Experimental Study of Natural Convection from Electrically Heated Vertical Cylinders Immersed in Air

Abstract

An experimental study of laminar steady-state natural convection heat transfer from electrically heated vertical cylinders immersed in air has been undertaken. Three stainless steel (316 SS) test sections of different slenderness ratios were employed. Surface temperature profiles along the vertical cylinders were obtained using miniature thermocouples when the cylinders were heated with different power levels resulting in different total wall heat fluxes. After the mandatory corrections for the radiation heat fluxes were made, three correlation equations relating the local Nusselt number Nu_y with the local modified Rayleigh number Ra^* _y and the position-to-cylinder diameter y/d were developed. The correlation equations are valid for Ra^* _y ≤ 2 × 10¹².     

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.     

Buoyancy-assisted mixed convective flow over backward-facing step in a vertical duct using nanofluids

Laminar mixed convective buoyancy assisting flow through a two-dimensional vertical duct with a backward-facing step using nanofluids as a medium is numerically simulated using finite volume technique. Different types of nanoparticles such as Au, Ag, Al₂O₃, Cu, CuO, diamond, SiO₂ and TiO₂ with 5 % volume fraction are used. The wall downstream of the step was maintained at a uniform wall temperature, while the straight wall that forms the other side of the duct was maintained at constant temperature equivalent to the inlet fluid temperature. The walls upstream of the step and the backward-facing step were considered as adiabatic surfaces. The duct has a step height of 4.9 mm and an expansion ratio of 1.942, while the total length in the downstream of the step is 0.5 m. The downstream wall was fixed at uniform wall temperature 0 ?? ??T?? 30 °C, which was higher than the inlet flow temperature. The Reynolds number in the range of 75 ?? Re ?? 225 was considered. It is found that a recirculation region was developed straight behind the backward-facing step which appeared between the edge of the step and few millimeters before the corner which connect the step and the downstream wall. In the few millimeters gap between the recirculation region and the downstream wall, a U-turn flow was developed opposite to the recirculation flow which mixed with the unrecirculated flow and traveled along the channel. Two maximum and one minimum peaks in Nusselt number were developed along the heated downstream wall. It is inferred that Au nanofluid has the highest maximum peaks while diamond nanofluid has the highest minimum peak. Nanofluids with a higher Prandtl number have a higher peak of Nusselt numbers after the separation and the recirculation flow disappeared.     

A numerical study of laminar natural convective heat transfer inside a closed cavity with different aspect ratio

Two-dimensional steady-state laminar natural convection was studied numerically for differentially heated air-filled closed cavity with adiabatic top and bottom walls. The temperature of the left heated wall and cooled right wall was assumed to be constant. The governing equations were iteratively solved using the control volume approach. In this paper, the effects of the Rayleigh number and the aspect ratio were examined. Flow and thermal fields were exhibited by means of streamlines and isotherms, respectively.Variations of the maximum stream function and the average heat transfer coefficient were also shown. The average Nusselt number and was correlated to the Rayleigh number based on curve fitting for each aspect ratio. The investigation covered the range 10⁴ ≤ RA ≤ 10⁷ and is done at Prandtl number equal to 0.693. The result shows the average Nusselt number is the increasing function of Rayleigh number. As the aspect ratio increases, Nusselt number decreases along the hot wall of the cavity. As Rayleigh number increases, Nusselt number increases. Result indicates that at constant aspect ratio, with increase in Rayleigh number the heat transfer rate increases.     

单面加热方管混合对流换热特性实验研究

本文对单壁面加热水平方管通道内混合对流换热进行了实验研究,其中加热面分别为底面、侧面、顶面,Re=1514～3028,Gr~*=2.06×10~6～8.22×10~6;通过对加热面温度进行曲线拟合减小壁面温度测量误差,得到考虑轴向导热的局部Nusselt数的变化规律。实验结果表明侧面加热和底面加热时,局部Nusselt数要明显高于顶面加热的情况;局部Nusselt数在管道前段受Re的影响较大,在后段受Gr~*的影响较大。     

