Laminar Natural Convection in a Square Cavity with a Partition on the Heated Vertical Wall

Abstract

The laminar natural convection in an air-filled square cavity with a partition on the heated vertical wall was experimentally investigated. Temperature measurements and flow visualizations were performed for cases with heated and cooled vertical walls (corresponding to a global Grashof number Gr _H of approximately 1.4 × 10⁸) and non dimensional top wall temperatures θ _T of 0.57 (insulated) to 2.3. Experiments were performed with an aluminum partition with non dimensional height H _P /H of 0.0625 and 0.125 attached to the heated vertical wall at y/H = 0.65 and 0.95. The blockage effect and/or the thermal effect of the partition resulted in changes to the temperature and flow fields but were mainly limited to the vicinity of the partition. For the cases with the heated top wall, the change in the height of the partition at y/H = 0.95 resulted in changes to the ambient temperature outside the boundary layer due to the reduction of the size of the recirculating flow in the corner region. The changes in the partition height and the top wall temperature affected the blockage effect of the partition, resulting in the local Nusselt number near the corner region to be affected. The local Nusselt number over most of the heated vertical wall of the partitioned cavity (y/H < 0.7) was correlated to the local Rayleigh number in the form Nu = C · Ra ⁿ .     

Laminar natural convection between vertical isothermal heated plates with different temperatures

Numerical investigation of laminar free convection heat transfer in the vertical parallel plate channel with asymmetric heating is presented. Both inlet and exit effects are included into the analysis. A numerical solution is obtained for a Prandtl number of 0.71 and for modified Rayleigh number [`(Ra)]\overline {Ra} = 10⁻¹ ÷ 10⁵, and varying heating ratio T_R = 0 ÷ 1 and aspect ratio A = 10. Fully elliptic Navier-Stokes and energy equations are solved using the finite volume techniques with staggered grid arrangements. The obtained results show a strong influence of the temperature ratio on local and average heat transfer coefficient on the hot and cold plates. With reduction of T_R the heat transfer parameter on the hot wall grows, and on the cold one, on the contrary, it decreases. As a result, the total heat exchange from two plates depends poorly on the parameter T_R.     

Study of heat transfer in a horizontal cylinder with fins

The purpose of this paper is to investigate, numerically, the effect of internal fins on the flow pattern, temperature distribution and heat transfer between concentric horizontal cylinders. A Galerkin finite element method is adopted for the discretization of the governing equations. The numerical procedure consists in solving series of transient problems of increasing Ra. Results are presented using air (Pr = 0.7) with Rayleigh numbers ranging from 10³ to 10⁶ for different fin configurations (1 and 2), geometries (sharp, round and divergent tip) and lengths (l = 0.25, 0.5 and 0.75). They are illustrated in terms of isotherms, velocity fields, Nusselt numbers and fin efficiencies. Configuration 2 presents a heat transfer rate 10% above that of configuration 1, at Ra = 10⁶. The heat transfer is about the same for the three geometries, but the best fin efficiency is associated with the fin with a round tip.     

TURBULENT NATURAL CONVECTION IN AN ENCLOSURE WITH LOCALIZED HEATING FROM BELOW

Natural-convection heat transfer in a cylindrical enclosure, heated partially from below by a disk-shaped heating surface and cooled from the top and the side, was investigated experimentally and numerically. Heat transfer measurements are presented for the range of Rayleigh numbers from 10⁸ to 2 × 10¹⁰. The total acceleration normal to the heating surface was varied from I to 100 times the standard gravitational acceleration. The heat flux was varied from 0.19 MW / m1 to 1.5 MW / m². The test results were correlated by an equation of the form Nu_D = 0.2Ra^0.325 _D for Prandtl number 2 and aspect ratio I. The flow field was studied numerically using FLUENT code.     

