Vertical Rectangular Enclosure Research Articles

Sensitivity of an electrical impedance-based sensor for the liquid fraction estimation during melting and solidification inside a vertical rectangular enclosure

Monitoring the liquid fraction in latent thermal energy storages (LTESs) can enable the implementation of smart control strategies for improved performance and increased utilization of renewable energy sources. However, measuring the liquid fraction is challenging because solid-liquid phase change processes occur at nearly constant temperature. The present study explores an electrical impedance-based sensing technique that could become a non-intrusive and accurate alternative to determine the liquid fraction. The study examines the melting and solidification of a phase change material (PCM) inside a vertical rectangular enclosure with an isothermal wall. Two sets of electrodes are located on each of the side walls of the enclosure. Initially, numerical simulations of melting and solidification are performed to generate physically meaningful solid and liquid phase distributions. Then, these phase distributions are used as input for electrical simulations to estimate the response to changes in the liquid fraction of the electrical impedance between electrode pairs in in-line, front-facing and crosswise configurations. Also, the effect of the contrast ratios between the electrical conductivity of the solid and liquid phase on the sensitivity is assessed. The front-facing electrodes are found to have the best performance across a large range of conductivity ratios. The in-line electrodes perform the lowest because the sensitivity drastically decreases as a layer of the more conductive phase starts forming on the wall where the electrodes are located. An improvement in the performance of in-line electrodes is observed when the conductivity ratio is decreased.

Natural Convection From Dual Surface Heat Sources in a Vertical Rectangular Enclosure.(Dept.M)

Natural Convection From Dual Surface Heat Sources in a Vertical Rectangular Enclosure.(Dept.M)

Effect of the Direction of Uniform Horizontal Magnetic Field on the Linear Stability of Natural Convection in a Long Vertical Rectangular Enclosure

The effect of the direction of external horizontal magnetic fields on the linear stability of natural convection of liquid metal in an infinitely long vertical rectangular enclosure is numerically studied. A vertical side wall is heated and the opposing vertical wall is cooled both isothermally, whereas the other two vertical walls are adiabatic. A uniform horizontal magnetic field is applied either in the direction parallel or perpendicular to the temperature gradient. In this study, the height of the enclosure is so long as to neglect the top and bottom effects where returning flow takes place, and thus the basic flow is assumed to be a parallel flow and the temperature field is in heat conduction state. The Prandtl number is limited to the value of 0.025 and horizontal cross-section is square. The natural convection is monotonously stabilized as increase in the Hartmann number when the applied magnetic field is parallel to the temperature gradient. However, when the applied magnetic field is perpendicular to the temperature gradient, it is once destabilized at a certain low Hartmann number, but it is stabilized at high Hartmann numbers.

A Numerical Investigation into the Heat Transfer and Melting Process of Lauric Acid in a Rectangular Enclosure with Three Values of Wall Heat Flux

A numerical study of melting of Lauric acid in a vertical rectangular cross-section enclosure was performed with FLUENT 18.2. The enclosure was subject to a constant heat flux on one side of 500, 750 and 1000 W/m2. For model validation purposes simulations were initially performed of experimental systems in the literature with predicted values compared to experimental measurements. Predictions indicate that during the initial stage of melting, conduction is the dominant mode of heat transfer, subsequently replaced by convection when there is sufficient liquid PCM. The simulations show that as the magnitude of heat flux is increased, average wall temperature increases and melting time reduces. The predicted results indicated that melting time decreases by 28.5 % as the wall flux increases by 50 % from 500 to 750 W/m2. The time required for melting reduces by about 50% when the wall heat flux is increased from 500 to 1000 W/m2.

Experimental investigation of natural convection heat transfer characteristics in MWCNT-thermal oil nanofluid

The carbon nanotubes are considered as one of the highest thermal conductive material which is having a variety of heat transfer applications. The suitability of carbon nanotubes in convective heat transfer is examined using multi-wall carbon nanotubes (MWCNT)-thermal oil-based nanofluids. Stable nanofluids are prepared in the concentration range of 0–1 mass% and Prandtl number range of 415 ≤ Pr ≤ 600 using ultrasonication. The natural convection heat transfer behavior is studied experimentally in a vertical rectangular enclosure with aspect ratio 4. The heat transfer experiments are conducted at varying heat flux in the range of 1594–3150 W m−2. The heat transfer coefficient, Nusselt number and Rayleigh number are estimated for MWCNT-thermal oil-based nanofluids and are compared with pure thermal oil. A significant deterioration in heat transfer coefficient is observed at higher concentrations of nanofluids. The study signifies the adverse impact on the cooling performance of MWCNT-thermal oil-based nanofluids in natural convection heat transfer, even though higher thermal conductivities are observed in nanofluids. It is found that not only thermal conductivity is essential property in heat transfer, but other thermophysical properties are also influential towards thermal management.

