Numerical solution of the curved rigid line problem in an infinite plate

Summary This paper deals with the problem of evaluating the stress singularity coefficients at the tips of a rigid line in an infinite plate. If the traction difference between the upper and lower borders of the rigid line is taken as an unknown function and the displacement of the curved rigid line as the right-hand term of the integral equation, then a new integral equation for the curved rigid line problem is obtained which is presented in this paper. The newly obtained integral equation has a logarithmic singular kernel. To solve the integral equation an interpolation equation for the traction difference functions (the undetermined functions in the integral equation) is proposed. A numerical examination is carried out to demonstrate the efficiency of the proposed technique. Also two numerical examples are given in this paper.

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Numerische lösung des problems einer gekrümmten linie als starrer einschlu\ in einer unendlichen platte

Übersicht Vorgeführt wird die Bestimmung von Spannungssingularitätsfaktoren an den Enden einer starren Kurve in einer unendlichen Platte. Wenn die Spannungsdifferenz an beiden Seiten der starren Linie als unbekannte Funktion und die Verschiebung dieser Linie als rechte Seite der Integralgleichung gewählt werden, erhält man eine neue Integralgleichung, die hier vorgestellt wird. Diese enthält einen logarithmisch singulären Kern. Um sie zu lösen, wird eine Interpolationsfunktion für die unbekannten Funktionen der Spannungsdifferenzen vorgeschlagen und ein numerischer Test zur Demonstration der Leistungsfähigkeit der Methode durchgeführt. Zwei numerische Beispiele werden vorgestellt.

     

An experimental technique for measuringtransient natural/forced convective heatfluxes in a vertical channel

A series of systematic experiments for measuring transient natural andforced convected heat fluxes in a one-sided heated vertical channel have beenconducted. The total heat input in transient natural and forced experiments iscomposed of four kinds modes: radiative heat loss, conductiveheat lossm, thermal capacity of the plate, and convective heat transfer in thetest channel. In the transient periods, the generalized correlations for estimatingtransient convective heat flux are proposed in natural and forced convectionexperiments. By using the proposed q_c^″ distributions, satisfactory agreementsare achieved between the transient Nu_x predictions and experimentaldata.     

Radiative melting of a horizontal clear ice layer

In this paper the horizontal layer of clear ice sticking to the substrate is melted by comparatively short wave radiation similar to solar radiation for the purpose of removing ice from the surface of the material subject to atmospheric icing. The radiating source used for melting is 300 wattages halogen lamps whose color temperature is 3200K at 100 voltages. From the present investigation, a typical phenomenon of backmelting is observed clearly and it can be found that the predicted results including the melting rate of upper and lower layers which are melted by radiant energy impinged on or penetrated the ice layer are in good agreement with the experimental results.

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Aufschmelzen einer waagerechten Klareisschicht durch Strahlung

Zusammenfassung Eine waagerechte Klareisschicht, die auf einer Unterlage aufgefroren war, wurde durch kurzwellige Strahlung, Ähnlich der Sonnenstrahlung, zum Schmelzen gebracht, um die Entfernung von Eis nach atmosphÄrischer Vereisung zu untersuchen. Die Strahlungsquelle war eine 300 Watt-Halogenlampe mit einer Farbtemperatur von 3200 Kelvin bei 100 Volt. Als typische Erscheinung wurde ein Rückseiten-Schmelzen gefunden, im übrigen sind die vorausberechneten Schmelzraten an der Ober- und der Unterseite durch aufgenommene oder durchgelassene Strahlungsenergie in guter übereinstimmung mit den Messungen.

