimes of the cold wall. Further case 3 illustrates the enhanced heat flows in presence of heated bottom and left side walls. Heatline is found as an effective numerical tool to visualize energy distribution in order to establish a suitable heating strategy.

CFD simulation and evaluation of controllable parameters effect on thermomagnetic convection in ferrofluids using Taguchi technique

In the present attempt a CFD simulation capable of coupling behaviors from the nano-scale through the full-scale system in which a ferrofluid containing magnetite particles suspended in kerosene carrier liquid is presented. The main objective of the work was to simulate the thermodiffusion and also to evaluate the factors influence on this phenomenon in a cylindrical geometry. In simulations a two-phase mixture model was used to predict the behavior of the system. To optimize the thermomagnetic effect, different parameters including temperature difference across the layer, initial magnetic phase concentration, aspect ratio of the geometry, magnetic field magnitude and diameter of magnetic particles were examined using L 16 orthogonal array of Taguchi at four levels. Analysis of the simulation data indicate that the magnetic Soret effect can even be higher than the conventional one and its strength depends on the magnetic field strength, confirmed experimentally by Völker and Odenbach [Völker T, Odenbach S. Thermodiffusion in magnetic fluids. J Magn Magn Mater 2005;289:289–91]. The statistic evaluation shows that temperature and initial concentration of magnetic phase have the maximum and minimum contribution on the thermodiffusion, respectively. According to the results temperature difference 80 K, initial concentration of magnetic phase 0.08, aspect ratio 0.2, magnetic field strength 100 kA/m and magnetic particles diameter 100 nm were obtained as optimum conditions in the presence of natural convection. The same result was gained in the lack of natural convection except the magnetic field strength was 160 kA/m. Finally, based on the primary results, a verification test was also performed to confirm the validity of the used statistical method.

An analytical and numerical study of coupled transient natural convection and solidification in a rectangular enclosure

The transient process of the solidification of a pure liquid phase-change material in the presence of natural convection in a rectangular enclosure is considered both analytically and numerically. One vertical boundary is held at a temperature below the melting-point of the material, the other above; the horizontal boundaries are both assumed adiabatic. A nondimensional analysis of the problem, principally in terms of the Rayleigh ( Ra) and Stefan ( St) numbers, indicates that some asymptotic simplification is possible for materials often considered in the literature (water, gallium, lauric acid). This observation suggests a way to simplify the full problem when Ra ≫ 1 and St ≪ 1, giving a conventional boundary value problem for the liquid phase and pointwise-in-space first-order ODEs for the evolution in time of the solidification front. The method is tested against full 2D finite-element-based transient numerical simulations of solidification. In addition, simpler approaches for determining the average thickness of the solid layer, based on boundary-layer and enclosure flow correlations, are also investigated.

Electrochemical reaction with RedOx electrolyte in toroidal conduits in the presence of natural convection

Transport processes in an upright, concentric, annular, electrochemical reactor filled with RedOx electrolyte solution are studied experimentally and theoretically. The electrodes form the two vertical surfaces of the reactor. The theoretical calculations consist of the solution of the Navier–Stokes and the Nernst–Planck equations accounting for species’ diffusion, migration, convection, and electrochemical reactions on the electrodes’ surfaces as a function of the difference in electrodes’ potentials and the average concentration of the electrolyte. Since the convection is driven by density gradients, the momentum and mass transport equations are coupled. The current transmitted through the electrolyte is significantly enhanced by natural convection. The current is measured as a function of the difference in the electrodes’ potentials. To obtain the reaction rate constants, an inverse problem is solved and the reaction rate constants are determined by minimizing the discrepancy between theoretical predictions and experimental observations. As an example, we study the reversible electrochemical reaction Fe +++ + e − = Fe ++ on platinum electrodes.

