Nonsimilar Boundary-Layer Heat Transfer of a Rotating Cone in Forced Flow

1967 ◽  
Vol 89 (2) ◽  
pp. 139-145 ◽  
Author(s):  
J. C. Y. Koh ◽  
J. F. Price
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Numerical Solutions ◽  
Cone Angle ◽  
Rotating Disk ◽  
Forced Flow ◽  
Degenerate Problem ◽  
Prandtl Numbers ◽  
Half Cone ◽  
Half Cone Angle

The nonsimilar boundary-layer flow and heat transfer of a cone rotating in a forced-flow field are investigated. Numerical solutions are shown for a half-cone angle of 53.5 deg with parameters (vw/ue)2 ranging from 0 to 20, and with Prandtl numbers from 0.2 to 10. With a half-cone angle of 90 deg (so that one has a rotating disk), the degenerate problem is solved in the same manner.

Heat Transfer in the Laminar Boundary Layer Over an Impulsively Started Flat Plate

1975 ◽  
Vol 97 (3) ◽  
pp. 482-484 ◽  
Author(s):  
C. B. Watkins
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Laminar Flow ◽  
Flat Plate ◽  
Constant Temperature ◽  
Laminar Boundary Layer ◽  
Temperature Difference ◽  
Thermal Boundary Layer ◽  
Numerical Solutions ◽  
Prandtl Numbers

Numerical solutions are described for the unsteady thermal boundary layer in incompressible laminar flow over a semi-infinite flat plate set impulsively into motion, with the simultaneous imposition of a constant temperature difference between the plate and the fluid. Results are presented for several Prandtl numbers.

Mathematical Modelling of Hydromagnetic Convection from a Rotating Sphere with Impulsive Motion and Buoyancy Effects

2006 ◽  
Vol 11 (3) ◽  
pp. 227-245 ◽  
Author(s):  
O. Anwar Bég ◽  
H. S. Takhar ◽  
G. Nath ◽  
A. J. Chamkha
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Boundary Layer ◽  
Chemical Engineering ◽  
Numerical Solutions ◽  
Forced Flow ◽  
Impulsive Motion ◽  
Rotating Sphere ◽  
Linear Partial Differential Equations ◽  
Layer Flow

The convective heat transfer on a rotating sphere in the presence of magnetic field, buoyancy forces and impulsive motion is examined theoretically and numerically in this paper. We apply a boundary layer model comprising the balance equations for x and y direction translational momentum and heat transfer, and solve these coupled non-linear partial differential equations using Blottner’s finite-difference method [1]. The numerical solutions are benchmarked with the earlier study by Lee [2] on laminar boundary layer flow over rotating bodies in forced flow and found to be in excellent agreement. The effects of magnetic field, buoyancy parameter, Prandtl number and thermal conductivity parameter on translational velocities and temperature and other variables (shear stress etc) are presented graphically and discussed at length. The problem finds applications in chemical engineering technologies, aerodynamics and planetary astrophysics.

Laminar Boundary Layer Transfer over Rotating Bodies in Forced Flow

1978 ◽  
Vol 100 (3) ◽  
pp. 496-502 ◽  
Author(s):  
Min-Hsiun Lee ◽  
D. R. Jeng ◽  
K. J. De Witt
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Experimental Studies ◽  
Rotating Disk ◽  
Rotation Parameter ◽  
Forced Flow ◽  
Rotating Sphere ◽  
Prandtl Numbers ◽  
Special Case

A procedure is described for the calculation of momentum and heat transfer rates through laminar boundary layers over rotating axisymmetric bodies in forced flow. By applying appropriate coordinate transformations and Merk’s type of series, the governing momentum equations can be expressed as a set of coupled ordinary differential equations that depend on a wedge parameter and on a rotation parameter. For the energy equation, a set of ordinary differential equations is obtained which depend explicitly on the Prandtl number and implicitly on the aforementioned parameters. These equations are numerically integrated for a range of parameter values for the special case of a rotating sphere, and the local friction coefficient and the local Nusselt number are presented for values of the rotation parameter B = 1, 4, and 10 with Prandtl numbers of 1, 10, and 100. These results are then compared with previous theoretical results. It is also shown how the flow and heat transfer characteristics for a rotating disk can be readily obtained as a special case from the formulation for the rotating sphere. The disk results are also compared with previous theoretical and experimental studies.

