Showing papers on "Nusselt number published in 1991"
TL;DR: In this article, the authors characterized local heat transfer coefficients for round, single-phase free liquid jets impinging normally against a flat uniform heat flux surface, and found that the local Nusselt number characteristics were dependent on nozzle diameter.
Abstract: The purpose of this investigation was to characterize local heat transfer coefficients for round, single-phase free liquid jets impinging normally against a flat uniform heat flux surface. The problems parameters investigated were jet Reynolds number Re, nozzle-to-plate spacing z, and jet diameter d. A region of near-constant Nusselt number was observed for the region bounded by 0 {le} r/d {le} 0.75, where is the radical distance from the impingement point. The local Nusselt number profiles exhibited a sharp drop for r/d > 0.75, followed by an inflection and a shower decrease thereafter. Increasing the nozzle-to-plate spacing generally decreased the heat transfer slightly. The local Nusselt number characteristics were found to be dependent on nozzle diameter. This was explained by the influence of the free-stream velocity gradient on local heat transfer, as predicted in the classical analysis of infinite jet stagnation flow and heat transfer. Correlations for local and average Nusselt numbers reveal an approximate Nusselt number dependence on Re{sup 1,3}.
219 citations
TL;DR: In this paper, the surface curvature effects on the impingement cooling flow and the heat transfer processes over a concave and a convex surface were investigated, where an electrical resistance wire is used to generate smoke and the local heat transfer Nusselt number along the surfaces is measured.
Abstract: Experiments are performed to study 'surface curvature effects on the impingement cooling flow and the heat transfer processes over a concave and a convex surface. A single air jet issuing from different size slots continuously impinges normally on the concave side or the convexside of a heated semicylindrical surface. An electrical resistance wire is used to generate smoke, which allows us to visualize the impinging flow structure. The local heat transfer Nusselt number along the surfaces is measured. For impingement on a convex surface, three-dimensional counterrotating vortices on the stagnation point are initiated, which result in the enhancement of the heat transfer process. For impingement on a concave surface, the heat transfer Nusselt number increases with increasing surface curvature, which suggests the initiation of Taylor-Gortler vortices along the surface. In the experiment, the Reynolds number ranges from 6000 to 350,000, the slot-to-plate spacing from 2 to 16, and the diameter-to-slot-width ratio D/b from 8 to 45.7. Correlations of both the stagnation point and the average Nusselt number over the curved surface, which account for the surface curvature effect, are presented. 1 Introduction Impingement cooling has been widely used to cool a heat transfer component exposed to a high temperature or a high heat flux environment. The impingement cooling jet has the advantage that it is readily moved to the location of interest and removes a large amount of heat. It has been widely used in such industrial systems as high-temperature gas turbines, paper drying, glass manufacturing, and high-density electronic equipment. The impinging jet used in these systems is air. Over the past 30 years, impingement cooling heat transfer has been extensively studied. Good review articles are available (Martin, 1977; Becko, 1976). The impinging flow structure (Donaldson and Snedeker, 1971a, 1971b), the local heat transfer, and the correlations of average Nusselt number in terms of relevant parameters have been well studied (Gardon and Cobonpue, 1963; Gardon and Akfirat, 1966; Korger and Krizek, 1965; Zumbrunnen et al., 1989). However, the impingement cooling studied in the past was on a flat plate. The situation of impingement cooling over a curved surface may frequently be encountered. However, the studies of impingement cooling on a curved surface are relatively few. Chupp et al. (1969) studied the impingement cooling heat transfer for an array of round jets impinging on a concave surface. The geometric configuration studied is very similar to the case for cooling of the leading edge of a gas turbine airfoil. They measure the local Nusselt number and correlate the average Nusselt number in terms of the Reynolds number, the nozzle-to-plate spacing, and some nondimensional parameters of geometry. However, the local heat transfer obtained is actually an average over a relatively large space. A similar geometry is also studied by Metzger et al. (1969,1972) and Hrycak (1978, 1981). Tabakoff and Clevenger (1972) study three different configurations of impinging jets on a concave surface: the single slot jet, the one-dimensional row of round jets, and the two-dimensional array of jets. Both the local and the average Nusselt number are determined. However, the local heat transfer Nusselt number obtained is again an average over a relatively large space. A few correlations of average Nusselt numbers for slot jet impingement cooling over a concave or a
210 citations
TL;DR: In this paper, the impingement cooling of uniformly heated surfaces is investigated analytically and experimentally for stable, unsubmerged, uniform velocity laminar jets in the absence of phase change.