Influence of thermophoresis on heat and mass transfer under non-Darcy MHD mixed convection along a vertical flat plate embedded in a porous medium in the presence of radiation

The paper presents an investigation of the influence of thermophoresis on MHD mixed convective heat and mass transfer of a viscous, incompressible and electrically conducting fluid along a vertical flat plate with radiation effects. The plate is permeable and embedded in a porous medium. To describe the deviation from the Darcy model the Forchheimer flow model is used. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The governing partial differential equations are transformed into a system of ordinary differential equations using similarity transformation. The nonlinear ordinary differential equations are linearized by using quasilinearization technique and then solved numerically by using implicit finite difference scheme. The numerical results are analyzed for the effects of various physical parameters such as magnetic parameter Ha, mixed convection parameter Ra _d /Pe _d , Reynolds number Red, radiation parameter R, thermophoretic parameter τ, Prandtl number Pr, and Schmidt number Sc. The heat transfer coefficient is also tabulated for different values of physical parameters.     

Scaling in convective evaporation and sidewall boundary layer

Turbulent convection at aspect ratios from 0.06 to 2 is investigated in the laboratory with evaporation experiments from vertical cylinders having different diameters and liquid levels. With alcohol, only diffusive evaporation takes place. With water, for small diameters, evaporation proceeds by diffusion whereas convective evaporation develops when the diameter is increased. This onset can be effectively interpreted in terms of a viscous sidewall boundary layer, whose thickness δ varies with respect to the available height h according to δ/h = 3.4 Ra^-0.28±0.01 versus Rayleigh number Ra. The Sherwood number Sh, analog of the Nusselt number, exhibits a power law variation Sh = 0.6 Ra^0.27±0.02 for Ra varying from 10⁴ to 3 ×10⁸. The scaling observed in this case of an open boundary is thus similar to the scaling measured in confined Rayleigh-Bénard convection.     

Numerical simulation of turbulent natural convection of oxide heat generating melt in a core catcher at NPP with VVER-1000

The problem statement and simulation results are presented concerning turbulent natural convection in a vertical cylindrical molten pool with internal heat generation and other parameters (inner Rayleigh number Ra _i ∼ 10¹⁶–10¹⁷) corresponding to oxide core melt in a core catcher for NPP with VVER-1000. Commercial code FLUENT 6.3 was used for CFD calculations. The results on heat transfer are approximated by power law correlations for mean Nusselt numbers vs. Rayleigh number and pool height, describing the heat transfer at upper, lateral, and total boundaries of the cylinder. The influence of volumetric heat generation and material properties is studied. Spatial distribution of wall heat transfer is analyzed for different pool heights possible in the real core catcher. Along with serial calculations with isothermal boundary conditions, the cases with heat radiation conditions are considered. The results may be used for estimations of heat transfer and melt overheating in a VVER core catcher and for coefficient identification of simplified models of integrated system severe-accident codes.     

Buoyancy induced flow in a nanofluid filled enclosure partially exposed to forced convection

A numerical study was performed on natural convection for water–CuO nanofluid filled enclosure where the top surface was partially exposed to convection. The cavity has a square cross-section and differentially heated. Except exposed convection part on the top, all sides are adiabatic on horizontal walls. Effects of Rayleigh number (10³ ? Ra ? 10⁵), Biot number (0 ? Bi ? ∞), length of partial convection (0.0 ? L ? 1.0) and volume fraction of nanoparticles (0.0 ? φ ? 0.1) on heat and fluid flow were investigated. The results showed that for the case of high Biot number that heat transfer along the heated was enhanced by increasing the Rayleigh number mainly at the upper portion of the heated wall. When the top wall was totally exposed to convection, the results prevail that the heat transfer was more effective at high Biot number especially at the upper portion of the heated wall. For the case of high Biot number, the results prevailed that the heat transfer at the upper portion of the heated wall increases considerably at high exposed length to convection (L); however, for L ? 0.75 the effect of L was less pronounced. Contour maps for percentage of heat transfer enhancement were presented and it was shown that the location of maximum enhancement in heat transfer was sensitive to Ra, φ and L.     

EFFECTS OF FREE STREAM VELOCITY ON TURBULENT NATURAL CONVECTION FLOW OVER A VERTICAL FORWARD-FACING STEP

Measurements of heat transfer and fluid flow of turbulent boundary-layer air flow in natural and mixed convection over an isothermal two-dimensional, vertical forward-facing step are reported. The upstream and downstream walls and the step itself were heated to a uniform and constant temperature. Air velocity and temperature distributions and their turbulent fluctuations are measured simultaneously using a two-component laser-Doppler velocimeter (LDV) and a cold wire anemometer, respectively. The present study treats buoyancy-dominated mixed convection over a vertical forward-facing step and examines the effect of a small free stream velocity on turbulent natural convection. The experiment was carried out for a step height of 22 mm, for a range of free stream air velocities 0 m/s ? u_∞ ? 0.55 m/s (corresponding to a range of Reynolds numbers of 0 ? Re\abinf{s} ? 712), and a temperature difference, ΔT, of 30°C between the heated walls and the free stream air (corresponding to a local Grashof number Gr_xi = 6.45 × 10¹⁰). It was found that the reattachment length increases while the heat transfer rate from the downstream heated wall decreases as the small free stream velocity increases.     

