Radiant Interchange Between Circular Disks Having Arbitrarily Different Temperatures

1961 ◽  
Vol 83 (4) ◽  
pp. 494-502 ◽  
Author(s):  
E. M. Sparrow ◽  
J. L. Gregg
Keyword(s):  
Heat Transfer ◽  
Numerical Solutions ◽  
Local Heat Transfer ◽  
Disk Surface ◽  
Radiant Heat ◽  
Local Heat ◽  
Radiant Heat Transfer ◽  
Disk Radius ◽  
Integral Equation Formulation ◽  
Different Temperatures

The problem of radiant heat transfer between parallel disks has been analyzed by generalizing the standard gray-body enclosure theory. In particular, the assumption that the radiant flux leaving a surface and the local heat flux are uniformly distributed over the surface has been lifted by an integral equation formulation. It has been shown that the general problem of disks at arbitrarily different temperatures can be conveniently broken down into two subproblems, each of which can be solved independently of the temperature level. Numerical solutions of the governing integral equations have been carried out for spacing ratios h/R (h = spacing, R = disk radius) ranging from 5.0 to 0.05 and for emissivities ranging from 0.1 to 0.9. Local heat-transfer results have been presented which, depending on spacing and emissivity, display marked variations over the disk surface. Over-all heat-transfer results have been calculated and compared with the predictions of the standard simplified enclosure theory. These predictions of the simplified theory were found to be unexpectedly good, especially in view of the large surface variations of the local heat transfer.

Experiments on Hydrodynamic and Thermal Behaviors of Thin Liquid Films

2003 ◽  
Author(s):  
B. Ozar ◽  
B. M. Cetegen ◽  
A. Faghri
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Liquid Flow ◽  
Local Heat Transfer ◽  
Disk Surface ◽  
Local Heat ◽  
Liquid Films ◽  
Local Heat Transfer Coefficient ◽  
Flow Rates

An experimental study of heat transfer into a thin film of liquid water on a rotating disk is described. The film was introduced from a flow collar at the center of a heated, horizontal disk at a fixed initial film thickness with a uniform radial velocity. Radial distribution of the disk surface temperatures was measured using a thermocouple / slip ring arrangement. Experiments were performed for a range of liquid flow rates between 3.0 lpm and 15.0 lpm corresponding to Reynolds numbers (based on the liquid inlet gap height and velocity) between 238 and 1188. The angular speed of the disk was varied from 0 rpm to 500 rpm. The local heat transfer coefficient was determined based on the heat flux supplied to the disk and the temperature difference between the measured disk surface temperature and the entrance temperature of the liquid onto the disk. The local heat transfer coefficient was seen to increase with increasing flow rate as well as increasing angular velocity of the disk. Effect of rotation on heat transfer was largest for the lower liquid flow rates with the effect gradually decreasing with increasing liquid flow rates. Semi-empirical correlations are presented in this study for the local and average Nusselt numbers. In addition to the heat transfer characterization, the thickness of the liquid film on the disk surface was measured by an optical method, including the characteristics of the hydraulic jump and the subcritical and supercritical flow regions.

The Free Convection of Heat from a Vertical Plate to Several Non-Newtonian “Pseudoplastic” Fluids

1972 ◽  
Vol 94 (1) ◽  
pp. 64-72 ◽  
Author(s):  
J. D. Dale ◽  
A. F. Emery
Keyword(s):  
Heat Transfer ◽  
Free Convection ◽  
Power Law ◽  
Vertical Plate ◽  
Numerical Solutions ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Minor Importance ◽  
Large Tank ◽  
Pseudoplastic Fluids

The local heat transfer, temperature, and velocity profiles were measured and numerically predicted for the free convection of heat from a vertical constant flux plate to several concentrations of carboxymethylcellulose (CMC) and carboxypolymethylene (Carbopol) powders in water. The fluids were found to have the thermal properties of water and in the shear stress range of interest to follow the power law of Ostwald–de Waele with flow indices varying from 0.395 to 1.0 and with fluid consistencies of 30 to 2300 times that of water. The tests were conducted using either of two plates (12 and 24 in. high) immersed in such a large tank (3000 lb of fluid) that the viscometric properties of the fluid remained unchanged, even for the long test periods used. All fluids, including those with yield stresses and those which suffered free surface effects, were found to transfer heat which could be correlated by the generalized Newtonian correlation Nux=C(Grx*Prx*n)13n+2 which suggests that the precise velocity characteristics of the fluid are of minor importance in determining the heat transfer performance of the system. The numerical solutions, based upon the boundary layer assumptions and the power-law model, were in excellent agreement with the experimental measurements.