Abstract: The impingement of circular, liquid jets provides a convenient method of cooling surfaces. Here, jet impingement cooling of uniformly heated surfaces is investigated analytically and experimentally for stable, unsubmerged, uniform velocity laminar jets in the absence of phase change. Analytical and numerical predictions are developed for a laminar radial film flow. Experiments using undisturbed laminar jets were performed to determine local Nusselt numbers from the stagnation point to radii of up to 40 diameters. Turbulent transition in the film flow is observed experimentally at a certain radius. Beyond this transition radius, a separate turbulent analysis is constructed. Integral method results are compared to numerical results, and Prandtl number effects are investigated. The predictions are found to agree well with the measurements for both laminar and turbulent flow. Predictive formulae are recommended for the entire range of radii.
208 citations
TL;DR: In this paper, the authors presented numerical calculations for the steady three-dimensional structure of thermal convection of a fluid with strongly temperature-dependent viscosity in a bottom-heated rectangular box.
Abstract: Numerical calculations are presented for the steady three-dimensional structure of thermal convection of a fluid with strongly temperature-dependent viscosity in a bottom-heated rectangular box. Viscosity is assumed to depend on temperature T as exp ( --ET), where E is a constant ; viscosity variations across the box r (= exp (E)) as large as lo5 are considered. A stagnant layer or lid of highly viscous fluid develops in the uppermost coldest part of the top cold thermal boundary layer when r > rcl, where r = rcl = 1.18 x 103R,0~308 andR, is the Rayleigh number based on the viscosity at the top boundary. Three-dimensional convection occurs in a rectangular pattern beneath this stagnant lid. The planform consists of hot upwelling plumes at or near the centre of a rectangle, sheets of cold sinking fluid on the four sides, and cold sinking plume concentrations immersed in the sheets. A stagnant lid does not develop, i.e. convection involves all of the fluid in the box when r rc2 = 3.84 x 106R;1.36. The planform of the convection is rectangular with the coldest parts of the sinking fluid and the hottest part of the upwelling fluid occurring as plumes at the four corners and at the centre of the rectangle, respectively. Both hot uprising plumes and cold sinking plumes have sheet-like extensions, which become more well-developed as r increases. The whole-layer mode of convection occurs as two-dimensional rolls when r < min (rcl, rc2). The Nusselt number Nu depends on the viscosity at the top surface more strongly in the regime of whole-layer convection than in the regime of stagnant-lid convection. In the whole-layer convective regime, Nu depends more strongly on the viscosity at the top surface than on the viscosity at the bottom boundary.
176 citations
TL;DR: Similarity solutions for buoyancy induced heat and mass transfer from a vertical plate embedded in a saturated porous medium are reported for constant wall temperature and concentration, constant wall heat and flux.
141 citations
TL;DR: In this article, the Nusselt number and friction factor increase with increasing relative roughness height and decrease with increasing roughness pitch, but not in direct proportions, and design curves have been developed that give the optimal thermohydraulic performance combination of these parameters.
134 citations
TL;DR: In this paper, an experimental investigation is performed to characterize the convective heat transfer from a flat surface to a row of impinging, circular, submerged air jets formed by square-edged orifices having a length/diameter ratio of unity.
112 citations
TL;DR: In this paper, a second-order integral boundary-layer approximation for long waves at intermediate Re of O(e−1) was developed, where e is the dimensionless wavenumber scaled with respect to the film thickness.