Experimental Investigation of Mixed Convection in a Channel With an Open Cavity

Mixed convection in an open cavity with a heated wall bounded by a horizontally unheated plate is investigated experimentally. The cavity has the heated wall on the inflow side. Mixed convection fluid flow and heat transfer within the cavity is governed by the buoyancy parameter, Richardson number (Ri), and Reynolds number (Re). The results are reported in terms of wall temperature profiles of the heated wall and flow visualization for Re = 100 and 1000, Ri in the range 30–110 (for Re = 1000) and 2800–8700 (for Re = 100), the ratio of the length to the height of cavity (L/D) is in the range 0.5–1.5, and the ratio of the channel height to cavity height (H/D) is in the range of 0.5 and 1.0. The present results show that the maximum dimensional temperature rise values decrease as the Reynolds and the Richardson numbers decrease. The flow visualization points out that for Re = 1000 there are two nearly distinct fluid motions: a parallel forced flow in the channel and a recirculation flow inside the cavity. For Re = 100 the effect of a stronger buoyancy determines a penetration of thermal plume from the heated plate wall into the upper channel. Nusselt numbers increase when L/D increase in the considered range of Richardson numbers.     

Investigations on the Effect of Backward-Facing and Forward-Facing Steps on Turbulent Mixed-Convection Flow Over a Flat Plate

The effects of backward-facing and forward-facing steps on a turbulent buoyancy-dominated mixed-convection flow over a flat plate are examined experimentally. Air velocity and temperature distributions and their turbulent fluctuations are measured simultaneously by using a two-component laser-Doppler velocimeter and a cold wire anemometer, respectively. The experiment was carried out for a step (backward-facing/forward-facing) height of 22 mm, 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), and a free-stream velocity of 0.48 m/s. It was found that the introduction of backward- and forward-facing steps increases the turbulence intensity of the velocity and temperature fluctuations downstream of the step. The present results also reveal that the maximum local Nusselt number occurs in the vicinity of the reattachment zone, and it is approximately twice for the case of the backward-facing step and three times for the case of the forward-facing step than that of the flat plate value at similar flow and thermal conditions.     

Triple convective flow of micropolar nanofluids in double lid-driven enclosures partially filled with LTNE porous layer under effects of an inclined magnetic field

In this paper, free, forced and Marangoni convective flows within an open enclosure partially filled with a porous medium under impacts of an inclined magnetic field are investigated. The forced convection is due to the movement of the side walls, the free convection induces from the heated part in the bottom wall and the Marangoni convection is a responsible on the thermal interaction at the free surface (top wall). The flow domain is partially heated from below and partially filled by a porous medium. The local thermal non-equilibrium model (LTNEM) is used to represent the thermal field in the porous layer (bottom layer) while the two-phase model is used to simulated the micropolar nanofluid behavior. Two cases based on the direction of the movement of the side walls are considered, namely, assisting flow (downward lid motion) and opposing flow (upward lid motion). Numerical analysis based on the finite volume method is conducted and the obtained are presented in terms of the streamlines, isotherms, angular velocity, and the cup-mixing temperature θ_cup, the bulk-averaged temperature θ_ave and the average Nusselt numbers. The controlling parameters, in this situation, are the Darcy number Da, the Marangoni number Ma, the Nield number H, the vortex viscosity Δ, the Biot number Bi and the Hartmann number Ha. The results revealed that the increase in the Nield number enhances the cup-mixing temperature θ_cupand bulk-averaged temperature θ_ave regardless the direction of the side walls motion. Also, the average Nusselt number is boosted as the Marangoni number is grown.     

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.     

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.     

Natural Convection from a Corrugated Heated Surface at the Bottom of Vented Rectangular Enclosure

Natural convection heat transfer characteristics enclosures from a tilted rectangular enclosure heated at the corrugated bottom wall and vented by uniform slots opening at the top wall are experimentally investigated. The experiments were carried out to study the effects of the angle of opening of the corrugated surface, opening ratio, enclosure's tilt angle, and Rayleigh number on the passive cooling of the enclosure. The experiments were carried out at Rayleigh numbers ranging from 2 × 10⁸ to 1.52 × 10⁹ for enclosure tilt angles ranging from 0° to 90° and angle of opening of corrugated surface ranging from 0° to 25°. The top venting arrangement was studied at different opening ratios of 1, 0.75, 0.5, and 0.25. The results gave an optimum angle of opening of the corrugated surface at which Nusselt number is maximum.     

