Heat Transfer and Flow in a Short, Vertical, Internally Heated Annulus with a Rotating Outer Boundary

1972 ◽  
Vol 14 (6) ◽  
pp. 393-399
Author(s):  
J. S. Coombs ◽  
S. D. Probert
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Outer Boundary ◽  
Outer Cylinder ◽  
Heat Fluxes ◽  
Secondary Flows ◽  
End Effects ◽  
Concentric Cylinders ◽  
The Mean ◽  
Steady State Heat

Experimental determinations were made of the steady-state heat fluxes and velocity profiles in water between two vertical concentric cylinders, the heated inner cylinder being stationary while the outer cylinder was rotated in ambient temperature air. Secondary flows, due to end effects, existed in the annulus at all rotational speeds and profoundly influenced the rate of heat transfer across the annulus. When the circulation of the secondary flows opposed those due to natural convection, the mean Nusselt number decreased almost to unity.

scholarly journals Natural convection of Newtonian fluids between two concentric cylinders of a special cross-sectional form

2020 ◽  
pp. 190-190
Author(s):  
Houssem Laidoudi ◽  
Mustapha Helmaoui ◽  
Mohamed Bouzit ◽  
Abdellah Ghenaim
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Inclination Angle ◽  
Average Nusselt Number ◽  
Outer Cylinder ◽  
Cross Sectional ◽  
The Mean

In this paper, we performed a numerical simulation of natural convection of Newtonian fluids between two cylinders of different cross-sectional form. The inner cylinder is supposed to be hot and the outer cylinder is assumed to be cold. The diameter of inner cylinder to the diameter of outer cylinder defines the radii ratio (RR= 2.5). The governing equations describing the physical behavior of fluid flow and heat transfer are solved using finite volume method. The effects of Prandtl number (Pr = 0.71 to 100), Rayleigh number (Ra = 103 to 105) and inclination angle of inner cylinder (? = 0? to 80?) on streamlines, isotherms and dimensionless velocity are presented and discussed. Also, the mean average Nusselt number of inner cylinder is plotted versus the governing parameters. All present simulations are considered in two-dimensions for steady laminar flow regime. The obtained results showed that the flow between cylinders is more stable for the inclination angle ? = 0?. Increase in Rayleigh number increases the heat transfer rate for all values of inclination angle. Furthermore, the effect of Prandtl number on the mean average Nusselt number becomes negligible when Pr is over the value 7.01. For example at Pr = 0.71 and Ra =105, increase in inclination from 0? to 40?decreases the average Nusselt number by 5.4%. A new correlation is also provided to describe the average Nusselt number as function of Pr and Ra at ? = 0?.

Heat Transfer Enhancement in a Rectangular (AR = 3:1) Channel With V-Shaped Dimples

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
C. Neil Jordan ◽  
Lesley M. Wright
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Liquid Crystal ◽  
Pressure Drop ◽  
Heat Transfer Enhancement ◽  
Thermal Performance ◽  
Secondary Flows ◽  
Transfer Enhancement ◽  
Reduced Pressure

An alternative to ribs for internal heat transfer enhancement of gas turbine airfoils is dimpled depressions. Relative to ribs, dimples incur a reduced pressure drop, which can increase the overall thermal performance of the channel. This experimental investigation measures detailed Nusselt number ratio distributions obtained from an array of V-shaped dimples (δ/D = 0.30). Although the V-shaped dimple array is derived from a traditional hemispherical dimple array, the V-shaped dimples are arranged in an in-line pattern. The resulting spacing of the V-shaped dimples is 3.2D in both the streamwise and spanwise directions. A single wide wall of a rectangular channel (AR = 3:1) is lined with V-shaped dimples. The channel Reynolds number ranges from 10,000–40,000. Detailed Nusselt number ratios are obtained using both a transient liquid crystal technique and a newly developed transient temperature sensitive paint (TSP) technique. Therefore, the TSP technique is not only validated against a baseline geometry (smooth channel), but it is also validated against a more established technique. Measurements indicate that the proposed V-shaped dimple design is a promising alternative to traditional ribs or hemispherical dimples. At lower Reynolds numbers, the V-shaped dimples display heat transfer and friction behavior similar to traditional dimples. However, as the Reynolds number increases to 30,000 and 40,000, secondary flows developed in the V-shaped concavities further enhance the heat transfer from the dimpled surface (similar to angled and V-shaped rib induced secondary flows). This additional enhancement is obtained with only a marginal increase in the pressure drop. Therefore, as the Reynolds number within the channel increases, the thermal performance also increases. While this trend has been confirmed with both the transient TSP and liquid crystal techniques, TSP is shown to have limited capabilities when acquiring highly resolved detailed heat transfer coefficient distributions.