Experimental Investigation of Transient Forced Convection of Liquid Methane in a Channel at High Heat Flux Conditions

Transient heat transfer of liquid methane under forced convection in a 1.8 mm × 1.8 mm asymmetrically heated square channel was investigated. This study is aimed at understanding the heat transfer behavior of cryogenic propellant in cooling channels of a regeneratively cooled rocket engine at the start-up condition. To simulate high heat load conditions representative of regeneratively cooled rocket engines, a high heat flux test facility with cryogenic liquid handing capabilities was developed at the Center for Space Exploration Technology Research. The time history of inlet and outlet fluid temperatures and test section channel wall temperatures were measured at high heat flux conditions (from 1.19 to 3.80 MW/m²) and a Reynolds number (Re) range of 1.88 × 10⁵ to 3.45 × 10⁵. The measured wall temperature data point toward possible film boiling within the test section during certain tests, particularly with higher heat fluxes and lower Reynolds number conditions that resulted in higher wall temperatures. The transient average Nusselt numbers (Nu_L) of the channel obtained from the experimental measurements are lower than those calculated from the Sieder–Tate correlation (Nu_O); however, the ratio (Nu_L/Nu_O) increases with the increase in Reynolds number. The ratio is around 0.25 at the lower end of Re and then increases to 0.7 at the maximum Re studied in the present investigation.     

Experimental and Numerical Study of Free Convection on an Isothermal Downward Cone

Abstract

The laminar free-convection heat transfer from an isothermal downward cone in air is investigated experimentally and numerically. The experimental investigation is carried out by Mach-Zehnder interferometery technique and the numerical simulation was done by Fluent. The cone tip angle has been kept constant to 45° and it was suspended from its base throughout the experiment. This article focuses on the effect of Rayleigh number variation on the local and average free-convection heat transfer coefficient over the conical surface. The local and average Nusselt numbers were determined for the Rayleigh number range of 4.9×10⁵ to 1.1×10⁶. Also, the experiment and the numerical simulation were carried out on a vertical isothermal cylinder of circular cross section in order to compare results with other researchers for the verification of our experimental and numerical results. The significant influence of the upper end surface of the cone, both in the experimental and numerical studies, indicated a recirculation region above the upper end surface which affects the local convection heat transfer at the slant trailing edge and causes it to increase. Also, a correlation for the calculation of the local Nusselt number over the cone is proposed.     

Stagnation Region Heat Transfer for Circular Jets Impinging on a Flat Plate

The heat transfer characteristics in a stagnation region were investigated experimentally for five circular free jets impinging into a heated flat plate. The local temperature distributions are estimated from the thermal images obtained from an infrared camera. To get a precise heat transfer data over the plate, fully developed straight pipe jets were used in this study. Mean jet Reynolds number varied from 1,000 to 45,000, jet-to-plate vertical non-dimensional distance H/D varied from 2 to 6, and the spacing distance jet-to-jet S/D varied from 2 to 8. A geometrical arrangement of one jet surrounded by four jets an in-line array was tested. The results show that the stagnation point Nusselt number is correlated to a jet Reynolds number as Nu_st∝Re^0.61. The average Nusselt number is higher at a separation distance of 2D for three cases of spacing distances, S/D = 2, 4, and 6.     

Magnetic behaviour of Eu x (Rh1−y Fe y )3B2;x=0.6, 0.75, 1.04 andy=0.02

⁵⁷Fe ME spectra taken for Eu_x(Rh_1–yFe_y)₃B₂ compounds (x=0.6, 0.75, 1.04 and y=0.02) show quadrupole doublet and a magnetically split pattern for T < T_c ^*. Above T_c ^* the spectra merge into a single quadrupole doublet. It is seen that the addition of Fe shifts the T_c corresponding to undoped compound to T_c ^*, T_c ^*>300 K for all the three samples.     

