Heat Transfer From a Rotating Disk to Fluids for a Wide Range of Prandtl Numbers Using the Asymptotic Model

2008 ◽  
Vol 130 (1) ◽  
Author(s):  
M. M. Awad
Keyword(s):  
Heat Transfer ◽  
Correlation Method ◽  
Rotating Disk ◽  
Compact Model ◽  
Asymptotic Model ◽  
Simple Method ◽  
Nusselt Numbers ◽  
Proposed Model ◽  
Wide Range ◽  
Prandtl Numbers

A simple method for calculating heat transfer from a rotating disk to fluids for a wide range of Prandtl numbers using asymptotic analysis is presented. Nusselt numbers for a heated rotating disk for different Prandtl numbers is expressed in terms of the asymptotic Nusselt numbers corresponding to a very small value of Prandtl numbers and Nusselt numbers corresponding to a very large value of Prandtl numbers. The proposed model uses a concave downward asymptotic correlation method to develop a robust compact model. Using the methods discussed by Churchill and Usagi (1972, “General Expression for the Correlation of Rates of Transfer and Other Phenomena,” AIChE J., 18(6), pp. 1121–1128), the fitting parameter in the proposed model can be determined at Prandtl numbers corresponding to the intersection of the two asymptotes.

Heat Transfer From a Wedge to Fluids at Any Prandtl Number Using the Asymptotic Model

2014 ◽  
Vol 136 (9) ◽  
Author(s):  
M. M. Awad
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Correlation Method ◽  
Independent Parameter ◽  
Asymptotic Model ◽  
Surface Shear Stress ◽  
Surface Shear ◽  
Wedge Flow ◽  
First Case ◽  
Proposed Model

Heat transfer from a wedge to fluids at any Prandtl number can be predicted using the asymptotic model. In the asymptotic model, the dependent parameter Nux/Rex1/2 has two asymptotes. The first asymptote is Nux/Rex1/2Pr→0 that corresponds to very small value of the independent parameter Pr. The second asymptote is Nux/Rex1/2Pr→∞, that corresponds to very large value of the independent parameter Pr. The proposed model uses a concave downward asymptotic correlation method to develop a robust compact model. The solution has two general cases. The first case is β ≠ −0.198838. The second case is the special case of separated wedge flow (β = −0.198838) where the surface shear stress is zero, but the heat transfer rate is not zero. The reason for this division is Nux/Rex1/2 ∼ Pr1/3 for Pr ⪢ 1 in the first case while Nux/Rex1/2 ∼ Pr1/4 for Pr ⪢ 1 in the second case. In the first case, there are only two common examples of the wedge flow in practice. The first common example is the flow over a flat plate at zero incidence with constant external velocity, known as Blasius flow and corresponds to β = 0. The second common example is the two-dimensional stagnation flow, known as Hiemenez flow and corresponds to β = 1 (wedge half-angle 90 deg). Using the methods discussed by Churchill and Usagi (1972, “General Expression for the Correlation of Rates of Transfer and Other Phenomena,” AIChE J., 18(6), pp. 1121–1128), the fitting parameter in the proposed model for both isothermal wedges and uniform-flux wedges can be determined.

Heat transfer from an air-cooled rotating disk

1974 ◽  
Vol 336 (1607) ◽  
pp. 453-473 ◽  
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Numerical Solutions ◽  
Rotating Disk ◽  
Experimental Results ◽  
Boundary Layer Equations ◽  
Nusselt Numbers ◽  
Wide Range ◽  
The Mean ◽  
Radial Outflow

This paper describes a combined theoretical and experimental investigation into the heat transfer from a disk rotating close to a stator with a radial outflow of coolant. Experimental results are obtained from a 762 mm diameter disk, rotating up to 4000 rev/min at axial clearances from 2 to 230 mm from a stator of the same diameter, with coolant flow rates up to 0.7 kg/s. Mean Nusselt numbers are presented for the free disk, the disk rotating close to an unshrouded stator with no coolant outflow, the disk rotating close to a shrouded and unshrouded stator with coolant outflow, and for the unshrouded stator itself. Numerical solutions of the turbulent boundary layer equations are in satisfactory agreement with the experimentally determined mean Nusselt numbers for the air-cooled disk over a wide range of conditions. At large ratios of mass flow rate/rotational speed the mean Nusselt numbers for the air-cooled disk are independent of rotation, and both the numerical solutions and experimental results become asymptotic to an approximate solution of the boundary layer equations.