Heat Transfer and Flowfield Measurements in the Leading Edge Region of a Stator Vane Endwall

1999 ◽  
Vol 121 (3) ◽  
pp. 558-568 ◽  
Author(s):  
M. B. Kang ◽  
A. Kohli ◽  
K. A. Thole
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Secondary Flows ◽  
Edge Region ◽  
Leading Edge Vortex ◽  
Stator Vane ◽  
Edge Vortex ◽  
The Mean

The leading edge region of a first-stage stator vane experiences high heat transfer rates, especially near the endwall, making it very important to get a better understanding of the formation of the leading edge vortex. In order to improve numerical predictions of the complex endwall flow, benchmark quality experimental data are required. To this purpose, this study documents the endwall heat transfer and static pressure coefficient distribution of a modern stator vane for two different exit Reynolds numbers (Reex = 6 × 105 and 1.2 × 106). In addition, laser-Doppler velocimeter measurements of all three components of the mean and fluctuating velocities are presented for a plane in the leading edge region. Results indicate that the endwall heat transfer, pressure distribution, and flowfield characteristics change with Reynolds number. The endwall pressure distributions show that lower pressure coefficients occur at higher Reynolds numbers due to secondary flows. The stronger secondary flows cause enhanced heat transfer near the trailing edge of the vane at the higher Reynolds number. On the other hand, the mean velocity, turbulent kinetic energy, and vorticity results indicate that leading edge vortex is stronger and more turbulent at the lower Reynolds number. The Reynolds number also has an effect on the location of the separation point, which moves closer to the stator vane at lower Reynolds numbers.

Effect of Viscous Dissipation on Heat Transfer Between Two Concentric Cylinders for Carreau Fluids

2010 ◽  
Author(s):  
Meriem Amoura ◽  
Noureddine Zeraibi
Keyword(s):  
Heat Transfer ◽  
Viscous Dissipation ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Mixed Finite Element ◽  
Outer Cylinder ◽  
Flow Characteristics ◽  
Weissenberg Number ◽  
Stress Strain Relation ◽  
Concentric Cylinders

In this paper, we present a numerical study of the flow characteristics and heat transfer mechanism of a non-Newtonian fluid in an annular space between two coaxial rotating cylinders taking into account the effect of viscous dissipation. The Carreau stress-strain relation was adopted to model the rheological fluid behavior. The problem is studied when the heated inner cylinder rotates around the common axis with constant angular velocity and the cooled outer cylinder is at the rest. The horizontal endplates are assumed adiabatic. In-house code which is based on a Galerkin mixed finite element is developed to obtain numerical solutions of the complete governing equations and associated boundary conditions and is validated with the results reported in the literature. It is found that five parameters can describe the problem under consideration, the Reynolds number (Re), the Grashof number (Gr), the index of structure (n), Weissenberg number (We) and the Eckert number (Ec). The velocity, temperature and stream function distributions and the local Nusselt number variations are drawn for different dimensionless groups.

Heat Transfer by Mixed Convection Opposing Laminar Flow From the Inside Surface of Uniformly Heated Inclined Circular Tube

2006 ◽  
Author(s):  
H. Mohammed ◽  
T. Yusaf
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Flow Direction ◽  
Convection Heat Transfer ◽  
Heat Transfer Process ◽  
Secondary Flows ◽  
Opposed Flow ◽  
Wide Range