Rotating turbulent Rayleigh–Bénard convection subject to harmonically forced flow reversals

The characteristics of turbulent flow in a cylindrical Rayleigh–Bénard convection cell which can be modified considerably in case rotation is included in the dynamics. By incorporating the additional effects of an Euler force, i.e., effects induced by non-constant rotation rates, a remarkably strong intensification of the heat transfer efficiency can be achieved. We consider turbulent convection at Rayleigh number Ra = 10⁹ and Prandtl number σ = 6.4 under a harmonically varying rotation, allowing complete reversals of the direction of the externally imposed rotation in the course of time. The dimensionless amplitude of the oscillation is taken as 1/Ro^* = 1 while various modulation frequencies 0.1 ≤ Ro_ω ≤ 1 are applied. Both slow and fast flow-structuring and heat transfer intensification are induced due to the forced flow reversals. Depending on the magnitude of the Euler force, increases in the Nusselt number of up to 400% were observed, compared to the case of constant or no rotation. It is shown that a large thermal flow structure accumulates all along the centreline of the cylinder, which is responsible for the strongly increased heat transfer. This dynamic thermal flow structure develops quite gradually, requiring many periods of modulated flow reversals. In the course of time, the Nusselt number increases in an oscillatory fashion up to a point of global instability, after which a very rapid and striking collapse of the thermal columnar structure is seen. Following such a collapse is another, quite similar episode of gradual accumulation of the next thermal column. We perform direct numerical simulation of the incompressible Navier–Stokes equations to study this system. Both the flow structures and the corresponding heat transfer characteristics are discussed at a range of modulation frequencies. We give an overview of typical time scales of the system response.     

EXPERIMENTAL STUDY OF MARANGONI-BENARD CONVECTION IN A LIQUID LAYER INDUCED BY EVAPORATION

Marangoni-Bénard instability and convection in evaporating liquid layers have been studied experimentally through flow visualization and temperature profile measurement. Bénard cells have been observed in an evaporating thin liquid layer whether it is heated, adiabatic, or cooled from below. This experimental study has revealed a different mechanism from the traditional Rayleigh-Bénard and Marangoni-Bénard instabilities and convections, which require a negative temperature gradient in the thin liquid layer. Evaporation rate and enthalpy of evaporation have been found to be important parameters of instability and convection in an evaporating liquid layer. A modified form of Marangoni number, Ma^*, is proposed and its critical values, Ma^* _c, for alcohol and Freon-113 evaporating layers are determined experimentally. A quantitative comparison between Ma^* and the traditional Marangoni number, Ma, shows that Ma^* is an adequate indicator of the stability status in evaporating liquid layers.     

Dynamic deformation of light nuclei in excited states

An important property—the dynamic deformation of B* light aligned nuclei—is investigated for the nuclear reactions A(x, y)B* → γ + B ₀ by measuring the y-γ correlations. Dynamic deformation is determined from the orientation tensors of multipolar moments. Normalization constants of the contributions from even-rank orientation tensors are determined from the condition of coincidence between dynamic and static deformations of the B* nucleus for θ _y = 0°. Experimental dynamic deformations of ¹²C(2⁺) nuclei caused by the inelastic scattering of α particles and deuterons are determined, along with the ¹⁰Be(2⁺) nuclei formed in reaction ⁹Be(d, p)¹⁰Be(2⁺). It is shown that the dynamic deformation of the aligned nuclei depends on how they are formed and their structure, and evolves substantially when the angle θ _y is varied.     

Natural convection in a square cavity containing a nanofluid and an adiabatic square block at the center

The problem of free convection fluid flow and heat transfer of Cu–water nanofluid inside a square cavity having adiabatic square bodies at its center has been investigated numerically. The governing equations have been discretized using the finite volume method. The SIMPLER algorithm was employed to couple velocity and pressure fields. Using the developed code, a parametric study was conducted and the effects of pertinent parameters such as Rayleigh number, size of the adiabatic square body, and volume fraction of the Cu nanoparticles on the fluid flow and thermal fields and heat transfer inside the cavity were investigated. The obtained results show that for all Rayleigh numbers with the exception of Ra = 10⁴ the average Nusselt number increases with increase in the volume fraction of the nanoparticles. At Ra = 10⁴ the average Nusselt number is a decreasing function of the nanoparticles volume fraction. Moreover at low Rayleigh numbers (10³ and 10⁴) the rate of heat transfer decreases when the size of the adiabatic square body increases while at high Rayleigh numbers (10⁵ and 10⁶) it increases.     

