Flow and Heat Transfer in Convectively Cooled Underground Electric Cable Systems: Part 2—Temperature Distributions and Heat Transfer Correlations

1978 ◽  
Vol 100 (1) ◽  
pp. 36-40 ◽  
Author(s):  
R. S. Abdulhadi ◽  
J. C. Chato
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Cross Section ◽  
Thermal Boundary Layer ◽  
Electric Cable ◽  
Nusselt Numbers ◽  
Temperature Distributions ◽  
Cable Systems ◽  
Heat Transfer Correlations

Temperature distributions and heat transfer correlations have been obtained experimentally for a wide range of physical, flow and thermal parameters in three models of oil-cooled underground electric cable systems. The results show that in the laminar range, with the oils used, the thermal boundary layer thickness around the heated cables is only of the order of 2–3 mm over the entire length of the test section. Consequently, the best correlation of the heat transfer results is obtained if the Nusselt number, based on the cable diameter, is plotted against Re·Pr0.4, where the Reynolds number is based on the overall hydraulic diameter of the cross section of the flow. For laminar flows, the oil temperatures in the restricted flow channels between three cables or two cables and the pipe wall are about 11°C higher than corresponding bulk temperatures. As the flow becomes turbulent, the thermal boundary layer tends to vanish and the oil temperature becomes uniform over the entire flow cross section. Laminar Nusselt numbers are independent of the skid wire roughness ratio and the flow Reynolds number, but increase with increasing Rayleigh number and axial distance from the inlet, indicating significant natural convection effect. The range of laminar Nusselt numbers was 5–16. Turbulent Nusselt numbers increase with increasing roughness ratios. The Nusselt numbers at Re = 3000 are 30 and 60 for roughness ratios of 0.0216 and 0.0293, respectively.

scholarly journals Heat Transfer Around Sharp 180 Degree Turns in Smooth Rectangular Channels

1985 ◽  
Author(s):  
D. E. Metzger ◽  
M. K. Sahm
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Forced Convection ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Side Wall ◽  
Bottom Wall ◽  
Channel Depth ◽  
Nusselt Numbers ◽  
Rectangular Channels

Measured Nusselt numbers are presented for forced convection within and around sharp 180 degree turns in smooth channels of rectangular cross section. Separately determined top wall, bottom wall, and side wall values are presented individually along with azimuthal averages. The geometry of the channels and connecting turn is characterized by parameters W*, the ratio of upstream and downstream channel widths; D*, the non-dimensional channel depth; and H*, the non-dimensional clearance at the tip of the turn. Results from nine combinations of these parameters are presented at several values of channel Reynolds number to illustrate the effect of turn geometry on the heat transfer distributions.

Heat Transfer Around Sharp 180-deg Turns in Smooth Rectangular Channels

1986 ◽  
Vol 108 (3) ◽  
pp. 500-506 ◽  
Author(s):  
D. E. Metzger ◽  
M. K. Sahm
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Forced Convection ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Side Wall ◽  
Bottom Wall ◽  
Channel Depth ◽  
Nusselt Numbers ◽  
Rectangular Channels

Measured Nusselt numbers are presented for forced convection within and around sharp 180-deg turns in smooth channels of rectangular cross section. Separately determined top wall, bottom wall, and side wall values are presented individually along with azimuthal averages. The geometry of the channels and connecting turn is characterized by the parameters W*, the ratio of upstream and downstream channel widths; D*, the nondimensional channel depth; and H*, the nondimensional clearance at the tip of the turn. Results from nine combinations of these parameters are presented at several values of channel Reynolds number to illustrate the effect of turn geometry on the heat transfer distributions.