This paper aims to investigate the effect of the flow pattern on the mixed convection heat transfer. A 28 thermocouples wire were installed along a 900mm copper tube to measure the temperature distribution. Three insulation layers of fiber glass, asbestos and gypsum were used to minimize to heat lost to the surrounding. A forced convection at the entrance region of a fully developed opposing laminar air flow was investigated to evaluate the flow direction effect on the Nusselt number. The investigation covered a wide range of Reynolds number from 410 to 1600 and heat flux varied from 63W/m2 to 1260W/m2, with different angles of tube inclination of 30°, 45°, 60°, and 90°. It was found that the surface temperature variation along the tube for opposed flow higher than the assisted flow but lower than the horizontal orientation. The Reynolds number has a significant effect on Nusselt number in opposed flow while the effect of Reynolds number was found to be small in the case of assisted flow. The Nusselt number values were lower for opposed flow than the assisted flow. The temperature profiles results have revealed that the secondary flows created by natural convection have a significant effect on the heat transfer process. The obtained average Nusselt number values were correlated by dimensionless groups as Log Nu against Log Ra/Re.

Bubble Injection to Enhance Heat Transfer in Microchannel Heat Sinks

2009 ◽  
Author(s):  
Amy Rachel Betz ◽  
Daniel Attinger
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Single Phase ◽  
Heat Fluxes ◽  
Heat Sinks ◽  
Segmented Flow ◽  
Liquid Cooling ◽  
Microchannel Heat Sinks ◽  
Convective Resistance ◽  
Parallel Microchannels

Liquid cooling is an efficient way to remove heat fluxes with magnitude of 1 to 10,000 W/cm2. One limitation of current single-phase microchannel heat sinks is the relatively low Nusselt number, because of laminar flow. In this work, we experimentally investigate how to enhance the Nusselt number in the laminar regime with the periodic injection of non-condensable bubbles in a water-filled array of microchannels in a segmented flow pattern. We designed a polycarbonate heat sink consisting of an array of parallel microchannels with a low ratio of heat to convective resistance, to facilitate the measurement of the Nusselt Number. Our heat transfer and pressure drop measurements are in good agreement with existing correlations, and show that the Nusselt number of a segmented flow is increased by more than a hundred percent over single-phase flow provided the mass velocity is within a given range.

Convection in a long box driven by heating and cooling on the horizontal boundaries

1996 ◽  
Vol 310 ◽  
pp. 61-87 ◽  
Author(s):  
J. J. Sturman ◽  
G. N. Ivey ◽  
J. R. Taylor
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Turbulent Flow ◽  
Flow Visualization ◽  
Turbulent Flows ◽  
Heat Fluxes ◽  
Temperature Fields ◽  
Glycerol Water ◽  
Heating And Cooling ◽  
Scaling Arguments

Convection driven by spatially variable heat transfer across the water surface is an important transport mechanism in many geophysical applications. This flow is modelled in a rectangular tank with an aspect ratio, H/L, of 0.1 (where H and L are the tank height and length, respectively). Heat fluxes are applied through horizontal copper plates of length 0.1 L located at the top of one end of the tank and at the bottom of the other end. Experimental flows have been forced with heating at the bottom of the tank and cooling at the top, which gives rise to unstable convection in the end regions. Using water and a glycerol/water mix as the experimental fluids, flow visualization studies and measurements of temperature, velocity and heat flux have been made. Flow visualization studies revealed that complex unsteady turbulent flows occupied the end regions, while cubic velocity profiles characterized the horizontal laminar flow in the interior of the tank. Simple scaling arguments were developed for steady-state velocity and temperature fields, which are in good agreement with the experimental data. In the current experiments the portion of the plates closest to the tank interior (and to the tank endwall in the case of the glycerol/water experiments) were occupied by laminar boundary layers, while the remainder of the plates were occupied by turbulent flow. An effective Rayleigh number Ra* was defined, based upon the portion of the plate occupied by turbulent flow, as was a corresponding modified Nusselt number Nu*. The heat transfer was well predicted by classical Rayleigh-Bénard scaling with the Nusselt number Nu* ∼ Ra*1/3. The range of Ra* was 4.3 × 105 ≤ Ra* ≤ 1.7 × 108. Scaling arguments predicted the triple occupancy of the plates by differing boundary layer regimes within the range of 105 ≤ Ra* ≤ 1014.