Soft modes and phonon interactions in studied by neutron scattering

The low frequency lattice dynamics and its relationship to the second order paraelectric-to-ferroelectric transition in Sn₂P₂S₆ is studied. The dispersion branches of the acoustic and lowest lying optical phonons in the a^*-c^* plane have been obtained in the ferroelectric phase, for x-polarized phonons. Close to the phase transition a considerable softening is found for the lowest optical mode (P_x), comparable to the behaviour observed in previous Raman investigations. As found previously in Sn₂P₂Se₆, a strong coupling between the TO(P_x) and TA(u_xz) phonons is observed, although, apparently, not strong enough to lead to an incommensurate phase. The soft TO(P_x) mode at the zone center is observed. The temperature dependence of its frequency and damping shows that the transition is not entirely displacive. At low temperatures an unusual apparent negative LO-TO splitting is observed which is shown to arise from the coupling of the x-polarized soft mode to the nearby z-polarized optical phonon. For comparison, the soft TO(P_x) dispersion in the a^*-b^* plane is measured in both the paraelectric and ferroelectric phases. Consistent frequency changes and LO-TO splitting are observed, revealing a significant interaction between the TA(u_yx) and LA(u_xx) acoustics branches and the TO and LO soft optic branches, respectively. In contrast, the nearby y-polarized optic branch shows almost no temperature dependence. Finally, the influence of piezoelectric effects on the limiting acoustic slopes in the ferroelectric phase is discussed. Received: 11 May 1998 / Revised and Accepted: 15 June 1998     

151Eu Mössbauer effect study of T′- and T*-phase superconductors

The (La,Eu(₂ CuO ₄ system shows superconductivity by dopingCe orSr. Carriers inT′-phase doped withCe are electrons and those inT ^*-phase doped withSr are holes. In this work,¹⁵¹ Eu Mössbauer analysis is applied for theT′-phase(La _1?x Eu _x)_2?y Ce _y CuO ₄ and theT ^*-phase(La _1?x Eu _x)_2?y Sr _y CuO ₄ in order to compare the electronic state and the lattice vibration ofEu in these superconductors. In addition, correlations betweenT _c and Mössbauer parameters are examined. The isomer shift of¹⁵¹ Eu is 0.784–0.840 mm/s in theT ^*-phase and 0.689–0.733 mm/s in theT′-phase, which shows that the lanthanide in these superconductors is tri-valent. The Debye temperature of¹⁵¹ Eu is 180–208 K in theT ^*-phase and 160–192 K in theT′-phase. The difference of isomer shift between these two phases is explained by theEu?O distance. For(La _1?x Eu _x)_2?y Ce _y CuO ₄, a light correlation betweenT _c and the Debye temperature is observed, which means the importance of the lattice vibration in high-Tc superconductivity.     

Isotope effect and characteristic features of the phase diagram for cobaltites with spin-state transitions

The effect of ¹⁶O → ¹⁸O oxygen isotope substitution has been studied for (Pr_1−y Eu _y )_0.7Ca_0.3CoO₃ cobaltites (0.12 < y < 0.26). A pronounced isotope shift has been found for the spinstate transition temperature, which increases with the oxygen isotope mass. In contrast, the ferromagnetic transition temperature has slightly lower values for the samples with heavier oxygen. The observed phenomena and constructed phase diagram confirm the results reported previously for (Pr_{1 − y} Sm _y )_0.7Ca_0.3CoO₃ in [G. Y. Wang, X. H. Chen, T. Wu, et al., Phys. Rev. B 74, 165113 (2006)]. The measurements of the specific heat have been performed for (Pr_{1 − y} Eu _y )_0.7Ca_0.3CoO₃ with the main emphasis on the analysis of the isotope effect. The contributions to the isotope effect coming from the lattice and magnetic components of the specific heat have been separated. The mechanisms underlying the large isotope effect are discussed.