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Nomenclature a_v monochromatic absorption coefficient - A transmission (= q _r ⁺ {h_i}/q_ro) - c_p specific heat - E_bv monochromatic emissive power - h_D mass transfer coefficient - h_i initial thickness of ice layer - h_m thickness of substrate - L_i latent heat of melting - L_w latent heat of evaporation or condensation - heat flux absorbed at surface of substrate - q_r0 radiant heat flux impinged onto ice or free surface - q _r ⁺ {y} forward radiant heat flux - q _r ^– {y} backward radiant heat flux - S₁ thickness of upper melt layer - S₂ thickness of lower melt layer - S'₂ distance from free surface to bottom surface of ice layer - t time - T temperature - T₁ temperature of air-water or air-ice interface - T₂ temperature of substrate surface - T₃ temperature of back side surface of substrate - T_b temperature of radiating source - T_i temperature in ice layer - T_w1 temperature in upper melt layer - T_w2 temperature in lower melt layer - T environmental temperature - W_w saturated vapor concentration at free surface - W_t8 vapor concentration at environment - y distance from free or ice surface - y grid size of water or ice - y_m grid size of substrate Greek symbols heat transfer coefficient - spectral absorptivity - _t total absorptivity - _i thermal diffusivity of ice - _m thermal diffusivity of substrate - _w thermal diffusivity of water - _i thermal conductivity of ice - _m thermal conductivity of substrate - _w thermal conductivity of water - wavelength - _av densitiy of air-vapor mixture - _i density of ice - Stefan-Boltzman constant     

FREE VIBRATION OF ANISOTROPIC RECTANGULAR PLATES BY GENERAL ANALYTICAL METHOD

According to the differential equation for transverse displacement function of anisotropic rectangular thin plates in free vibration, a general analytical solution is established. This general solution, composed of the composite solutions of trigonometric function and hyperbolic function, can satisfy the problem of arbitrary boundary conditions along four edges. The algebraic polynomial with double sine series solutions can also satisfy the problem of boundary conditions at four corners. Consequently, this general solution can be used to solve the vibration problem of anisotropic rectangular plates with arbitrary boundaries accurately. The integral constants can be determined by boundary conditions of four edges and four corners. Each natural frequency and vibration mode can be solved by the determinate of coefficient matrix from the homogeneous linear algebraic equations equal to zero. For example, a composite symmetric angle ply laminated plate with four edges clamped has been calculated and discussed.     

Upper limit of enhancement of boiling heat transfer in a narrow vertical rectangular channel due to passing bubbles

An experimental study has been made of saturated boiling heat transfer for water and R113 in a narrow vertical rectangular channel (2 mm space, 20 mm wide, and 200 mm long) at atmospheric pressure, in which the vertical heated surface (10 mm long and 20 mm wide) is located on one side at a position of 150 mm from its entrance and bubbles are forcibly passed through it at a designated period from 0.33 to 1.0 sec. The experiment shows that the heat transfer coefficients are increased by the bubble passing through the heated surface for the value of thermal diffusivity,a, times period, T₀, of the passing bubbles above about 6×10^–9 m² (a T ₀>6×10^–9 m²) while fora T ₀< 6×10^–9 m², the heat transfer coefficients become independent of the period and the effectiveness of the enhancement of the heat transfer owing to the passing bubble disappears.

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Die obere Grenze der Verbesserung des Wärmeübergangs beim Sieden in einem vertikalen, rechteckigen Kanal infolge von aufsteigenden Blasen

Zusammenfassung Es wurden Experimente über den Wärmeübergang beim Sättigungssieden mit Wasser und R113 in einem engen, vertikalen, rechteckigen Kanal (2 mm Abstand, 20 mm Breite und 200 mm Länge) bei Umgebungsdruck durchgeführt, wobei die vertikale, beheizte Oberfläche (10 mm lang und 20 mm breit) auf der einen Seite in einem Abstand von 150 mm vom Eintritt angeordnet ist und die Blasen zwangsweise durch den Kanal sich mit einem Periodenabstand von 0,033 bis 1,0 s bewegen. Das Experiment zeigt, daß die Wärmeübergangskoeffizienten durch das Vorbeistreichen der Blasen an der beheizten Oberfläche verbessert werden, wenn das Produkt aus Temperaturleitfähigkeit,a, mal der Periode, T₀, der vorbeistreichenden Blasen größer als 6×10^–9 m² liegt, während unterhalb dieses Wertes der Wärmeübergangskoeffizient unabhängig von der Blasenperiode ist und die Effektivität der Wärmeübergangsverbesserung infolge der Blasenströmung verschwindet.

