Heat conduction and thermal stress induced by an electric current in an infinite thin plate containing an elliptical hole with an edge crack

A uniform electric current at infinity was applied to a thin infinite conductor containing an elliptical hole with an edge crack. The electric current gives rise to two states, i.e., uniform and uneven Joule heat. These two states must be considered to analyze the heat conduction problem. The uneven Joule heat gives rise to uneven temperature and thus to heat flux, and to thermal stress.Using a rational mapping function, problems of the electric current, the Joule heat, the temperature, the heat flux, the thermal stress are analyzed, and each of their solutions is obtained as a closed form. The distributions of the electric current, the Joule heat, the temperature, the heat flux and the stress are shown in figures.The heat conduction problem is solved as a temperature boundary value problem. Solving the thermal stress problem, dislocation and rotation terms appear, which complicates this problem. The solutions of the Joule heat, the temperature, the heat flux and the thermal stress are nonlinear in the direction of the electric current. The crack problems are also analyzed, and the singular intensities at the crack tip of each problem are obtained. Mode II (sliding mode) stress intensity factor (SIF) is produced as well as Mode I (opening mode) SIF, for any direction of the electric current. The relations between the electric current density and the melting temperature and between the electric current density and SIF are investigated for some crack lengths in an aluminum plate.     

Interaction of an internal gravity current with a submerged circular cylinder

The problem of hydrodynamic loads due to the interaction of a gravity current propagating over a bottom channel with a submerged circular cylinder is studied experimentally. It was shown that in the examined range of parameters, the hydrodynamic loads are simulated after Froude. The hydrodynamic loads are maximal if the cylinder lies on the bottom, and they decrease rapidly with increase in the distance from the cylinder to the channel bottom. The effects of mixing and entrainment on the nature of the hydrodynamic loads are considered.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 81–90, March–April, 2005.     

Scission induced by circular shear and heat conduction in an elastomeric cylinder

Constitutive equations for the thermo-mechanics of elastomeric materials generally assume that they do not undergo microstructural change. A constitutive theory is discussed here which accounts for such changes arising from continuous scission of macromolecular junctions of elastomeric networks due to deformation and high temperatures and the subsequent cross-linking of molecules into new networks with new reference states. The total stress is the superposition of the stresses in the remainder of the original network and in each subsequently formed network. Each network acts as a temperature-dependent non-linear elastic material. The interaction of this material response with inhomogeneous deformation and temperature fields is studied for finite circular shear of a cylinder. Numerical results illustrate how the mechanical response of the cylinder depends on the temperature dependence of both the scission–cross-linking process and the properties of the elastic networks.     

Heat conduction in a rock mass with an annular hot water store

Vast subterranean caverns may be used for hot water storage in distinct heating schemes; such caverns can be annular, with a central pillar. This paper considers the quasi-steady solution of the heat conduction equation for this geometry with periodic temperature variations     

Heat conduction in an undulating heating wire

An undulating electric wire generates internal heat by Joule heating. The surface temperature is maintained constant by forced convection. The heat conduction in the wire is solved by using intrinsic coordinates and a perturbation about the (small) ratio of the wire radius to the minimum radius of curvature of the centerline. For the non-uniformly heated wire undulations cause an increase in total heat transfer in comparison with a straight wire of same length and volume.Nomenclature a radius of wire - A surface area - f function of - G function of , - I current - I _n , J _n Bessel functions of order n - k a - K thermal conductivity - L differential operator - N unit normal - q ₀ Joule heating per volume - r radial coordinate - R position vector of axis - R ₀ resistance at T ₀ - s arc length along axis - t s/a - T temperature - u local heat transfer - U total heat transfer - V volume - x position vector - X, Y Cartesian coordinates - z _n J _n or I _n - a/(K/q ₀ )^1/2 - temperature coefficient of electric resistivity - a|| max - r/a - angle - curvature - 2a/period of undulation - normalized temperature     

Magneto-elastic stress induced by an electric current in an infinite thin plate with an elliptical hole