Heat transfer to pulsating turbulent flow in an abrupt pipe expansion

2003 ◽  
Vol 13 (3) ◽  
pp. 286-308 ◽  
Author(s):  
S.A.M. Said ◽  
M.A. Habib ◽  
M.O. Iqbal
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Prandtl Number ◽  
Turbulent Flow ◽  
Pulsation Frequency ◽  
Pipe Expansion ◽  
Cent Increase ◽  
The Mean ◽  
Mean Time

A numerical investigation aimed at understanding the flow and heat transfer characteristics of pulsating turbulent flow in an abrupt pipe expansion was carried out. The flow patterns are classified by four parameters; the Reynolds number, the Prandtl number, the abrupt expansion ratio and the pulsation frequency. The influence of these parameters on the flow was studied in the range 104<Re<5×104, 0.7<Pr<7.0, 0.2<d/D<0.6 and 5<f<35. It was found that the influence of pulsation on the mean time‐averaged Nusselt number is insignificant (around 10 per cent increase) for fluids having a Prandtl number less than unity. This effect is appreciable (around 30 per cent increase) for fluids having Prandtl number greater than unity. For all pulsation frequencies, the variation in the mean time‐averaged Nusselt number, maximum Nusselt number and its location with Reynolds number and diameter ratio exhibit similar characteristics to steady flows.

The Influence of Coolant Unsteadiness on Impingement Heat Transfer

2014 ◽  
Author(s):  
Victor J. Zimmer ◽  
James L. Rutledge ◽  
Chris Knieriem ◽  
Shichuan Ou
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Coolant Flow ◽  
Time Resolved ◽  
Average Mass ◽  
Flow Unsteadiness ◽  
Nusselt Numbers ◽  
Jet Cooling ◽  
The Mean ◽  
The Impact

Interest in impingement jet cooling and the associated convection phenomena has grown in the past few decades due in part to the desire for higher operating temperatures and reduced coolant flow in turbines. This study utilizes an array of 55 impingement jets to explore both steady and unsteady impingement flow conditions to evaluate the impact of the inherent unsteadiness present in engines compared to traditional steady experiments. Although unsteadiness occurs naturally in engines, intentional pulsation of coolant flow has also been proposed for flow control purposes, further underscoring the need for examination of the impact of pulsation on the heat transfer. Flow unsteadiness of varying amplitudes was induced at Strouhal numbers of magnitude 10−3 to 10−4. Infrared thermography was used to determine high spatial and temporal resolution Nusselt numbers. Time-resolved Nusselt number and mass flow characteristic waveforms were found to differ substantially as a function of the fluctuation amplitude relative to the mean. In some cases, transient coolant flow increases were associated with non-monotonic behavior in the time resolved Nusselt number. Although with certain configurations unsteady flow demonstrated time-averaged Nusselt numbers equivalent to steady flow with equivalent average mass flux, those with the greatest fluctuation in the amplitude of flow unsteadiness relative to the mean resulted in lower average Nusselt numbers.

scholarly journals An electrical detector of condensation in high-velocity steam

1942 ◽  
Vol 181 (985) ◽  
pp. 134-154 ◽  
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
High Velocity ◽  
Wilson Line ◽  
Pressure Rise ◽  
Short Length ◽  
Fine Wire ◽  
The Mean ◽  
The Wire ◽  
Griffith’S Theory

A new method has been developed for finding where condensation in a convergent-divergent steam nozzle commences. When a short length of fine wire, mounted on a rod, was traversed axially through the nozzle, it was found th at its resistance altered sharply at a certain point. The position of this point agreed closely with that of a small sudden pressure rise in the nozzle, which an earlier investigation had shown to indicate the beginning of condensation of the supersaturated steam. The mean temperature of the wire upstream from this point was found (as predicted by Griffith’s theory) to be nearly the same as that of the steam at entrance to the nozzle; it was greatly in excess of the temperature of the high-velocity steam passing the wire. The wire was heated electrically, and the Nusselt number of heat transfer to the steam was measured under the prevailing supersonic conditions. The Wilson line, showing the position of condensation on the Mollier diagram, was determined, and is compared with the line previously obtained for another nozzle of different shape.

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