Heat Transfer Around a Circular Cylinder Near a Plane Surface

1985 ◽  
Vol 107 (4) ◽  
pp. 916-921 ◽  
Author(s):  
S. Aiba
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Experimental Study ◽  
Reynolds Number ◽  
Circular Cylinder ◽  
Boundary Layer Thickness ◽  
Plane Surface ◽  
Cross Flow ◽  
Nusselt Numbers ◽  
Characteristic Features

An experimental study has been conducted on the effect of the clearance (c) between a circular cylinder and a plane surface on the heat transfer from the cylinder to a cross flow of air. The test cylinder diameters (d) were 10.1, 15.2, and 25.2 mm. The turbulent boundary layer thickness (δ) along the wall with no cylinder present was varied from 15 to 19 mm. The Reynolds number (Re) based on the undisturbed uniform flow velocity above the wall ranged from 104 to 6.6×104. Variations of the characteristic features of the local and mean Nusselt numbers are discussed in relation to the values c/d, δ/d, and Re investigated.

Effect of a non-uniform alternating electric field on the thermal boundary layer near a heated vertical plate

1971 ◽  
Vol 49 (4) ◽  
pp. 693-703 ◽  
Author(s):  
Robert J. Turnbull
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Electric Field ◽  
Thermal Boundary Layer ◽  
Vertical Plate ◽  
Uniform Electric Field ◽  
Heated Plate ◽  
Uniform Field ◽  
Nusselt Numbers ◽  
Alternating Electric Field

A thermal boundary layer is established by heating a vertical plate in a dielectric liquid. An alternating voltage is applied between the heated plate and another plate which is not parallel to the heated plate. This voltage produces a non-uni- form electric field which in turn produces electrical forces acting on the gradients in dielectric permittivity which result from the temperature gradients. These electrical forces alter the boundary layer. In this paper approximate equations are developed which allow one to calculate the boundary-layer,thickness, velocity, and Nusselt numbers for the boundary layer in the presence of the non-uniform electric field. Numerical calculations show that the heat-transfer coefficient can be either increased or decreased by the non-uniform field, depending on whether the field is strongest at the top or bottom of the plates and also on the field strength. Experiments were performed which demonstrate the change in heat transfer caused by the non-uniform field.

Conjugate Heat Transfer Numerical Validation and PSE Analysis of Transonic Internally-Cooled Turbine Cascade

2010 ◽  
Author(s):  
Peigang Yan ◽  
Zhenfeng Wang ◽  
Wanjin Han
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Stability Analysis ◽  
Turbulence Model ◽  
Thermal Boundary Layer ◽  
Conjugate Heat Transfer ◽  
Turbulence Models ◽  
Transition Model ◽  
Momentum Thickness

Conjugate heat transfer numerical simulation of a transonic internal cooled turbine vane is carried out with a third-order accuracy TVD (Total Variation Diminishing) scheme and multi-block structured grids using the code developed in this paper. Comparison between results of commercial CFD codes with several turbulence models and those of this code show that it is incorrect of computational codes to predict the thermal boundary layer with traditional turbulence models, and that the turbulence models considering transitional phenomenon is able to acquire better accurate heat transfer in thermal boundary layer despite of certain deficiencies yet. The predicted distributions of aerodynamic parameters agree well with the experiments except for the temperature and heat transfer coefficient over the profile surface, which are largely different from the measured data. Results by Star-CD with V2-F model meet the same problem. Results by the code of this paper are close to those by CFX with K-ω-SST-ML transition model. Adopting transition model of Menter & Langtry (Shear-Stess-Transition model) gives the best results by adjusting the transition onset momentum thickness Reynolds number and the inlet viscosity ratio, especially for the mid part of the suction side where the validation accuracy is of a serious shortage by traditional turbulence model. It is proved in this paper that commercial codes have the ability to simulate transition process and thermal boundary layer accurately, but the designer’s experience is of utmost importance. Robust transition turbulence model should be developed further. PSE stability analysis equation and e-N prediction method are both integrated in this paper. It is concluded that boundary layer stability analysis by PSE method can be applied to the prediction of the transition onset without too many experiences and is able to define the empirical turbulence parameters for the accurate simulation of thermal boundary layer for any airfoil, such as the very important transition onset momentum thickness Reynolds number.