MHD natural convective flow through a porous medium in a square cavity filled with liquid gallium

This article contains a computational study of free convective flow through a square enclosure filled with liquid gallium saturated porous medium in the presence of a uniform inclined magnetic field. Lower boundary of enclosure is considered to be heated uniformly, upper horizontal boundary is taken insulated, left wall of the cavity is heated linearly, and right wall is heated linearly or taken cold. Navier–Stokes equations governing the flow problem are first exposed to penalty method to eliminate the pressure terms and then Galerkin FEM is employed to solve reduced equations. Grid independent results are achieved and shown in tabular form for numerous ranges of physical flow parameters. To ensure the accuracy of developed code, computed results are compared with those available in earlier studies through figures. It is found that the strength of streamlines circulation is increased due to increase in Darcy number while imposition of vertical magnetic field instead of horizontal magnetic field causes slow rate of increase in strength of streamlines circulation. Whereas, in the case of linearly heated right wall, the average Nusselt number is an increasing function of the Darcy number, and vertical magnetic field causes higher values for average Nusselt number as compared to horizontal magnetic field along bottom and side walls of cavity. Contrarily, in the case of cold right wall, the horizontal magnetic field results in higher values of average Nusselt number as compared to the vertical magnetic field case, and the average Nusselt number reduces as we move along lower and right boundary while increases along left wall with increase in distance.     

Natural-Convection Thermosyphon Heat Transfer from a Stack of Horizontal Plates

Steady laminar natural convection of water about vertically stacked, two-sided, horizontal heated plates was studied experimentally over a range of plate gap to plate half-width ratio, H/a, from 0.078 to 0.94. Measurements were made of power input per plate, plate temperatures, and inlet and outlet bulk fluid temperatures. From these data were determined average Nusselt and Rayleigh numbers for each plate, which were correlated with a power law Nu = C Raⁿ for each gap height. The Nusselt numbers increased with gap height up to H/a 0.47 (from 8 to 48), and then became independent of H/a. The exponent n increased from n 0.2 at the lowest gap height tested (H/a 0.078), to a high value of n approximately equal to 0.4 at H/a = 0.24 and then decreased back to n = 0.2 for H/a greater than or equal to 0.47.     

Experimental Investigation of Opposing Mixed Convection in a Channel with an open Cavity Below

Abstract

In this article, mixed convection in an open cavity with a heated wall bounded by a horizontal unheated plate is investigated experimentally. The heated wall is on the opposite side of the forced inflow. The results are reported in terms of wall temperature profiles of the heated wall and flow visualization. The range of pertinent parameters used in this experiment are Reynolds numbers (Re) from 100 to 2,000 and Richardson numbers (Ri) from 4.3 to 6,400. Also, the ratio between the length and the height of cavity (L/D) ranges from 0.5–2.0, and the ratio between the channel and cavity height (H/D) is equal to 1.0. The lack of experimental results on mixed convection in a channel with an open cavity below was an impetus for investigating this configuration when one cavity vertical wall is heated at uniform heat flux. The present results show that at the lowest investigated Reynolds number, the surface temperatures are lower than the corresponding surface temperatures for Re = 2,000 at the same ohmic heat flux. The flow visualization shows that for Re = 1,000, there are two nearly distinct fluid motions: a parallel forced flow in the channel and a recirculation flow inside the cavity. For Re = 100, the effect of a stronger buoyancy determines a penetration of thermal plumes from the heated plate wall into the upper channel. Moreover, the flow visualization shows that for lower Reynolds numbers, the forced motion penetrates inside the cavity, and a vortex structure is adjacent to the unheated vertical plate. At higher Reynolds numbers, the vortex structure has a larger extension while L/D is held constant.     

Fermionic solution of the Andrews-Baxter-Forrester model. I. Unification of TBA and CTM methods

The problem of computing the one-dimensional configuration sums of the ABF model in regime III is mapped onto the problem of evaluating the grandcanonical partition function of a gas of charged particles obeying certain fermionic exclusion rules. We thus obtain a newfermionic method to compute the local height probabilities of the model. Combined with the originalbosonic approach of Andrews, Baxter, and Forrester, we obtain a new proof of (some of) Melzer's polynomial identities. In the infinite limit these identities yield Rogers-Ramanujan type identities for the Virasoro characters _l,1 ^(r–l,r) (q) as conjectured by the Stony Brook group. As a result of our work the corner transfer matrix and thermodynamic Bethe Ansatz approaches to solvable lattice models are unified.     