Heat Transfer From a Wedge to Fluids at Any Prandtl Number Using the Asymptotic Model

2010 ◽  
Author(s):  
M. M. Awad
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Correlation Method ◽  
Independent Parameter ◽  
Asymptotic Model ◽  
Surface Shear Stress ◽  
Surface Shear ◽  
Wedge Flow ◽  
First Case ◽  
Proposed Model

Heat transfer from a wedge to fluids at any Prandtl number can be predicted using the asymptotic model. In the asymptotic model, the dependent parameter Nux/Rex1/2 has two asymptotes. The first asymptote is Nux/Rex1/2Pr→0 that corresponds to very small value of the independent parameter Pr. The second asymptote is Nux/Rex1/2Pr→∞ that corresponds to very large value of the independent parameter Pr. The proposed model uses a concave downward asymptotic correlation method to develop a robust compact model. The solution has two general cases. The first case is β ≠ −0.198838. The second case is the special case of separated wedge flow (β = −0.198838) where the surface shear stress is zero, but the heat transfer rate is not zero. The reason for this division is Nux/Rex1/2 ∼ Pr1/3 for Pr ≫ 1 in the first case while Nux/Rex1/2 ∼ Pr1/4 for Pr ≫ 1 in the second case. In the first case, there are only two common examples of the wedge flow in practice. The first common example is the flow over a flat plate at zero incidence with constant external velocity, known as Blasius flow and corresponds to β = 0. The second common example is the two-dimensional stagnation flow, known as Hiemenez flow and corresponds to β = 1 (wedge half-angle 90°). Using the methods discussed by Churchill and Usagi (1972, “General Expression for the Correlation of Rates of Transfer and Other Phenomena,” AIChE J., 18(6), pp. 1121–1128), the fitting parameter in the proposed model for both isothermal wedges and uniform-flux wedges can be determined.

Heat Transfer in a Rotating Cavity With a Stationary Stepped Casing

1999 ◽  
Vol 121 (2) ◽  
pp. 281-287 ◽  
Author(s):  
I. Mirzaee ◽  
P. Quinn ◽  
M. Wilson ◽  
J. M. Owen
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Flow Parameter ◽  
Rotating Disk ◽  
Nusselt Numbers ◽  
Rotating Cavity ◽  
Wide Range ◽  
Heated Disc ◽  
Turbine Disks ◽  
Cooling Air

In the system considered here, corotating “turbine” disks are cooled by air supplied at the periphery of the system. The system comprises two corotating disks, connected by a rotating cylindrical hub and shrouded by a stepped, stationary cylindrical outer casing. Cooling air enters the system through holes in the periphery of one disk, and leaves through the clearances between the outer casing and the disks. The paper describes a combined computational and experimental study of the heat transfer in the above-described system. In the experiments, one rotating disk is heated, the hub and outer casing are insulated, and the other disk is quasi-adiabatic. Thermocouples and fluxmeters attached to the heated disc enable the Nusselt numbers, Nu, to be determined for a wide range of rotational speeds and coolant flow rates. Computations are carried out using an axisymmetric elliptic solver incorporating the Launder–Sharma low-Reynolds-number k–ε turbulence model. The flow structure is shown to be complex and depends strongly on the so-called turbulent flow parameter, λT, which incorporates both rotational speed and flow rate. For a given value λT, the computations show that Nu increases as Reφ, the rotational Reynolds number, increases. Despite the complexity of the flow, the agreement between the computed and measured Nusselt numbers is reasonably good.

Heat Transfer in a “Cover-Plate” Preswirl Rotating-Disk System

1999 ◽  
Vol 121 (2) ◽  
pp. 249-256 ◽  
Author(s):  
R. Pilbrow ◽  
H. Karabay ◽  
M. Wilson ◽  
J. M. Owen
Keyword(s):  
Heat Transfer ◽  
Rotating Disk ◽  
Reynolds Numbers ◽  
Turbine Disk ◽  
Cover Plate ◽  
Blade Cooling ◽  
Nusselt Numbers ◽  
Flow And Heat Transfer ◽  
Cooling Air ◽  
Plate System