Local Heat Transfer in Turbine Disk-Cavities: Part II — Rotor Cooling With Radial Location Injection of Coolant

1990 ◽  
Author(s):  
R. S. Bunker ◽  
D. E. Metzger ◽  
S. Wittig
Keyword(s):  
Heat Transfer ◽  
Gas Turbines ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Computer Assisted ◽  
Transfer Coefficients ◽  
Disk Radius ◽  
Radial Location ◽  
Heat Transfer Coefficients ◽  
Experimental Apparatus

Detailed radial distributions of rotor heat transfer coefficients are presented for three basic disk-cavity geometries applicable to gas turbines. The experimental apparatus has been designed to obtain local heat transfer data on a number of easily interchangeable rotor surfaces. The method employs thin thermochromic liquid crystal coatings upon the rotor surfaces together with video system data acquisition and computer-assisted image analysis to detect surface color display and to extract heat transfer information. A thermally transient, aerodynamically steady technique is used which attains consistent thermal boundary conditions over the entire disk-cavity. Cooling air is introduced into the disk-cavity via a single circular jet mounted perpendicularly into the stator at one of three radial locations; 0.4, 0.6 or 0.8 times the rotor radius. Rotor heat transfer coefficients have been obtained over a range of parameters including disk rotational Reynolds numbers of 2 to 5 · 105, rotor/stator hub spacing-to-disk radius ratios of .025 to .15, and jet mass flow rates between .10 and .40 times the turbulent pumped flow rate of a free disk. The rotor surfaces include a parallel rotor-stator system, a rotor with 5 percent diverging taper, and a similarly tapered rotor with a rim sealing lip at its extreme radius. Results are presented showing the effects of the parallel rotor, which indicate strong variations in local Nusselt numbers for all but rotational speed. These results are compared to associated hub injection data of Part I of this study, demonstrating that overall rotor heat transfer is optimized by either hub injection or radial location injection of coolant dependent upon the configuration. Results with the use of the tapered rotor show significant local Nusselt number radial variation changes over those of the parallel rotor, while the addition of a rim sealing lip appears to increase the level of the radial distribution.

scholarly journals Local Heat Transfer in Turbine Disk-Cavities: Part I — Rotor and Stator Cooling With Hub Injection of Coolant

1990 ◽  
Author(s):  
R. S. Bunker ◽  
D. E. Metzger ◽  
S. Wittig
Keyword(s):  
Heat Transfer ◽  
Liquid Crystal ◽  
Mass Flow ◽  
Flow Rate ◽  
Gas Turbines ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Computer Assisted ◽  
Disk Radius ◽  
Wide Range

Results are presented from an experimental study designed to obtain detailed radial heat transfer coefficient distributions applicable to the cooling of disk-cavity regions of gas turbines. An experimental apparatus has been designed to obtain local heat transfer data on both the rotating and stationary surfaces of a parallel geometry disk-cavity system. The method employed utilizes thin thermochromic liquid crystal coatings together with video system data acquisition and computer-assisted image analysis to extract heat transfer information. The color display of the liquid crystal coatings is detected through the analysis of standard video chromanance signals. The experimental technique used is an aerodynamically steady but thermally transient one which provides consistent disk-cavity thermal boundary conditions while yet being inexpensive and highly versatile. A single circular jet is used to introduce fluid from the stator into the disk-cavity by impingement normal to the rotor surface. The present study investigates hub injection of coolant over a wide range of parameters including disk rotational Reynolds numbers of 2 to 5 · 105, rotor/stator spacing-to-disk radius ratios of .025 to .15, and jet mass flow rates between .10 and .40 times the turbulent pumped flow rate of a free disk. The results are presented as radial distributions of local Nusselt numbers. Rotor heat transfer exhibits regions of impingement and rotational domination with a transition region between, while stator heat transfer shows flow reattachment and convection regions with evidence of an inner recirculation zone. The local effects of rotation, spacing, and mass flow rate are all displayed. The significant magnitude of stator heat transfer in many cases indicates the importance of proper stator modeling to rotor and disk-cavity heat transfer results.