An experimental study on the natural convection heat transfer in rectangular enclosure using functionalized alumina-thermal oil-based nanofluids

The nanofluids are considered as an effective medium for thermal transport in various applications due to improved properties. Limited experimental studies are accomplished on the convective heat transfer of nanofluids. Natural convective heat transfer behavior in nanofluids is experimentally studied in a vertical rectangular enclosure (aspect ratio=4) with one heating and one cooling wall. The fluid under investigation is a novel and highly stable functionalized alumina-thermal oil-based nanofluid. The investigations are carried out for different concentrations of nanofluids ranging from 0 to 3wt%. The effectiveness of the natural convection heat transfer process is mainly dependent on the properties of cooling media. The measured thermophysical properties of nanofluids are used for the estimation of heat transfer characteristics with a Prandtl number range of 228–592. The heat transfer coefficient and Nusselt number are obtained at different nanoparticle concentrations. A heat flux is applied on the hot wall with a range of 1593.75–3150W/m2. An improvement in the cooling performance of nanofluids is observed. The high nanoparticle concentrations of nanofluids exhibit higher heat transfer coefficient as compared to the pure thermal oil. A correlation is developed for the Nusselt number in terms of Rayleigh number (4.43×105–2.59×106), nanoparticle concentration and effective thermophysical properties.

Melting processes of phase change materials in an enclosure with a free-moving ceiling: An experimental and numerical study

This work aims to examine, via a complementary approach of experimental measurement and numerical simulation, transient transport processes associated with melting of a phase change material (PCM) placed inside a vertical rectangular enclosure with a free-moving ceiling. The core phase change material is n-octadecane with melting temperature about Tm=28°C. The vertical side walls of the enclosure were differentially heated isothermally while the remaining side walls were thermally insulated. Experiments have been undertaken for the air-saturated enclosure filled with MECPCM particles with the relevant parameters in the following ranges: the enclosure aspect ratio Asp=24; the subcooling number Sc=1.06–11.5; Stefan number Ste=0.179–0.370; and the Rayleigh number Ra=0.897–8.60×108. Meanwhile, numerical simulations have been performed based on a mathematical modeling mimicking the experimental configuration considered to further elucidate the transient transport processes of the free-moving ceiling of the enclosure. Finally, the formula of the dimensionless displacement of the top ceiling subjected to various thermal conditions are proposed and correlated with the related parameters, including the Stefan number Ste, the subcooling parameter Sc, Rayleigh number Ra and the Fourier number Fo.

Simulation on melting processes in a vertical rectangular enclosure with a free-moving ceiling

Transport processes associated with melting of a phase change material (PCM) placed inside a vertical rectangular enclosure with a free-moving ceiling are simulated numerically. The enclosure is side-heated isothermally. Buoyancy-induced flow in the melt region is modeled utilizing the Boussinesq approximation. The effect of solid–liquid density change upon melting is accounted that liquid density of the PCM is assumed to be lower than the solid density and as a result, the melt bulk expands while melting, transmitting a linear motion of the free-moving ceiling of the enclosure. Numerical simulations for the two-dimensional melting process using a finite-difference method on a fixed grid are undertaken to delineate the motion characteristics of the ceiling related to the melting process of solid PCM inside the enclosure with the relevant dimensionless parameters in the following ranges: the enclosure aspect ratio Asp=2–12; the Stefan number Ste=0.1, 0.3, and 0.5; the Rayleigh number Ra=103–106; and the Prandtl number Pr=41.7. Simulation results clearly reveal the influence of the Rayleigh number on the displacement of movable ceiling of the enclosure and the average Nusselt number over the isothermally heated wall of the enclosure tend to degrade greatly with the increase of the aspect ratio.

Numerical and Theoretical Modeling of Natural Convection of Nanofluids in a Vertical Rectangular Cavity Investigate the Effects of a Magnetic Field

In this work, the stencil adaptive method is applied to investigate the effects of a magnetic field on mixed convection of Al2O3-water nanofluid in a vertical rectangular enclosure filled. The enclosure is bounded by two isothermal vertical walls at temperatures Th and Tc and by two horizontal adiabatic walls. A uniform magnetic field is applied in a horizontal direction. The main objective of this study is to investigate the influence of several pertinent parameters in the following ranges: Rayleigh number of the base fluid, Hartmann number and the solid volume fraction of the nanoparticles on the heat transfer performance of the nanofluid. Based on the obtained numerical results, the heat transfer rate increases with an increase of the Rayleigh number but, it decreases with an increase of the Hartmann number. Also, the results indicate that the heat transfer of the nanofluid could be either enhanced or mitigated with respect to that of the base fluid depending on the Rayleigh number.