Inverse solution for a biochemical heat source in a porous medium in the presence of natural convection

The inverse problem approach by conjugate gradient with adjoint equations is adapted to the context of a non-isothermal bioprocess, controlled by internal heat generation from microbial oxidation, as could be found in a composting reactor for instance, to determine the heat source from internal temperature measurements. The volumetric heat source is assumed proportional to the rate of consumption of a substrate by a biomass, as described by a Monod model. Computations are performed for Rayleigh numbers equal to 0.25 and 25, for a representative biochemical reaction under typical boundary conditions, for constant and temperature-dependent model parameters. The influence of noisy input data is also considered. It is found that good solutions can be obtained when heat release and diffusion occur over very different time scales. The variation of the model parameters with temperature must be taken into account, but single sensor solutions are possible at relatively small Rayleigh numbers when convection is present.

A scaling analysis of Sal'nikov's reaction, P→A→B, in the presence of natural convection and the diffusion of heat and matter

Sal'nikov's chemical reaction is very simple; it consists of two consecutive first-order steps, producing a product B from a precursor P via an active intermediate A, in P→A→B. The first step is assumed to be thermoneutral, with zero activation energy, while the second step is exothermic and has a positive activation energy. These properties make this mechanism one of the simplest to display thermokinetic oscillations, as seen in cool flames. We consider a pure gas, P, undergoing Sal'nikov's reaction in a closed spherical vessel, whose walls are held at a constant temperature. Natural convection becomes significant once the temperature is high enough for the Rayleigh number to reach approximately 10 3 . The subsequent behaviour of the system depends on the interaction between convection, diffusion of heat and mass, and chemical kinetics. By examining the governing equations, we develop and evaluate scales for the characteristic velocity, concentration of the intermediate A and the temperature rise during the progress of the reaction. These scales depend on the characteristic time-scales for the interacting phenomena of chemical reaction, diffusion and natural convection. Our theoretical predictions are verified by full numerical simulation for the two limiting cases when transport is dominated, respectively, by diffusion and natural convection.

Solid/Liquid Phase Change in Presence of Natural Convection: A Thermal Energy Storage Case Study

Solid/liquid phase change process has received great attention for its capability to obtain high energy storage efficiency. In order to analyze these systems, undergoing a solid/liquid phase change, in many situations the heat transfer process can be considered conduction-dominated. However, in the past years, it has been shown that natural convection in the liquid phase can significantly influence the phase change process in terms of temperature distributions, interface displacement and energy storage. In this paper, a procedure to analyze systems undergoing liquid/solid phase change in presence of natural convection in the liquid phase based on the utilisation of a commercial computer code (FLUENT), has been developed. This procedure is applied to the study of a cylinder cavity heated from above and filled with a phase change material. It was found that when the coupling with the environment, even if small, is considered, natural convection in the liquid phase occurs. The numerical results are then compared with available experimental data. The analysis shows that the agreement between numerical and experimental results is significantly improved when the results are obtained considering the presence of circulation in the liquid phase instead of considering the process only conduction-dominated. Furthermore, some interesting features of the flow field are presented and discussed.

Numerical solution of the phase change problem around a horizontal cylinder in the presence of natural convection in the melt region

This paper deals with the numerical study of melting of phase change material around a horizontal circular cylinder in the presence of the natural convection in the melt phase. A two dimensional unsteady mathematical model has been formulated in terms of primitive variables and a coordinate transformation technique has been used to fix the moving front. The finite volume approach was used to discretize the system of governing equations, boundary and initial conditions and obtain a system of linear algebraic equations. In the numerical solution an implicit scheme was used for the momentum and energy equations and an explicit scheme for the energy balance at the interface. The numerical predictions were compared with available results to establish the validity of the model and the numerical approach.

On the Prediction of Local Ice Formation in Pipes in the Presence of Natural Convection

Pipe freezing is a pipeline maintenance technique which is used to isolate sections of a liquid-filled pipeline by freezing the contents to form a solid pressure-resistant plug. This paper describes the development of a numerical model of natural convection and solidification in a vertical water-filled pipe. The natural convection-driven flows are examined in detail and the interaction with the forming ice plug is studied. The results are compared with experimental data. The numerical approach is contrasted with a simpler one-dimensional analytical method and criteria are proposed to aid the choice of modeling technique under different conditions.