Local Heat Transfer in Turbine Disk Cavities: Part I—Rotor and Stator Cooling With Hub Injection of Coolant

1992 ◽  
Vol 114 (1) ◽  
pp. 211-220 ◽  
Author(s):  
R. S. Bunker ◽  
D. E. Metzger ◽  
S. Wittig
Keyword(s):  
Heat Transfer ◽  
Liquid Crystal ◽  
Mass Flow ◽  
Flow Rate ◽  
Gas Turbines ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Computer Assisted ◽  
Disk Radius ◽  
Wide Range

Results are presented from an experimental study designed to obtain detailed radial heat transfer coefficient distributions applicable to the cooling of disk-cavity regions of gas turbines. An experimental apparatus has been designed to obtain local heat transfer data on both the rotating and stationary surfaces of a parallel geometry disk-cavity system. The method employed utilizes thin thermochromic liquid crystal coatings together with video system data acquisition and computer-assisted image analysis to extract heat transfer information. The color display of the liquid crystal coatings is detected through the analysis of standard video chromanance signals. The experimental technique used is an aerodynamically steady but thermally transient one, which provides consistent disk-cavity thermal boundary conditions yet is inexpensive and highly versatile. A single circular jet is used to introduce fluid from the stator into the disk cavity by impingement normal to the rotor surface. The present study investigates hub injection of coolant over a wide range of parameters including disk rotational Reynolds numbers of 2 to 5 × 105, rotor/stator spacing-to-disk radius ratios of 0.025 to 0.15, and jet mass flow rates between 0.10 and 0.40 times the turbulent pumped flow rate of a free disk. The results are presented as radial distributions of local Nusselt numbers. Rotor heat transfer exhibits regions of impingement and rotational domination with a transition region between, while stator heat transfer shows flow reattachment and convection regions with evidence of an inner recirculation zone. The local effects of rotation, spacing, and mass flow rate are all displayed. The significant magnitude of stator heat transfer in many cases indicates the importance of proper stator modeling to rotor and disk-cavity heat transfer results.

Laminar Free Convection From a Sphere

1964 ◽  
Vol 86 (4) ◽  
pp. 537-541 ◽  
Author(s):  
T. Chiang ◽  
A. Ossin ◽  
C. L. Tien
Keyword(s):  
Heat Transfer ◽  
Surface Heat Flux ◽  
Numerical Solutions ◽  
Local Heat Transfer ◽  
Thermal Conditions ◽  
Local Heat ◽  
Surface Heat ◽  
Sphere Surface ◽  
Free Convective Flow ◽  
Boundary Layer Equations

The present paper is concerned with the solution to the problem of external free-convective flow from a sphere with various prescribed thermal conditions on the surface. Exact numerical solutions and heat-transfer results of the boundary-layer equations were obtained for the case of uniform surface temperature and the case of uniform surface heat flux, both at a Prandtl number of 0.70. Temperature and velocity profiles at various angular positions along the sphere surface and local heat-transfer results are presented. A comparison between the exact solution and the approximate solution from the integral method is also presented.

Local Heat Transfer in Enclosed Co-rotating Disks With Axial Throughflow

1994 ◽  
Vol 116 (1) ◽  
pp. 66-72 ◽  
Author(s):  
S. Y. Kim ◽  
J. C. Han ◽  
G. L. Morrison ◽  
E. Elovic
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Axial Flow ◽  
Local Heat Transfer ◽  
Disk Surface ◽  
Local Heat ◽  
Outer Radius ◽  
Rotating Disks ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients

Local heat transfer in enclosed co-rotating disks with axial through flow is investigated. The rotating cavity has two plane disks and a cylindrical rim (shroud). The ratio of the rim span to the disk outer radius is 0.4 and the ratio of the disk inner radius to outer radius is 0.25. The objectives of this study are to investigate the effects of axial coolant flow rate, rotation speed, and disk surface temperature on the local heat transfer coefficients inside the disk cavity. Both uniform disk surface heat flux and uniform disk surface temperatures are tested for axial flow Reynolds numbers between 2500 and 25,000 rotational Reynolds numbers between 0 and 5.11 × 105, and rotational Grashof numbers between 5 × 106 and 1.3 × 1010. The results show that the local heat transfer coefficients for the nonrotating cavity increase with increasing axial flow Reynolds number. In general, the local Nusselt numbers at large radii of the disks and rim increase with increasing rotational Reynolds number. However, the local Nusselt numbers at small radii of the disks initially decrease and then increase with increasing rotational Reynolds number. The uniform heat flux condition provides slightly higher heat transfer coefficients than those for the uniform wall temperature condition.

Local Heat Transfer in Turbine Disk Cavities: Part II—Rotor Cooling With Radial Location Injection of Coolant

1992 ◽  
Vol 114 (1) ◽  
pp. 221-228 ◽  
Author(s):  
R. S. Bunker ◽  
D. E. Metzger ◽  
S. Wittig
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Gas Turbines ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Computer Assisted ◽  
Transfer Coefficients ◽  
Disk Radius ◽  
Radial Location ◽  
Heat Transfer Coefficients

Detailed radial distributions of rotor heat transfer coefficients are presented for three basic disk-cavity geometries applicable to gas turbines. The experimental apparatus has been designed to obtain local heat transfer data on a number of easily interchangeable rotor surfaces. The method employs thin thermochromic liquid crystal coatings upon the rotor surfaces together with video system data acquisition and computer-assisted image analysis to detect surface color display and to extract heat transfer information. A thermally transient, aerodynamically steady technique is used, which attains consistent thermal boundary conditions over the entire disk cavity. Cooling air is introduced into the disk cavity via a single circular jet mounted perpendicularly into the stator at one of the three radial locations: 0.4, 0.6, or 0.8 times the rotor radius. Rotor heat transfer coefficients have been obtained over a range of parameters including disk rotational Reynolds numbers of 2 to 5 × 105, rotor/stator hub spacing-to-disk radius ratios of 0.025 to 0.15, and jet mass flow rates between 0.10 and 0.40 times the turbulent pumped flow rate of a free disk. The rotor surfaces include a parallel rotor-stator system, a rotor with 5 percent diverging taper, and a similarly tapered rotor with a rim sealing lip at its extreme radius. Results are presented showing the effects of the parallel rotor, which indicate strong variations in local Nusselt numbers for all but rotational speed. These results are compared to associated hub injection data of Part I of this study, demonstrating that overall rotor heat transfer is optimized by either hub injection or radial location injection of coolant dependent upon the configuration. Results with the use of the tapered rotor show significant variations in local Nusselt number compared with those of the parallel rotor, while the addition of a rim sealing lip appears to increase the Nusselt number level.

Effects of Microstructure on the Conjugated Mixed Forced and Free Convection-Conduction Analysis of Heat Transfer in a Vertical Plate Fin

1986 ◽  
Vol 108 (3) ◽  
pp. 580-584 ◽  
Author(s):  
Fue-Sang Lien ◽  
Cha’o-Kuang Chen
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Free Convection ◽  
Transfer Coefficient ◽  
Micropolar Fluid ◽  
Vertical Plate ◽  
Numerical Solutions ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Local Heat Transfer Coefficient

A conjugated convection-conduction analysis has been made for a vertical plate fin which exchanges heat with its micropolar fluid environment by mixed forced and free convection. The analysis is based on a one-dimensional model for the plate fin whereby the heat conduction equation for the fin is solved simultaneously with the conservation equations for mass, momentum, angular momentum, and energy in the micropolar fluid boundary layer adjacent to the fin. The local heat transfer coefficient is not specified in advance but is one of the results of the numerical solutions. Numerical results of the overall heat transfer rate, the local heat transfer coefficient, the local heat flux, and the fin temperature distribution for Pr = 5 are presented for various values of Δ (dimensionless material parameter), Nc (conjugated convection-conduction parameter), and Ω (buoyancy parameter).

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