Numerical and Theoretical Modeling of Natural Convection of Nanofluids in a Vertical Rectangular Cavity

In this work, we have conducted a numerical and theoretical study of a non-stationary laminar natural convection in a vertical rectangular enclosure filled with a mixture of water and nanoparticles, and heated from the vertical sides. The governing equations have been discretized by the finite volume method using a hybrid scheme. A numerical code was conceived and realized in this context to solve the obtained equations. A parametric study was conducted by considering the Rayleigh number, the type of nanofluid and the solid volume fraction. Enhanced and mitigated heat transfer effects due to the presence of nanoparticles are identified and highlighted. Based on these insights, we determine the impact of fluid temperature on the heat transfer of nanofluids. An increase in mean Nusselt number was found with the volume fraction of nanoparticles for the whole range of Rayleigh number. It was found that the heat transfer enhancement, using nanofluids, is more pronounced at low aspect ratio than at high aspect ratio.

Linear Stability Analysis of Thermal Convection in an Infinitely Long Vertical Rectangular Enclosure in the Presence of a Uniform Horizontal Magnetic Field

Stability of thermal convection in an infinitely long vertical channel in the presence of a uniform horizontal magnetic field applied in the direction parallel to the hot and cold walls was numerically studied. First, in order to confirm accuracy of the present numerical code, the one-dimensional computations without the effect of magnetic field were computed and they agreed with a previous study quantitatively for various values of the Prandtl number. Then, linear stability analysis for the thermal convection flow in a square horizontal cross section under the magnetic field was carried out for the case of Pr = 0.025. The thermal convection flow was once destabilized at certain low Hartmann numbers, and it was stabilized at high Hartmann numbers.

Numerical and theoretical study of natural convection in a nanofluid-filled vertical rectangular enclosure

The objective of the present research is to characterize the numerical and theoretical study of a non-stationary laminar natural convection in a vertical rectangular enclosure filled with a mixture of water and nanoparticles, and heated from the vertical sides. The governing equations have been discretized by the finite volume method. A numerical code was conceived and realized in this context to solve the obtained equations. A parametric study was conducted by considering the Rayleigh number, the type of nanofluid and the solid volume fraction. The results are in agreement with those obtained by others working in the same field.

Natural Convection in a Vertical Rectangular Enclosure

Natural Convection in a Vertical Rectangular Enclosure

Numerical study of melting in an enclosure with discrete protruding heat sources

In order to explore the capability of a solid–liquid phase change material (PCM) for cooling electronic or heat storage applications, melting of a PCM in a vertical rectangular enclosure was studied. Three protruding generating heat sources are attached on one of the vertical walls of the enclosure, and generating heat at a constant and uniform volumetric rate. The horizontal walls are adiabatic. The power generated in heat sources is dissipated in PCM (n-eicosane with the melting temperature, T m = 36 °C) that filled the rectangular enclosure. The advantage of using PCM is that it is able to absorb high amount of heat generated by heat sources due to its relatively high energy density. To investigate the thermal behaviour and thermal performance of the proposed system, a mathematical model based on the mass, momentum and energy conservation equations was developed. The governing equations are next discretised using a control volume approach in a staggered mesh and a pressure correction equation method is employed for the pressure–velocity coupling. The PCM energy equation is solved using the enthalpy method. The solid regions (wall and heat sources) are treated as fluid regions with infinite viscosity and the thermal coupling between solid and fluid regions is taken into account using the harmonic mean of the thermal conductivity method. The dimensionless independent parameters that govern the thermal behaviour of the system were next identified. After validating the proposed mathematical model against experimental data, a numerical investigation was next conducted in order to examine the thermal behaviour of the system by analyzing the flow structure and the heat transfer during the melting process, for a given values of governing parameters.

Numerical study on characteristics of turbulent two-phase gas-particle flow using multi-fluid model

The purpose of this research is to study numerically the turbulent gas-particle two-phase flow characteristics using the Eulerian-Eulerian method. A computer code is developed for the numerical study by using the k-ɛ-kp two-phase turbulent model. The developed code is applied for particle-laden flows in which the particle volume fraction is between 10−5 and 10−2 for the Stokes numbers smaller than unity. The gas and particle velocities and the particle volume fraction obtained by using this code are in good agreement with those obtained by a commercial code for the gas-particle jet flows within a rectangular enclosure. The gas-particle jet injected into a vertical rectangular 3D enclosure is numerically modeled to study the effect of the Stokes number, the particle volume fraction and the particle Reynolds numbers. The numerical results show that the Stokes number and the particle volume fraction are important parameters in turbulent gas-particle flows. A small Stokes number (St ≤ 0.07) implies that the particles are nearly at the velocity equilibrium with the gas phase, while a large Stokes number (St ≥ 0.07) implies that the slip velocity between the gas and particle phase increases and the particle velocity is less affected by the gas phase. A large particle volume fraction (αp ≥ 0.0001) implies that the effect of the particles on the gas phase momentum increases, while a small particle volume fraction (αp ≤ 0.0001) implies that the particles would have no or small effect on the gas flow field. For fixed Stokes number and particle volume fraction, an increase of the particle Reynolds number results in a decrease of the slip velocity between the gas and particle velocities.