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.

Numerical Investigation of the Effect of Capsule Half-Cone Angle on a Supersonic Parachute System

2016 ◽  
Vol 29 (4) ◽  
pp. 06016001 ◽  
Author(s):  
Xiao-Peng Xue ◽  
Yusuke Nishiyama ◽  
Yoshiaki Nakamura ◽  
Koichi Mori ◽  
Chih-Yung Wen
Keyword(s):  
Numerical Investigation ◽  
Cone Angle ◽  
Parachute System ◽  
Half Cone ◽  
Half Cone Angle

Free-convection effects in the boundary layer along a vertically stretching flat surface

1992 ◽  
Vol 70 (12) ◽  
pp. 1253-1260 ◽  
Author(s):  
John E. Daskalakis
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Free Convection ◽  
Skin Friction ◽  
Flat Surface ◽  
Relaxation Method ◽  
Boussinesq Approximation ◽  
Axial Coordinate ◽  
Prandtl Numbers ◽  
Energy Equations

We assess the effects of free convection on the boundary layer formed along a flat surface stretching vertically in a quiescent fluid. The flow is laminar and incompressible, the buoyancy forces conform to the Boussinesq approximation and the surface temperature is variable. The two-point boundary value problem of the coupled momentum and energy equations is solved using a simple and accurate relaxation method that provides the general nonsimilar solution to the flow. The effect of free-convection currents on velocity and temperature profiles, skin friction, and heat transfer is studied by varying the flow Grashof and Prandtl numbers. Zero shear stress and heat-transfer rate are predicted at some axial coordinate on a surface with decreasing wall temperature. Also the skin friction is markedly modified by the buoyancy while the heat transfer at the surface is correspondingly only moderately influenced.

Comparison of Two Complete Solutions in an Axisymmetric Extrusion With Experiment

1969 ◽  
Vol 91 (3) ◽  
pp. 543-548 ◽  
Author(s):  
A. H. Shabaik ◽  
E. G. Thomsen
Keyword(s):  
Strain Rate ◽  
Effective Strain ◽  
Cone Angle ◽  
Low Friction ◽  
First Approximation ◽  
Strain And Strain Rate ◽  
Conical Die ◽  
Stream Lines ◽  
Half Cone ◽  
Half Cone Angle

An upper-bound and a potential solution to a forward extrusion problem were compared with experimental results obtained by the visioplasticity method. The process consisted of extruding a 2-in-dia billet of preforged lead through a conical die having a half-cone angle of 45 deg under the condition of relatively low friction. The comparison was made for steady state stream lines, velocities, strain rate components, effective strain and strain rate, grid distortion, and stress distribution. It was found that the curves were generally of similar shape and that some differences existed in magnitude only. It is suggested that the theoretical solutions can be used to advantage to a first approximation in predicting all important variables.

scholarly journals Development technique for deep drawing without blank holder to produce circular cup of brass alloy

2015 ◽  
Vol 4 (1) ◽  
pp. 187 ◽  
Author(s):  
Ali Hassan Saleh ◽  
Ammer Khalaf Ali
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Deep Drawing ◽  
Cone Angle ◽  
Element Model ◽  
Drawing Ratio ◽  
Clearance Ratio ◽  
Blank Holder ◽  
Half Cone ◽  
Half Cone Angle