A simplified model of dendritic growth in the presence of natural convection

The terrestrial growth of fixed dendrites is accompanied by a natural convection process which manifests as a buoyancy-induced flow field surrounding the dendrite tip. This flow field is intrinsically coupled to the temperature field that evolves around a dendrite and acts to thin the thermal boundary layer, resulting in increased growth velocity for a fixed supercooling. An exact analytical treatment of this phenomenon requires solving coupled energy and momentum equations. As reviewed in the literature, these solutions are varied and difficult to apply in a rapid estimation of the growth velocity. The present study attempts to simplify the representation and solution of the convection process by deriving a modified Ivanstov growth model. The convective process is analyzed by a simple superposition technique. The thermal field, emanating from a single dendrite tip, generates a natural convection process and adjusts the energy transport in a lumped fashion. The direct analogy is the prediction of the heat transfer rate from a sphere due to natural convection. An interfacial energy balance is written at the dendrite tip, from which the nondimensional supercooling is written as a function of an undetermined tip-local Nusselt number. The Nusselt number is formulated in terms of a Rayleigh number, the undetermined dendrite tip radius and the supercooling. The equation for the nondimensional supercooling is then solved approximately by applying marginal stability theory and the baseline advection–diffusion result, and is written as the product of the Ivanstov solution, and a multiplier which is determined by the Peclet number and a convection grouping. The model is tested against experimental data from five references. The Peclet and Prandtl number data range from 10 −4⩽Pe⩽10 −2 and 2⩽Pr⩽130, respectively. Despite the simplicity of the model, the nondimensional supercooling data are predicted with an average absolute deviation of 18.2%. The clarity-of-prediction suggests that the natural convection process is fundamental and can be simplified using this control-volume technique with negligible loss of fidelity.

Convection-based model for a PCM vertical storage unit

This paper presents a two-dimensional axi-symmetrical model for the formulation of the problem of fusion of PCM around a vertical cylinder in the presence of natural convection. The basic equations of mass, momentum and energy were formulated in terms of the vorticity and the stream function. The numerical predictions were compared with available experimental results indicating good agreement. Additional results show the effects of the geometrical and operational parameters on the solid–liquid interface, stream function, energy stored and melt mass fraction. The model was extended to produce charts and correlations for the mean heat transfer rate, total solidification (or fusion) time in terms of the geometrical parameter, the modified Rayleigh number and the Stefan number. These charts and correlations are helpful in engineering design of PCM storage units. © 1998 John Wiley & Sons, Ltd.

Influence of Buoyancy on Convective Heat Transfer in Helicoidal Pipes

The combined effects of curvature and buoyancy forces on convective heat transfer in axially vertical and horizontal helicoidal pipes have been explored in this investigation. Distilled water and ethylene glycol were used as working fluids. It has been observed that natural convection causes the peripheral maximum Nusselt number location to shift from the outer coil wall to the bottom of the tube cross section in the vertical coil. In the horizontal coil, the axial temperature distribution becomes periodically wavy with the presence of natural convection. The three following heat transfer regimes have been observed from the local temperature and Nusselt number distributions in the experiment of vertical helicoidal pipes: 1) a regime in which centrifugal force is dominant, 2) a regime in which both the centrifugal and buoyancy forces are effective (mixed regime), and 3) a regime in which the buoyancy force is dominant. Furthermore, it has been found that natural convection enhances heat transfer significantly for high Prandtl number fluids (e.g., ethylene glycol), but its effect is minor on the average Nusselt number for low Prandtl number fluids (e.g., water).