In most gas turbines, blade-cooling air is supplied from stationary preswirl nozzles that swirl the air in the direction of rotation of the turbine disk. In the “cover-plate” system, the preswirl nozzles are located radially inward of the blade-cooling holes in the disk, and the swirling airflows radially outward in the cavity between the disk and a cover-plate attached to it. In this combined computational and experimental paper, an axisymmetric elliptic solver, incorporating the Launder–Sharma and the Morse low-Reynolds-number k–ε turbulence models, is used to compute the flow and heat transfer. The computed Nusselt numbers for the heated “turbine disk” are compared with measured values obtained from a rotating-disk rig. Comparisons are presented, for a wide range of coolant flow rates, for rotational Reynolds numbers in the range 0.5 X 106 to 1.5 X 106, and for 0.9 < βp < 3.1, where βp is the preswirl ratio (or ratio of the tangential component of velocity of the cooling air at inlet to the system to that of the disk). Agreement between the computed and measured Nusselt numbers is reasonably good, particularly at the larger Reynolds numbers. A simplified numerical simulation is also conducted to show the effect of the swirl ratio and the other flow parameters on the flow and heat transfer in the cover-plate system.

Analytical Prediction of Heat Transfer in Tape Generated Swirl Flow

2017 ◽  
Author(s):  
R. J. Yadav ◽  
Sandeep Kore ◽  
V. N. Riabhole
Keyword(s):  
Heat Transfer ◽  
Circular Tube ◽  
Swirl Flow ◽  
Twisted Tape ◽  
Analytical Prediction ◽  
Transfer Coefficients ◽  
Numerical Predictions ◽  
Twisted Tapes ◽  
Wide Range ◽  
Prandtl Numbers

Heat transfer and pressure drop characteristics in a circular tube with twisted tapes have been investigated experimentally and numerically using different working fluids by many researchers for wide range of Reynolds number. The swirl was generated by tape inserts of various twist ratios. The various twist ratios are considered Many researchers formed generalized correlations to predict friction factors and convective heat transfer coefficients with twisted tapes in a tube for a wide range of Reynolds numbers and Prandtl numbers. Satisfactory agreement was obtained between the present correlations and the data of others validate the proposed correlations. The experimental or numerical predictions were compared with earlier correlations revealing good agreement between them. From the literature review it is observed that most studies are mainly focused on the heat transfer enhancement using twisted tape by experimental or numerical solution. An investigation with analytical approach is rarely reported. Therefore, the main aim of the present work is to form a correlation from theoretical approach for Nusselt number for circular tube with twisted tape. Application of dimensional analysis to heat transfer in tape generated swirl flow is carried out.

A Short Method to Compute Nusselt Numbers in Rectangular and Annular Channels With any Ratio of Constant Heat Rate

2010 ◽  
Author(s):  
Alexandre Malon ◽  
Thierry Muller
Keyword(s):  
Differential Equation ◽  
Nusselt Number ◽  
Heat Rate ◽  
Equation System ◽  
Radius Ratio ◽  
Differential Equation System ◽  
Simple Method ◽  
Nusselt Numbers ◽  
Annular Channels ◽  
Wide Range

An analytic investigation of the thermal exchanges in channels is conducted with the prospect of building a simple method to determine the Nusselt number in steady, laminar or turbulent and monodimensional flow through rectangular and annular spaces with any ratio of constant and uniform heat rate. The study of the laminar case leads to explicit laws for the Nusselt number while the turbulent case is solved using a Reichardt turbulent viscosity model resulting in easy to solve one-dimensional ordinary differential equation system. This differential equation system is solved using a Matlab based boundary value problems solver (bvp4c). A wide range of Reynolds, Prandtl and radius ratio is explored with the prospect of building correlation laws allowing the computing of Nusselt numbers for any radius ratio. Those correlations are in good agreement with the results obtained by W.M. Kays and E.Y. Leung in 1963 [1]. They conduced a similar analysis but with an experimental basis, they explored a greater range of Prandtl but only a few discreet radius ratio. The correlations are also compared with a CFD analysis made on a case extracted from the Re´acteur Jules Horowitz.