Abstract: At large Reynolds number (Re > 10), waves on inclined films grow rapidly downstream in both amplitude and wavelength to the extent that linear stability theory cannot adequately describe their velocity–wavenumber relationship. The wavelength increases indefinitely until solitary waves are formed very far downstream. In a recent experiment of Brauner & Maron (1982), this evolution to long waves is observed to occur by successive wavelength doubling. In this analysis, we develop a second-order integral boundary-layer approximation for long waves at intermediate Re of O(e−1), where e is the dimensionless wavenumber scaled with respect to the film thickness. (A second-order theory is needed because it introduces important dissipation terms which allow periodic and solitary waveforms to exist when surface tension is negligible.) After showing that this model can adequately describe infinitesimal waves at inception, we verify the existence of solitary waves and long-wavelength periodic waves near the critical Reynolds number with a weakly nonlinear analysis. These finite-amplitude waves are then numerically continued into the more important high-Re and strongly nonlinear regions. It is shown that the solitary wave speed approaches 1.67 times the Nusselt velocity, and the thickness of the substrate film approaches 0.47 times the Nusselt film thickness at large Re. These results are favourably compared to experimental data of Chu & Dukler (1974, 1975). We also confirm the period-doubling scenario of Brauner & Maron by showing that short finite-amplitude monochromatic waves are unstable to subharmonic instability.
101 citations
TL;DR: In this article, the effect of wall heat flux ratio on the local heat transfer augmentation in a square channel with two opposite in-line ribbed walls was investigated for Reynolds numbers from 15,000 to 80,000.
Abstract: The effect of wall heat flux ratio on the local heat transfer augmentation in a square channel with two opposite in-line ribbed walls was investigated for Reynolds numbers from 15,000 to 80,000. The square channel composed of ten isolated copper sections has a length-to-hydraulic diameter ratio (L/D) of 20. The rib height-to-hydraulic diameter ratio (e/D) is 0.0625 and the rib pitch-to-height ratio (P/e) equals 10
100 citations
TL;DR: In this article, the full elliptic forms of the Navier-Stokes and energy equations are solved using novel inlet flow boundary conditions, and the results cast doubt on the validity of previous elliptic solutions.
Abstract: Steady two-dimensional laminar free convection between isothermal vertical plates including entrance flow effects has been numerically investigated. The full elliptic forms of the Navier-Stokes and energy equations are solved using novel inlet flow boundary conditions. Results are presented for Prandtl number Pr = 0.7, Grashof number range 50 {le} Gr{sub b} {le} 5 {times} 10{sup 4}, and channel aspect ratios of L/b = 10, 17, 24. New phenomena, such as inlet flow separation, have been observed. The results cast doubt on the validity of previous elliptic solutions. Comparisons with the approximate boundary-layer results show that a full elliptic solution is necessary to get accurate local quantities near the channel entrance.
96 citations
TL;DR: In this article, an examination of heat transfer between two parallel plates due to electroconvection is presented, showing that the electrical effects dominate totally over buoyancy effects for all cases considered.
TL;DR: In this article, a parametric study of chaotic Rayleigh-Benard convection over moderate Rayleigh numbers is made, where mean quantities, r.m.s. fluctuations, Reynolds number, probability distributions and power spectra are considered.
Abstract: A parametric study is made of chaotic Rayleigh-Benard convection over moderate Rayleigh numbers. As a basis for comparison over the Rayleigh number (Ra) range we consider mean quantities, r.m.s. fluctuations, Reynolds number, probability distributions and power spectra. As a further means of investigating the flow we use the Karhunen-Loeve procedure
TL;DR: In this article, the phenomenon of natural convection in a square enclosure heated and cooled in the horizontal direction was investigated numerically in the Prandtl number range 0.01-10 and the Rayleigh number range 102-1011.
Abstract: The phenomenon of natural convection in a square enclosure heated and cooled in the horizontal direction was investigated numerically in the Prandtl number range 0.01-10 and the Rayleigh number range 102-1011. The numerical method relied on the full governing equations for time-dependent flows. The study focused on the detection of inertia-sustained fluctuations in the flow field and on the highest Rayleigh number where steady-state laminar flows are possible. It was found that the highest Rayleigh number decreases dramatically as the Prandtl number decreases. This finding agrees qualitatively with experimental observations of transition to turbulent natural convection and with the “local Reynolds number” criterion of transition to turbulence recommended by the buckling theory of turbulent flow.
TL;DR: In this paper, an experimental study of convective heat transfer in radially rotating isothermal rectangular ducts with various height and width aspect ratios is presented. And the effects of the main flow, the rotational speed, and the aspect ratio {gamma} on heat transfer are subjects of major interest.