Effect of vent aspect ratio on unsteady laminar buoyant flow through rectangular vents in large enclosures

The effects of vent aspect ratio on oscillatory flow regime through a horizontal opening were studied numerically. The physical model consisted of a vertical rectangular enclosure divided into two chambers by a horizontal partition. The partitions contained a slot that connected the two chambers. The upper chamber contains cold air and the lower chamber contains hot air. A density differential due to the different temperatures drives the interaction between the two chambers. The opposing forces at the interface between the two chambers create a gravitationally unstable system, and an oscillating exchange of fluid develops. Results were obtained for cases with L/ D = 1, 0.5, and 2.0, where L represents the thickness of the partition and D represents the slot width of the opening in the partition. Results indicate that the flow exchange increases with partition thickness L/ D = 0.5 and decreases for L/ D = 2. The frequency of the oscillatory flow pattern is also examined for the different cases. Sudden bursts of upflow with a corresponding downflow have been documented and compared with experimental observations in the literature. The time traces of velocity and temperature fields for this flow regime reveal interesting mechanisms, which have been explained.

Time-dependent buoyant convection in an enclosure with discrete heat sources

A numerical study is performed for the time-dependent laminar natural convection air cooling in a vertical rectangular enclosure with three discrete flush-mounted heaters. The lowest-elevation heater changes the thermal condition between the ‘on’ and ‘off’ modes. In Case 1 (Case 2), the lowest-elevation heater is abruptly switched on (off) from the ‘off’ (‘on’) state. In Case 3, the ‘on’ and ‘off’ modes are repeated periodically. Numerical simulations were conducted for a range of non-dimensional period and for the Rayleigh number based on the cavity width between 10 5 and 10 7 with given heater size and locations. The results show the influence of the time-dependent thermal condition of the lowest-elevation heater on the temperatures of the other heaters. At low Rayleigh number, the cycle-averaged temperatures of all heaters are little affected by the periodic change. At high Rayleigh number, the temperatures of the heaters reach peak values when the non-dimensional period of the change in thermal condition takes intermediate values. The evolutions of global flow and temperature fields are exemplified to provide physical interpretations. The study emphasizes that the transient-stage temperatures at the heaters can exceed the corresponding steady-state values. This is relevant to practical design of electronic devices.

Natural convection in a vertical rectangular enclosure with symmetrically localized heating and cooling zones

Numerical and experimental studies of natural convection in a single-phase, closed thermosyphon were carried out, using a vertical, rectangular enclosure model. Two vertical plates, each 100×100 mm 2 in dimension, and placed symmetrically play the role of heat transfer surfaces. These symmetrical heat transfer surfaces are separated into three horizontal zones of equal height; the top and bottom thirds of these surfaces are the zones of, respectively, cooling and heating, the intermediate section being an adiabatic zone. Silicon oil is used as the working fluid. Variable parameters are the distance, D, between the two heat transfer surfaces, and temperature difference, ΔT, between the heating and cooling zones. By changing both D and ΔT, three regimes of natural convection flow; steady, quasi-two-dimensional, steady, three-dimensional, and unsteady flows were found in experiment. Converged solutions obtained by numerical simulation agreed well with experimental results with regard to the temperature and velocity of the fluid as visualized by means of thermo-sensitive liquid crystal powders.

Buoyant flow in long vertical enclosures in the presence of a strong horizontal magnetic field. Part 1. Fully-established flow

The buoyant convection in a long vertical rectangular enclosure under the presence of a horizontal uniform magnetic field is investigated. Two opposite vertical walls are kept at different temperatures and the other four walls are thermally insulating. The main parameters of this study are the Grashoff number Gr, and the Hartmann number Ha. The applied magnetic field is either perpendicular or parallel to the temperature gradient. In both configurations, if it is large enough, it damps out the buoyant flow and ensures a conductive heat flux, but with different scaling laws: Gr/Ha for the perpendicular case, Gr/Ha 2 for the parallel case. This first paper focuses on the fully-established flow, far from the top and the bottom of the enclosure, in the limit of high Ha. Analytical solutions are derived and serve as reference to validate the numerical results. An analytical model of the Hartmann layers describes directly their influence on the core flow, saves important computational resources and yields quite accurate results.

1208 鉛直矩形流体槽内の自然対流 : 対称伝熱面の場合(GS-6 自然対流)

1208 鉛直矩形流体槽内の自然対流 : 対称伝熱面の場合(GS-6 自然対流)