Effect of Sound Field on a Round Air Impingement Jet

The local heat transfer and static pressure on a heated plate is reported with an air jet produced by a circular nozzle under tone-excitation with a frequency range of f_e = 0–300 Hz. The Reynolds numbers were (1.7 – 4.2) × 10⁴, and the nozzle-to-plate spacings were L/d = 6, 8, and 10. For all spacing, the isopressure and Nusselt number contours changed a shape from a concentric circle to an elliptic or peanut shape and changed back to a concentric circle with an increase of the tone-exciting frequency. These phenomena might be attributed to the induced vorticities observed as a non circular orifice jet.     

Experimental studies on natural convection boiling of water in a vertical annulus of a closed-loop thermo-siphon

Experimental studies on natural convection boiling of water in an internally heated narrow vertical annulus, with the liquid circulating through a cold leg forming a closed-loop thermo-siphon, have been carried out. The radius and aspect ratios of the annulus are 1.184 and 352, respectively. The experimental data, which consist of wall and liquid temperatures, liquid and vapor flow rates, and differential pressure across the test section, are recorded on a data logging system. The experiments have been performed for a constant heat flux of 15–35 kW/m² from the startup period until the steady state to study the transient behavior of the system. The boiling and non-boiling zones in the annulus have been identified and presented graphically through the liquid and wall temperatures for the steady state. They have been also verified through the visual photographs of the flow patterns in the annulus. The flow is found to be oscillatory in nature with no particular trend. Although the experimental data seems to be scattered, but when analyzed for a short duration, they are found well within the ±3σ (three sigma). This confirms the quasi-steady-state condition of the system. The steady-state values of Reynolds number and liquid circulation rate come out to be 133.1–453.5 and 7.0–23.87 g/s, respectively, while the Nusselt number and heat transfer coefficient are 7.98–13.57 and 1433.57–2435.35 W/m²K, respectively. Mathematical correlations for liquid mass flow rates, heat transfer coefficient, Reynolds number, and Nusselt number have been developed and compared with the existing correlations, which are in good agreement.     

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.     

Numerical investigation of natural convection heat transfer of nanofluids in a Γ shaped cavity

This paper analyzes the heat transfer and fluid flow of natural convection in a Γ shaped enclosure filled with Al₂O₃/Water nanofluid that operates under differentially heated walls. The Navier–Stokes and energy equations are solved numerically. Heat transfer and fluid flow are examined for parameters of non-uniform nanoparticle size, mean nanoparticle diameter, nanoparticle volume fraction, Grashof number and different geometry of enclosure. Finite volume method is used for discretizating positional expressions, and the forth order Rung-Kuta is used for discretizating time expressions. Also an artificial compressibility technique was applied to couple continuity to momentum equations. Results indicate that using nanofluid causes an increase in the heat transfer and the Nusselt number so that for R = 0.001 in Gr = 10³, the Nusselt number 25%, in Gr = 10⁴ 26%, and in Gr = 10⁵ 28% increases. Furthermore; by decreasing the mean diameters of nanoparticles, Nusselt number increases. By increasing R parameter (d_p,min/d_p,max) and nano particle volume fraction, Nusselt number increases.     

A free convective boundary layer in a conducting fluid in the presence of a transverse magnetic field

The properties of free convection in a conducting fluid in laminar regime near a hot solid vertical w all in the presence of a transverse magnetic field are theoretically analyzed. The existence of two regimes of heat transfer from the wall to the fluid are established. In the first regime, at small heights x?x* where the magnetic field effect can be disregarded, heat transfer is described by the well-known results for a free convective boundary layer in a nonconducting fluid with the Nusselt number Nu_x∝x^3/4. In the second regime, at x? x* where the magnetic field plays a crucial role, the dependence of heat transfer on the height and field strength is \(Nu_x \propto {{\sqrt x } \mathord{\left/ {\vphantom {{\sqrt x } B}} \right. \kern-\nulldelimiterspace} B}\). The location of the boundary between these regimes strongly depends on the magnetic field, x*∝ B^?4.