Abstract: The paper presents an experimental study of convective heat transfer in radially rotating isothermal rectangular ducts with various height and width aspect ratios. The convective heat transfer is affected by secondary flows resulting from Coriolis force and the buoyancy flow, which is in turn due to the centrifugal force in the duct. The growth and strength of the secondary flow depend on the rotational Rayleigh number. The aspect ratio of the duct may affect the secondary flow and the buoyancy flow, and therefore is also a critical parameter in the heat transfer mechanism. In the present work the effects of the main flow, the rotational speed, and the aspect ratio {gamma} on heat transfer are subjects of major interest. Ducts of aspect ratios {gamma} = 5, 2, 1, 0.5, and 0.2 at rotational speed up to 3,000 rpm are studied. The main flow Reynolds number ranges from 700 to 20,000 to cover the laminar, transitional, and turbulent flow regimes in the duct flow. Thest data and discussion are presented.
TL;DR: In this article, the effect of jet inclination on the local heat transfer under an obliquely impinging, round, free liquid jet striking a constant heat flux surface is investigated experimentally.
TL;DR: In this paper, a method of analysis applying Nusselt's liquid film theory to the close-contact melting heat transfer in the rectangular capsule is presented, and the analytical results show good agreement with the experimental data.
TL;DR: In this article, the linear and weakly nonlinear thermoconvective stability of a ferrofluid, confined between rigid horizontal plates at different temperatures and subjected to a strong uniform external magnetostatic field in the vertical direction, was analyzed.
Abstract: We analyse the linear and weakly nonlinear thermoconvective stability of a ferrofluid, confined between rigid horizontal plates at different temperatures and subjected to a strong uniform external magnetostatic field in the vertical direction. When this magnetically saturated ferrofluid is heated from below our critical parameters for the linear stability problem agree with those of Finlayson. The corresponding weakly nonlinear analysis predicts that under microgravity conditions, the ratio of the steady heat transfer by convection to that by conduction can be up to 10% greater than when the magnetic field is absent. If the ferrofluid is heated from above, critical temperature gradients can attain extremely high values and the horizontal separation of roll cells can be less than half the spacing observed when the lower plate is warmer. In this non-standard regime, where convection is due to magnetic body forces, the Nusselt numbers for a given supercritical temperature gradient are significantly higher than when the ferrofluid is heated from below.
TL;DR: In this article, the influence of high mainstream turbulence on leading edge heat transfer was studied, and the results indicate that the leading-edge heat transfer increases significantly with increasing mainstream turbulence intensity, but the effect diminishes at the end of the flat sidewall.
Abstract: The influence of high mainstream turbulence on leading edge heat transfer was studied. High mainstream turbulence was produced by a bar grid (Tu = 3.3–5.1 percent), passive grid (Tu = 7.6–9.7 percent), and jet grid (Tu = 12.9–15.2 percent). Experiments were performed using a blunt body with a semicylinder leading edge and flat sidewalls. The mainstream Reynolds numbers based on leading edge diameter were 25,000, 40,000, and 100,000. Spanwise and streamwise distributions of local heat transfer coefficients on the leading edge and flat sidewall were obtained. The results indicate that the leading edge heat transfer increases significantly with increasing mainstream turbulence intensity, but the effect diminishes at the end of the flat sidewall because of turbulence decay. Stagnation point heat transfer results for high turbulence intensity flows agree with the Lowery and Vachon correlation, but the overall heat transfer results for the leading edge quarter-cylinder region are higher than their overall correlation for the entire circular cylinder region. High mainstream turbulence tends not to shift the location of the separation-reattachment region. The reattachment heat transfer results are about the same regardless of mainstream turbulence levels and are much higher than the turbulent flat plate correlation.
TL;DR: In this paper, the authors measured the flow structure and heat transfer of impinging flame jets as well as impinging isothermal jets from two rapid-heating burners, and showed that heat transfer from isothermal and flame jets can be described in the same way with this velocity gradient and a turbulence enhancement factor.
TL;DR: In this article, the effects of body shape and orientation on laminar natural convection heat transfer from isothermal, two-dimensional, and axisymmetric bodies are investigated.