Two-dimensional magnetic field and stress analyses have been presented for soft ferromagnetic, paramagnetic, and diamagnetic materials of an infinite thin plate with an elliptical hole under steady electric current. The magnetic stress has been analyzed in the Maxwell Stress Model. Except for the approximation of the plane stress state since the plate is the thin plate, any assumption is not made for the stress analysis, though the Maxwell stress components are expressed by nonlinear terms. The boundary condition expressed by Maxwell’s stress is completely satisfied without any linear assumptions on the boundary. Two ways for the boundary condition are stated. The analysis of σ _z in the direction of the plate thickness is also carried out. Figures of the magnetic field and stress distribution are shown. Stress intensity factors are also derived, and the magnitude of the stress intensity factor for the magnetic stress and thermal stress due to the Joule heat caused by the electric current is discussed.     

The distortion of a cylinder with non-uniform axial heat conduction

Closed form expressions are developed for the thermoelastic curvature of the initially plane end faces of a traction free cylinder subjected to arbitrary axisymmetric heat flux, the curved surfaces being assumed insulated. The solution is developed from a potential function representation of displacement and temperature for an elastic layer. The reciprocal theorem is invoked to show that the tractions at the curved surface of the cylinder vary linearly along the axis and they are removed by superposition of biaxial bending. It is found that the curvature of the plane ends depends on the local heat flux and the mean heat flux, whilst the cylindrical face distorts into a cone.     

Radiation from an electric dipole in the presence of a corrugated cylinder

Summary A solution is outlined for the problem of an electric dipole which is located outside and parallel to the axis of a circular cylinder fo infinite length. The corrugated surface of the cylinder is assumed to be described by an anisotropic boundary impedance which specifies the ratios of the tangential electric and magnetic fields. It is shown that, in general, the radiated field is elliptically polarized.     

Heat transfer by laminar flow of an elastico-viscous liquid in a circular cylinder with linearly varying wall temperature

Summary The heat transfer by laminar flow of elastico-viscous liquids in a circular cylinder with linearly varying wall temperature has been studied by using the constitutive equation of motion for elastico-viscous liquids and energy equation. The flow phenomenon are characterized by two parameters R _c and S. The presence of the elastic elements in the viscous liquid considerably affects the velocity and temperature distributions.     

Heat transfer enhancement in a channel with a built-in rectangular cylinder

A two dimensional numerical investigation of the unsteady laminar flow pattern and forced convective heat transfer in a channel with a built-in rectangular cylinder is presented. The channel in the entrance region has a length to plate spacing of ten. The computations were made for several Reynolds number and two rectangular cylinder aspect ratios. Hydrodynamic behavior and heat transfer results are obtained by solution of the complete Navier-Stokes and energy equation. The results show that these flow exhibits laminar self-sustained oscillations for Reynolds numbers above the critical one. This study show that oscillatory separated flows result in a significant heat transfer enhancement but also in a significant pressure drop increase.

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Erhöhung des Wärmeübergangs in einem Spaltkanal mit quer eingebautem Rechteckprisma

Zusammenfassung Es wird eine zweidimensionale numerische Untersuchung des instationären Wärmeübergangs und Druckverlustes im laminar durchströmten Spaltkanal mit quer eingebautem Rechteckprisma dargelegt und zwar für verschiedene Reynoldszahlen und zwei Prismenabmessungen. Als Lösung der Navier-Stokes- und der Energiegleichung resultieren selbsterregt oszillieren de Strömungs- und Temperaturfelder, verbunden mit starker Erhöhung des Wärmeübergangs und des Druckverlustes.