Effect of 3D Diffusion Over Vertical Thin Rectangular Geometries in Natural Convection Heat Transfer

2006 ◽  
Author(s):  
Mustafa Gursoy ◽  
Mehmet Arik ◽  
Tunc Icoz ◽  
Michael Yovanovich ◽  
Theodorian Borca-Tasciuc
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Fluid Motion ◽  
Heat Removal ◽  
Air Entrainment ◽  
Published Data ◽  
Diffusion Term ◽  
Nusselt Numbers ◽  
Wide Range ◽  
Rayleigh Numbers

Natural convection over vertical plates is a very well known problem in heat transfer. There are many available correlations to predict Nusselt numbers for a wide range of Rayleigh numbers. These benchmark studies on natural convection for vertical plates were conducted on rather large surfaces leading to Rayleigh numbers in the range of 0.1 to 109. In natural convection the sole driving force of fluid motion is the change in fluid density, when the diffusive limit is small compared to convective heat transfer. However, conduction to air, as well as air entrainment from sides also contributes to the heat removal from heater surfaces. An experimental study has been carried out with small and large heaters compared to published data for 2×103&lt;Ra&lt;4×107. Square surfaces of 12.5 and 25.4 mm, and rectangular heaters of sizes 25.4×101.6 and 25.4×203.2 mm were tested for a range of heat inputs such that the surface temperatures are controlled between 30 °C and 80 °C. It is found that published correlations underpredict the Nusselt numbers as much as 20%. It is observed that widely known correlations underpredict the experimental values since the 3D conduction and side air drifts on heat transfer are not accounted for in these correlations. However, the cuboid model which includes the 3D diffusion term showed much better agreement with the experimental results.

Thermal–Hydraulic Performance Analysis of a Convergent Double Pipe Heat Exchanger

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Ahmed T. Al-Sammarraie ◽  
Kambiz Vafai
Keyword(s):  
Heat Transfer ◽  
Heat Exchanger ◽  
Hydraulic Performance ◽  
Operating Conditions ◽  
Contraction Ratio ◽  
Wide Range ◽  
Prandtl Numbers ◽  
Double Pipe ◽  
The Impact ◽  
Pipe Heat

The present investigation proposes an innovative convergent double pipe heat exchanger (C-DPHE). A two-dimensional (2D) axisymmetric heat transfer model with counterflow is employed to analyze the thermal and hydraulic performance of this configuration numerically. The impact of convergence in the flow direction, using a wide range of contraction ratio (Cr), is explored. The effect of Reynolds and Prandtl numbers on the flow and heat transfer is addressed, as well. The model results were validated with available data from the literature, and an excellent agreement has been confirmed. In general, the findings of the present study indicate that increasing the contraction ratio increases heat transfer and pressure drop in the C-DPHE. Moreover, this configuration has a prominent and sustainable performance, compared to a conventional double pipe heat exchanger (DPHE), with an enhancement in heat transfer rate up to 32% and performance factor (PF) higher than one. Another appealing merit for the C-DPHE is that it is quite effective and functional at low Reynolds and high Prandtl numbers, respectively, since no high-operating pumping power is required. Further, the optimal operating conditions can be established utilizing the comprehensive information provided in this work.

Effect of Circumferentially Nonuniform Heating on Laminar Combined Convection in a Horizontal Tube

1978 ◽  
Vol 100 (1) ◽  
pp. 63-70 ◽  
Author(s):  
S. V. Patankar ◽  
S. Ramadhyani ◽  
E. M. Sparrow
Keyword(s):  
Heat Transfer ◽  
Secondary Flow ◽  
Forced Convection ◽  
Horizontal Tube ◽  
Nonuniform Heating ◽  
Convection Flow ◽  
Nusselt Numbers ◽  
Wide Range ◽  
Bottom Heating ◽  
Over The Top

An analytical study has been made of how the circumferential distribution of the wall heat flux affects the forced/natural convection flow and heat transfer in a horizontal tube. Two heating conditions were investigated, one in which the tube was uniformly heated over the top half and insulated over the bottom, and the other in which the heated and insulated portions were reversed. The results were obtained numerically for a wide range of the governing buoyancy parameter and for Prandtl numbers of 0.7 and 5. It was found that bottom heating gives rise to a vigorous buoyancy-induced secondary flow, with the result that the average Nusselt numbers are much higher than those for pure forced convection, while the local Nusselt numbers are nearly circumferentially uniform. A less vigorous secondary flow is induced in the case of top heating because of temperature stratification, with average Nusselt numbers that are substantially lower than those for bottom heating and with large circumferential variations of the local Nusselt number. The friction factor is also increased by the secondary flow, but much less than the average heat transfer coefficient. It was also demonstrated that the buoyancy effects are governed solely by a modified Grashof number, without regard for the Reynolds number of the forced convection flow.

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