A remark on the construction of axes of an intersection of a plane and a quadratic cone surface

AbstractThe bidirectional reflectance distribution function (BRDF) that describes an angle-resolved distribution of surface reflectance is available for characterizing surface properties of a material. A one-shot BRDF imaging system can capture an in-plane color mapping of light direction extracted from a surface BRDF distribution. A surface roughness identification method is then proposed here using the imaging system. A difference between surface properties of a matt paper and a glossy paper is experimentally shown to be detected using the method. A surface reconstruction method of an axisymmetric micro-object using the imaging system is also proposed here. The imaging system experimentally shows that it can reconstruct an axisymmetric aluminium cone surface with a height of 37 μm.

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The effect of radiation on free convective flow and mass transfer past a vertical isothermal cone surface with chemical reaction in the presence of a transverse magnetic field

Canadian Journal of Physics ◽

10.1139/p04-009 ◽

2004 ◽

Vol 82 (6) ◽

pp. 447-458 ◽

Cited By ~ 19

Author(s):

A A Afify

Keyword(s):

Magnetic Field ◽

Mass Transfer ◽

Boundary Conditions ◽

Chemical Reaction ◽

Transverse Magnetic Field ◽

Convective Flow ◽

Transverse Magnetic ◽

Skin Friction Coefficient ◽

Free Convective Flow ◽

Cone Surface

The effects of radiation and chemical reactions, in the presence of a transverse magnetic field, on free convective flow and mass transfer of an optically dense viscous, incompressible, and electrically conducting fluid past a vertical isothermal cone surface are investigated. The nonlinear boundary-layer equations with the boundary conditions are transferred by a similarity transformation into a system of nonlinear ordinary differential equations with the appropriate boundary conditions. Furthermore, the similarity equations are solved numerically by using a fourth-order RungeKutta scheme with the shooting method. Numerical results for the skin-friction coefficient, the local Nusselt number, the local Sherwood number are given; as well, the velocity, temperature, and concentration profiles are presented for a Prandtl number of 0.7, the chemical-reaction parameter, the order of the reaction, the radiation parameter, the Schmidt number, the magnetic parameter, and the surface temperature parameter. PACS No.: 47.70.Fw

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New Geometry of Generating Spiral Bevel Gear

Volume 7: 10th International Power Transmission and Gearing Conference ◽

10.1115/detc2007-34485 ◽

2007 ◽

Author(s):

Kaihong Zhou ◽

Jinyuan Tang ◽

Tao Zeng

Keyword(s):

Gear Tooth ◽

Previous Method ◽

Bevel Gear ◽

Tooth Surface ◽

Spiral Bevel Gear ◽

Surface Geometry ◽

Numerical Examples ◽

Cone Surface ◽

Spiral Bevel ◽

Involute Curve

New geometry of generating spiral bevel gear is proposed. The key idea of the new proposed geometry is that the gear tooth surface geometry can be investigated in a developed curved surface based on the planar engagement principle. It is proved that the profile curve on the back of generating cone surface is a conical involute curve. The equations of generated gear tooth surface are achieved by the conical involute curve sweeping along the tooth trace of gear. The obtained equations are explicit and independent of the machine-tool settings. This differs from previous studies. The developed theory is illustrated with numerical examples to compare with the previous method, the comparison approves that the method is possible in this way. The new method indicates that there are new solutions to the design the production of spiral bevel gear.

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Turbulent film condensation on an isothermal cone surface

Heat and Mass Transfer ◽

10.1007/s00231-005-0638-5 ◽

2005 ◽

Vol 42 (5) ◽

pp. 378-386

Author(s):

Hai-Ping Hu ◽

Cha’o-Kuang Chen

Keyword(s):

Film Condensation ◽

Cone Surface

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A Design Model of Target-Hitting Trajectory Drilled Into the Reservoir with Elliptical Truncated Cone Surface

Chemistry and Technology of Fuels and Oils ◽

10.1007/s10553-021-01231-0 ◽

2021 ◽

Author(s):

Yue Gu ◽

Deli Gao ◽

Jin Yang

Keyword(s):

Design Model ◽

Truncated Cone ◽

Cone Surface

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Nanomechanical Concepts in Magnetically Guided Systems to Investigate the Magnetic Dipole Effect on Ferromagnetic Flow Past a Vertical Cone Surface

Coatings ◽

10.3390/coatings11091129 ◽

2021 ◽

Vol 11 (9) ◽

pp. 1129

Author(s):

Auwalu Hamisu Usman ◽

Zahir Shah ◽

Poom Kumam ◽

Waris Khan ◽

Usa Wannasingha Humphries

Keyword(s):

Magnetic Dipole ◽

Chemical Reaction ◽

Darcy Law ◽

Nonlinear Thermal Radiation ◽

Vertical Cone ◽

Temperature Changes ◽

Analysis Technique ◽

Homotopy Analysis ◽

Magnetic Nanomaterial ◽

Cone Surface

Because of the floating magnetic nanomaterial, ferrofluids have magneto-viscous properties, enabling controllable temperature changes as well as nano-structured fluid characteristics. The study’s purpose is to evolve and solve a theoretical model of bioconvection nanofluid flow with a magnetic dipole effect in the presence of Curie temperature and using the Forchheimer-extended Darcy law subjected to a vertical cone surface. The model also includes the nonlinear thermal radiation, heat suction/injection, viscous dissipation, and chemical reaction effects. The developed model problem is transformed into nonlinear ordinary differentials, which have been solved using the homotopy analysis technique. In this problem, the behavior of function profiles are graphically depicted and explained for a variety of key parameters. For a given set of parameters, tables representthe expected numerical values and behaviors of physical quantities. The nanofluid velocity decreases as the ferrohydrodynamic, local inertia, and porosity parameters increase and decrease when the bioconvection Rayleigh number increases. Many key parameters improved the thermal boundary layer and temperature. The concentration is low when the chemical reaction parameter and Schmidt number rises. Furthermore, as the bioconvection constant, Peclet and Lewis numbers rise, so does the density of motile microorganisms.

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A New Method of Constructing Tooth Surface for Logarithmic Spiral Bevel Gear

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.129-131.235 ◽

2010 ◽

Vol 129-131 ◽

pp. 235-240 ◽

Cited By ~ 2

Author(s):

Qiang Li ◽

Zi Liang Wei ◽

Hong Bo Yan ◽

Hai Yan Hu

Keyword(s):

Logarithmic Spiral ◽

Strength Distribution ◽

Bevel Gear ◽

Tooth Surface ◽

Spiral Bevel Gear ◽

Surface Equation ◽

Complex Curves ◽

Logarithmic Spirals ◽

Cone Surface ◽

Spiral Bevel

For a new type of bevel gear—logarithmic spiral bevel gear, establish its tooth direction curves and the mathematical model of tooth surface equation. With CAD software platform which can intuitive understanding of complex curves and combined with conical logarithmic spiral parameter equation build the logarithmic spiral on cone surface. Then array logarithmic spiral to make them evenly distributed in the cone surface, without any interference and to meet the strength distribution on both ends of circular truncated cone equally. Use two logarithmic spirals from different starpoint as tooth direction curves of lift and right tooth surface. Finally, use space geometric knowledge to build tooth surface equation by tooth direction curves and tooth profile curves.

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