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List of symbols C _f skin friction coefficient, Eq. (11) - C _D drag coefficient, Eq. (11) - D drag [N/m] - f _app apparent friction factor, Eq. (10) - h cylinder height [m] - H channel height [m] - k thermal conductivity of cylinder [W/mK] - k ₀ thermal conductivity of air [W/mK] - l cylinder length [m] - L channel length [m] - Nu Nusselt number, Eq. (7) - P dimensionless pressure - Pr Prandtl number of air - Re Reynolds number, Eq. (6) - t time [s] - T temperature [K] - T _b bulk temperature [K], Eq. (8) - U, V dimensionless velocity components - X, Y dimensionless coordinates Greek symbols thermal diffusivity [m²/s] - velocity factor, Eq. (11) - dimensionless temperature, Eq. (5) - fluid density [kg/m³] - kinematic viscosity [m²/s] - dimensionless time, Eq. (5) - difference     

Non-Fourier heat conduction in a finite hollow cylinder with periodic surface heat flux

Analytical solution of the non-Fourier axisymmetric temperature field within a finite hollow cylinder exposed to a periodic boundary heat flux is investigated. The problem studied considering the Cattaneo–Vernotte (CV) constitutive heat flux relation. The material is assumed to be homogeneous and isotropic with temperature-independent thermal properties. The standard method of separation of variables is used for solving the problem with time-independent boundary conditions, and the Duhamel integral is used for applying the time dependency. The solution is applied for the special cases of harmonic uniform heat flux and an exponentially pulsed heat flux with Gaussian distribution in outer surface for modeling a laser pulse, and their respective non-Fourier thermal behavior is studied.     

Explosive switching of an electric current

Experiments are described involving a circuit-breaker element capable of switching a current with a line density of up to 3 ·10⁵ A/cm in a time of 5 μ sec. A suggested application for this device is explosive-magnetic generators with tuned bank inductance.     

Effect of an electric current on necking in a tensile rod

Necking conditions in a tensile thermoviscoplastic rod with passage through it of an alternating electric current are studied. Modeling is performed with allowance for the complex constitutive relations for the rod material, heat transfer in the rod, and the current distribution across the section of the rod as a function of the current frequency (skin effect). The stability of uniform tension is examined by linear analysis of perturbations using the Routh-Hurwitz theory. The results were refined by nonlinear analysis taking into account the effect of the amplitude curve of perturbations on the stability of plastic deformation. Institute of Mechanics and Applied Mathematics, Rostov State University, Rostov-on-Don 344090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 173–178, September–October, 1999.     

Heat transfer and flow around a circular cylinder with tripping-wires

An experimental study was conducted on the heat transfer under the condition of constant heat flux and the flow around a circular cylinder with tripping-wires, which were affixed at ± 65° from the forward stagnation point on the cylinder surface. The testing fluid was air and the Reynolds number Red, based on the cylinder diameter, ranged from 1.2 × 10⁴ to 5.2×10⁴. Especially investigated are the interactions between the heat transfer and the flow in the critical flow state, in relation to the static pressure distribution along the cylinder surface and the mean and turbulent fluctuating velocities in the wake. It is found that the heat transfer from the cylinder to the cross flow is in very close connection with the width of near wake.     

Generation of nonstationary waves by a thick-walled piezoceramic cylinder excited by electric signals

Coupled electroelasticity theory, acoustic approximation, and two-wire transmission line theory are used to study the generation of waves by a submerged cylindrical piezoelectric transducer connected by a cable to a source of nonstationary electric signals. The problem is reduced to a system of integral Volterra equations using the Laplace transform and analytical inversion of boundary conditions. The results of calculations for different cable lengths are presented __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 11, pp. 127–136, November 2005.     

Heat transfer from a circular cylinder rotating about an orthogonal axis in quiescent air

Direct measurements of local heat flux and temperature from rotating cylinders have been carried out using Gardon type foil heat flux sensors and a power supply cum instrumentation slip ring set up. The local and average heat transfer results are presented covering a rotational Reynolds number range of 2 × 10⁴ to 6.2 x 10⁴ corresponding to the speeds varying from 400 to 1,400 rpm. A correlation has been derived for peripherally averaged values of Nusselt numbers: . The values of surface average Nusselt number for the cylinder under the present rotating conditions are found to be higher than for a stationary cylinder in crossflow and for a cylinder rotating about its own axis, in the range of present experiments.Research scholar on leave from Faculty of Engineering, Port Said, Egypt