Of this technique compared to the conventional deep drawing is that the circular cup can be carried out in single action press with limit In this paper a new mechanism for deep drawing was proposed to produce circular cup from thin plate without blank holder. In this technique the die assembly includes punch, die and die-punch. A 2D axisymmetric finite element model was built using DEFORM software. Effect of die geometry (half- cone angle) on maximum load, thickness distribution, strain distribution and effect of clearance ratio between punch and (die-punch) on the wrinkling of the cup were investigated. Three half-cone angles of die (15o, 30o and 45o) were used for forming sheet metal of brass (CuZn37) which had initial thickness of (1mm) at four clearance ratio (c/t) for die of 30o half-cone angle. Finite element model results showed good agreement with experimental results. Die of 30o half-cone angle with clearance ratio (c/t) of 0.9 gave the best product without wrinkling. The main advantage drawing ratio (LDR) of 1.86 and blank diameter to blank thickness ratio (d/t) < 86.

scholarly journals Experimental Investigation of the Performance and Spray Characteristics of a Supersonic Two-Phase Flow Ejector with Different Structures

Energies ◽  
2020 ◽  
Vol 13 (5) ◽  
pp. 1166 ◽  
Author(s):  
Shizhen Li ◽  
Wei Li ◽  
Yanjun Liu ◽  
Chen Ji ◽  
Jingzhi Zhang
Keyword(s):  
High Speed ◽  
Two Phase Flow ◽  
Fire Suppression ◽  
Cone Angle ◽  
Water Mist ◽  
Pulsation Period ◽  
Phase Flow ◽  
Two Phase ◽  
Half Cone ◽  
Half Cone Angle

A two-phase flow ejector is an important part of a water mist fire suppression system, and these devices have become a popular research topic in recent years. This paper proposes a supersonic ejector that aims to improve the efficiency of water mist fire suppression systems. The effects of ejector geometric parameters on the entrainment ratio (ER) were explored. The effects of primary flow pressure (PP) on the mixing process and flow phenomena were studied by a high-speed camera. The experimental results show that the ER first increases and then decreases with increasing PP. ER increases with increasing ejector area ratio (AR). The PP corresponding to the maximum ER of ejectors with a different nozzle exit position (NXP) is 3.6 bar. The ejector with an NXP of +1 and AR of 6 demonstrate the best performance, and the ER of this ejector reaches 36.29. The spray half-cone angle of the ejector increases with increasing ER, reaching a maximum value of 7.07°. The unstable atomization half-cone angle is mainly due to a two-phase flow pulsating phenomenon. The pulsation period is 10 ms. In the present study, a general rule that provides a reference for ejector design and selection was obtained through experiments.

Sampling of High-Quality Wet Steam from Steam Mains Operating at 11·4 Bar Pressure

1973 ◽  
Vol 187 (1) ◽  
pp. 381-393 ◽  
Author(s):  
D. J. Ryley ◽  
M. J. Holmes
Keyword(s):  
Static Pressure ◽  
Water Mass ◽  
Cone Angle ◽  
Wet Steam ◽  
High Quality ◽  
Flow Rates ◽  
Further Development ◽  
Half Cone ◽  
Steam Main ◽  
Half Cone Angle

A venturi device was employed to strip and entrain liquid from the wall of a 3 in (7·5 cm) diameter steam main prior to isokinetic sampling. By injecting heated water into dry steam the wetness fraction was controlled between 1 and 5 per cent. Venturi convergence half-cone angles of 20, 30, 40 and 50° were employed and steam flow rates varied from 360–730 kg/h (800–1600 1b/h). Observations were made of the distribution through the test section of static pressure, recovered temperature and film thickness (for pressure 3·8 bar (55 1b/in2 absolute) only). Sampling across a diameter showed that under the most advantageous conditions the ratio, aggregate mass of entrained water: mass of injected water did not exceed 23 per cent. The optimum venturi half-cone angle lay between 40 and 50°. While capable of further development, the stripping-sampling principle seems unlikely to lead to significant improvements in wet steam sampling for quality.

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