Effect of Nanofluid on Heat Transfer Enhancement for Mixed Convection Flow Over a Corrugated Surface

2020 ◽  
Vol 45 (4) ◽  
pp. 373-383
Author(s):  
Nepal Chandra Roy ◽  
Sadia Siddiqa
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Local Nusselt Number ◽  
Richardson Number ◽  
Thermal Boundary Layer ◽  
Volume Fraction ◽  
Convection Flow ◽  
Mixed Convection Flow

AbstractA mathematical model for mixed convection flow of a nanofluid along a vertical wavy surface has been studied. Numerical results reveal the effects of the volume fraction of nanoparticles, the axial distribution, the Richardson number, and the amplitude/wavelength ratio on the heat transfer of Al2O3-water nanofluid. By increasing the volume fraction of nanoparticles, the local Nusselt number and the thermal boundary layer increases significantly. In case of \mathrm{Ri}=1.0, the inclusion of 2 % and 5 % nanoparticles in the pure fluid augments the local Nusselt number, measured at the axial position 6.0, by 6.6 % and 16.3 % for a flat plate and by 5.9 % and 14.5 %, and 5.4 % and 13.3 % for the wavy surfaces with an amplitude/wavelength ratio of 0.1 and 0.2, respectively. However, when the Richardson number is increased, the local Nusselt number is found to increase but the thermal boundary layer decreases. For small values of the amplitude/wavelength ratio, the two harmonics pattern of the energy field cannot be detected by the local Nusselt number curve, however the isotherms clearly demonstrate this characteristic. The pressure leads to the first harmonic, and the buoyancy, diffusion, and inertia forces produce the second harmonic.

Numerical Simulation of Turbine Blade Boundary Layer and Heat Transfer and Assessment of Turbulence Models

1997 ◽  
Vol 119 (4) ◽  
pp. 794-801 ◽  
Author(s):  
J. Luo ◽  
B. Lakshminarayana
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Low Reynolds Number ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Bypass Transition ◽  
Boundary Layer Development ◽  
Low Reynolds ◽  
Layer Development

The boundary layer development and convective heat transfer on transonic turbine nozzle vanes are investigated using a compressible Navier–Stokes code with three low-Reynolds-number k–ε models. The mean-flow and turbulence transport equations are integrated by a four-stage Runge–Kutta scheme. Numerical predictions are compared with the experimental data acquired at Allison Engine Company. An assessment of the performance of various turbulence models is carried out. The two modes of transition, bypass transition and separation-induced transition, are studied comparatively. Effects of blade surface pressure gradients, free-stream turbulence level, and Reynolds number on the blade boundary layer development, particularly transition onset, are examined. Predictions from a parabolic boundary layer code are included for comparison with those from the elliptic Navier–Stokes code. The present study indicates that the turbine external heat transfer, under real engine conditions, can be predicted well by the Navier–Stokes procedure with the low-Reynolds-number k–ε models employed.

Condensation in a Variable Acceleration Field and the Condensing Thermosyphon

1965 ◽  
Vol 87 (4) ◽  
pp. 355-360 ◽  
Author(s):  
J. C. Chato
Keyword(s):  
Heat Transfer ◽  
Cross Section ◽  
Radial Distance ◽  
Constant Cross Section ◽  
Linear Variation ◽  
Temperature Differential ◽  
Acceleration Field ◽  
Nusselt Numbers ◽  
Increasing Temperature ◽  
Limiting Values

The general problem of condensation in a variable acceleration field was investigated analytically. The case of the linear variation, which occurs in a constant cross section, rotating thermosyphon, was treated in detail. The results show that the condensate thickness and Nusselt numbers approach limiting values as the radial distance increases. The effects of the temperature differential and the Prandtl number are similar to those in other condensation problems; i.e., the heat transfer increases slightly with increasing temperature differential if Pr > 1, but it decreases with increasing temperature differential if Pr ≪ 1.

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