Abstract: The effects of body shape and orientation on laminar natural convection heat transfer from isothermal, two-dimensional, and axisymmetric bodies are investigated. A new form of the body-gravity function is presented and its behavior is examined for various body shapes and orientations. The square root of the total surface area is obtained from the analysis as the charateristic body length. A definition of the aspect ratio is introduced, which can be used consistently for both two-dimensional and axisymmetric bodies. The resulting body-gravity function is observed to be weakly dependent on geometry and orientation of the bodies for a range of the aspect ratio from approximately 0.2 to 5, over which the body-gravity function resulted in a good agreement with values obtained from the existing experimental data.
TL;DR: In this paper, the thermal performance of Trombe wall solar collector systems is studied numerically and the results are presented in terms of temperature and velocity distributions in various parts of the system; the Nusselt number and the system thermal performance as a function of the Rayleigh number are also evaluated.
TL;DR: In this paper, numerical solutions based on the streamfunction-vorticity formulation were obtained for two-dimensional flow of air in a differentially heated, slender cavity with conducting fins on the cold wall, for Rayleigh numbers of 103-105, angles of inclination of 45° and 90°, overall aspect ratios of 20 and ∞, and microcavity aspect ratios (A) of 20-0.25.
Abstract: Numerical solutions, based on the streamfunction-vorticity formulation, were obtained for two-dimensional flow of air in a differentially heated, slender cavity with conducting fins on the cold wall, for Rayleigh numbers of 103-105, angles of inclination of 45° and 90°, overall aspect ratios of 20 and ∞, and microcavity aspect ratios (A) of 20-0.25. As A was decreased from a value of 20, the flow pattern evolved as follows: a primary circulation state, a boundary layer regime with recirculations and decreasing primary circulation, an increase in primary circulation, a separation of the recirculating stream from the interfin space, and a final state of primary circulation restricted to the unfinned side. The average Nusselt number at a given fin length also evolved during these transitions, showing maximum and minimum values whose locations depended only on Ra. Limited results showing the dependence of flow and heat transfer variables on dimension-less fin length are also given. A series of recommendations...
TL;DR: In this paper, the numerical results of natural convective flows between two vertical, parallel plates within a large enclosure were presented, and the results were in good agreement with the reported results in the literature for air for large aspect ratios.
Abstract: This paper presents the numerical results of natural convective flows between two vertical, parallel plates within a large enclosure A parametric study has been conducted for various Prandtl numbers and channel aspect ratios The results are in good agreement with the reported results in the literature for air for large aspect ratios However, for small aspect ratios, the present numerical results do not agree with the correlations given in the literature The discrepancy is due to the fact that the published results were obtained for channels where the diffusion of thermal energy in the vertical direction is negligible The results obtained in this paper indicate that vertical conduction should be considered for channel aspect ratios less than 10 for Pr = 07 Correlations are presented to predict the maximum temperature and the average Nusselt number on the plate as explicit functions of the channel Rayleigh number and the channel aspect ratio for air The plate temperature is a weak function of Prandtl number for Prandtl numbers greater than 07, if the channel Rayleigh number is chosen as the correlating parameter For Prandtl numbers less than 01, the plate temperature is a function of channel Rayleigh number and the Prandtl numbermore » A correlation for maximum temperature on the plate is presented to include the Prandtl number effect for large aspect ratio channels« less
TL;DR: In this article, the authors investigate the flow pattern and forced convective heat transfer in supercritical flows, such as those encountered in compact heat exchangers, and show that these flows exhibit laminar self-sustained oscillations at the plane channel Tollmien-Schlichting frequency for Reynolds numbers above the critical one.
Abstract: Numerical investigations of the flow pattern and forced convective heat transfer in supercritical flows, such as those encountered in compact heat exchangers, are presented. These flows exhibit laminar self-sustained oscillations at the plane channel Tollmien-Schlichting frequency for Reynolds numbers above the critical one. These studies indicate that oscillatory separated flow results in large-scale convective patterns that are responsible for significant heat transfer enhancement and leads to a reduction in the pumping power required to achieve a given Nusselt number. The hydrodynamic-heat transfer numerical results are obtained by direct simulation of the unsteady energy and Navier-Stokes equations using a spectral element method for the spatial discretization. The spectral element method is a high-order weighted-residual technique that exploits both the common features and the competitive advantages of low-order finite element methods (versatility) and spectral techniques (accuracy and rapid converge...
TL;DR: In this article, a two-fluid model using the thermal eddy diffusivity concept and Lumley's drag reduction theory is proposed to analyse heat transfer of the turbulent dilute gas-particle flow in a vertical pipe with constant wall heat flux.