Finite element analysis of solidification of aluminum with natural convection

It is well known that A segregation similar to that found in steel castings is the result of an upward flow of inter-dendritic liquid. The liquid steel rises because the density of the liquid in contact with the solid decreases with temperature decrease. The inter-dendritic liquid steel is thus lighter than the bulk liquid steel. Channels or A segregates are formed because the rising liquid steel must move towards the hotter center of the casting. As the temperature increases. the inter-dendritic liquid can dissolve the solid and a channel is formed. Once formed, a channel continues to grow, producing the well-developed A segregate in the final casting. Thus, detailed information during solidification in the presence of natural convection is of importance. Because of the non-linearity and complexity of the problem, analytic solutions of the solidification of pure metals and alloys are limited. In order to understand the interaction of fluid flow in solidifying system, a two-dimensional finite-element program which can be applied for solving the solidification of pure metals and alloys, including the effects of natural convection in liquid, was developed using a temperature-recovery scheme. Two numerical examples demonstrate the accuracy and the capability of the program developed.

Control of the freezing interface morphology in solidification processes in the presence of natural convection

AbstractThis paper presents a methodology for the solution of an inverse solidification design problem in the presence of natural convection. In particular, the boundary heat flux q0 in the fixed mold wall, δΩ0, is calculated such that a desired freezing front velocity and shape are obtained. As the front velocity together with the flux history qms on the solid side of the freezing front play a determinant role in the obtained cast structure, the potential applications of the proposed methods to the control of casting processes are enormous.The proposed technique consists of first solving a direct natural convection problem of the liquid phase in an a priori known shrinking cavity, ΩL(t), before solving an ill‐posed inverse design conduction problem in the solid phase in an a priori known growing region, ΩS(t). The direct convection problem is used to evaluate the flux qml in the liquid side of the freezing front. A front tracking deforming finite element technique is employed. The flux qml can be used together with the Stefan condition to provide the freezing interface flux qms in the solid side of the front. As such, two boundary conditions (flux qms and freezing temperature θm) are especified along the (known) freezing interface δΩI(t). The developed design technique uses the adjoint method to calculate in L2 the derivative of the cost functional, ∥θm – θ(x, t; q0)∥, that expresses the square error between the calculated temperature θ(x, t; q0) in the solid phase along δΩI(t) and the given melting temperature. The minimization of this cost functional is performed by the conjugate gradient method via the solutions of the direct, sensitivity and adjoint problems. A front tracking finite element technique is employed in this inverse analysis. Finally, an example is presented for the solidification of a superheated incompressible liquid aluminium, where the effects of natural convection in the moving interface shape are controlled with a proper adjustment of the cooling boundary conditions.

Analysis of solidification in the presence of high rayleigh number convection in an enclosure

A simple and convenient analysis of the process of time-dependent solidification in an enclosed liquid cooled from the side in the presence of natural convection is presented, the influence of each parameter on the process of solidification is carried out systematically. The accuracy of this model is justified by comparing its predicting values with the previous results.

The Prandtl Number Effect on Melting Dominated by Natural Convection

In a recent paper, Gobin and Benard considered the task of correlating the heat transfer data for melting in the presence of natural convection when the Pr value of the liquid phase is considerably smaller than 1. To correlate the low-Pr data is an important and timely task, especially in view of the voluminous work that has been dedicated to situations in which Pr is greater than 1. For the convection-dominated regime known also as quasi-stationary melting, Gobin and Benard correlated their low-Pr numerical data with the formula: Nu=0.29 Ra[sup 0.27]Pr[sup 0.18] They noted that this correlation does not agree with the Nu[approximately](RaPr)[sup 1/4] trend that might be expected from the single-phase natural convection scales for low Prandtl numbers. They concluded that: (1) The relevance of the group (RaPr) is not verified by their numerical results for convection-dominated melting, and (2) further work is required to determine the scaling laws that govern the transition from the initial (conduction) regime to the final (convection) regime of the process of melting by side heating. These two conclusions defined the work presented in this note. In it is reported that the correct scales of natural convection melting when the Prandtl number is small.more » Then construct a scaling-correct heat transfer correlation that spans the entire range of Prandtl numbers.« less