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Nomenclature a thermal diffusivity of liquid - ¯h time-averaged heat transfer coefficient - q _w heat flux at wall - T ₀ period of passing bubble - T _w(t) temperature of heated surface - T _w amplitude of heated surface temperature Greek symbols thermal conductivity - thickness of liquid film     

Two phase boundary layers in laminar film boiling

The laminar film boiling is analyzed by means of an integral procedure. The method treats the film boiling as a two phase boundary layer problem; thereby the effect of the interfacial shear on the heat transfer rate can be investigated. The problem is attacked by simultaneously solving the vapor and liquid boundary layer equations. An extensive comparison of the predicted results with the exact solutions substantiates the validity of the present integral procedure. Even the details of the velocity and temperature profiles turn out to be in close agreement with the exact solutions.     

FIXED POINTS OF INCREASING OPERATORS IN ORDERED SPACE WITH APPLICATIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｖｅｓｔｉｇａｔｉｎｇｔｈｅｆｏｌｌｏｗｉｎｇｂｏｕｎｄａｒｙｐｒｏｂｌｅｍｉｎｏｒｄｉｎａｒｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎ :¨ｘ+ｆ(ｔ,ｘ(ｔ) ) =0 ,ａ<ｔ<ｂ,αｘ(ａ) -β ｘ(ａ) =0 ,γｘ(ｂ) +δ ｘ(ｂ) =0 ,( 1 )ｗｈｅｒｅα ,β,γ ,δ≥ 0 ,Δ=(ｂ-ａ)αγ+αδ+ βγ>0 .ｆ(ｔ,ｓ)ｍａｙｂｅｓｉｎｇｕｌａｒｉｎｔ =ａ ,ｂ.Ｉｔｈａｓｂｅｅｎｄｉｒｅｃｔｌｙｖｅｒｉｆｉｅｄｔｈａｔｘ(ｔ)ｉｓｔｈｅｓｏｌｕｔｉｏｎｏｆ( 1 )ｉｎＣ2 [ａ ,ｂ]ｉｆａｎｄｏｎｌｙｉｆｘ(…     

VISCOPLASTIC SOLUTION TO FIELD AT STEADILY PROPAGATING CRACK TIP IN LINEAR- HARDENING MATERIALS

An elastic-viscoplastic constitutive model was adopted to analyze asymptotically the tip-field of moving crack in linear-hardening materials under plane strain condition. Under the assumption that the artificial viscosity coefficient was in inverse proportion to power law of the rate of effective plastic strain, it is obtained that stress and strain both possess power law singularity and the singularity exponent is uniquely determined by the power law exponent of the rate of effective plastic strain. Variations of zoning structure according to each material parameter were discussed by means of numerical computation for the tip-field of mode Ⅱ dynamic propagating crack, which show that the structure of crack tip field is dominated by hardening coefficient rather than viscosity coefficient. The secondary plastic zone can be ignored for weak hardening materials while the secondary plastic zone and the secondary elastic zone both have important influence on crack tip field for strong hardening materials. The dynamic solution approaches to the corresponding quasi-static solution when the crack moving speed goes to zero, and further approaches to the HR (Hui-Riedel) solution when the hardening coefficient is equal to zero.     

DYNAMIC ANALYSIS OF A SPATIAL COUPLED TIMOSHENKO ROTATING SHAFT WITH LARGE DISPLACEMENTS

ＩｎｔｒｏｄｕｃｔｉｏｎＲｏｔａｔｉｎｇｓｈａｆｔｓａｒｅｔｈｅｍｏｓｔｖｉｔａｌｃｏｍｐｏｎｅｎｔｓｏｆｍｏｄｅｒｎｉｎｄｕｓｔｒｉａｌａｎｄｐｏｗｅｒｇｅｎｅｒａｔｉｏｎｆａｃｉｌｉｔｉｅｓ.ＤｕｅｔｏｔｈｅｉｍｐｏｒｔａｎｃｅｏｆｔｈｅｓｅｃｏｍｐｏｎｅｎｔｓｔｈｅｒｅｗｅｒｅｗｉｄｅｌｙｓｔｕｄｉｅｓｏｎｔｈｅｖｉｂｒａｔｉｏｎｂｅｈａｖｉｏｒｏｆＥｕｌｅｒ＿Ｂｅｒｎｏｕｌｌｉｒｏｔａｔｉｎｇｓｈａｆｔｓｕｓｉｎｇａｎａｌｙｔｉｃａｌａｎｄｎｕｍｅｒｉｃａｌｍｅｔｈｏｄｓ[1- 4 ].Ｈｏｗｅ…