01 Jan 1991
TL;DR: In this article, a review of the recent developments in mixed convection in saturated porous media is presented, and a sufficient base of information exists so that correlations of practical value now exist for thermal engineering design for several flow geometries.
Abstract: Recent developments in mixed convection in saturated porous media are reviewed. Flow geometries include external flows (flat plates), horizontal layers and annuli, and vertical layers and annuli. Heat transfer results are generally presented in the form of Nusselt numbers as a function of Rayleigh and Peclet numbers. Generally, theoretical advances have left many key problems uninvestigated in the laboratory, and some areas remain where basic knowledge is needed to both test modelling assumptions and reveal fundamental flow phenomena. Nevertheless, a sufficient base of information exists so that correlations of practical value now exist for thermal engineering design for several flow geometries.
TL;DR: In this paper, the authors performed numerical experiments on an incompressible fluid contained in a tilted nonrectangular enclosure and found that the heat transfer and fluid motion within the enclosure are strong functions of Rayleigh number, Prandtl number, and orientation angle of the enclosure.
Abstract: Numerical experiments were performed on an incompressible fluid contained in a tilted nonrectangular enclosure. Rayleigh numbers of l02-l05 and Prandtl numbers of 0.001-100 are considered. The wall angles are 22.5°, 45°, and 77.5° with aspect ratios of 3 and 6. Results indicate that the heat transfer and fluid motion within the enclosure are strong functions of Rayleigh number, Prandtl number, and orientation angle of the enclosure. For Rayleigh numbers greater than 1& and Prandtl numbers greater than 0.1, a minimum and a maximum mean Nusselt number occurred as the angle of orientation was increased from 0° to 360°. A transition in the mode of circulation occurred at the angles corresponding to the minimum or maximum rate of heat transfer.
TL;DR: In this paper, the effect of repeated boundary condition and wall conduction on mass flow rate, maximum surface temperature, and average surface Nusselt number (Nu{sub h} and Nu{sub c}) is discussed.
Abstract: Laminar free convective heat transfer in channels formed between series of vertical parallel plates with an embedded line heat source was studied numerically. These channels resemble cooling passages in electronic equipment. The effect of a repeated boundary condition and wall conduction on mass flow rate (M), maximum surface temperature ({theta}{sub h,max} and {theta}{sub c,max}), an average surface Nusselt number (Nu{sub h} and Nu{sub c}) is discussed. Calculations were made for Gr* = 10 to 10{sub 6}, K = 0.1, 1, 10, and 100, and t/B = 0.1 and 0.3. The effect of a repeated boundary condition decreases the maximum hot surface temperature and increases the maximum cold surface temperature. The effect of a repeated boundary condition with wall conduction increases the mass flow rate. The maximum increase in mass flow rate due to wall conduction is found to be 155%. The maximum decrease in average hot surface Nusselt number due to wall conduction (t/B and K) occurs at Gr* = 10{sup 6} and is 18%. Channels subjected to a repeated boundary condition approach that of a symmetrically heated channel subjected to uniform wall temperature conditions at K {ge} 100.
TL;DR: In this article, the problem of natural convection in differentially heated vertical cavities filled with spherical particles saturated with Newtonian fluids is investigated numerically, where the Brinkman-Darcy-Ergun equation is used as the momentum equation and the wall effect on porosity variation is approximated by an exponential function.
Abstract: The problem of natural convection in differentially heated vertical cavities filled with spherical particles saturated with Newtonian fluids is investigated numerically. The Brinkman-Darcy-Ergun equation is used as the momentum equation, and the wall effect on porosity variation is approximated by an exponential function. The effect of variable stagnant thermal conductivities is taken into consideration in the energy equation. The formulation of the problem shows that the flow and heat transfer characteristics depend on six dimensionless parameters, namely, the Rayleigh and Prandtl numbers of the fluid phase, the dimensionless particle diameter, the conductivity ratio of the two phases, the bulk porosity, and the aspect ratio of the cavity. The influences of these parameters on the heat transfer rate are thoroughly investigated. The predicted Nusselt numbers are compared with existing experimental results. It is found that the computed Nusselt numbers based on the present model compare the best with experimental data.