Effect of axial heat flux on the temperature field of a hollow cylinder

Solutions are given for two-dimensional problems of heat conduction in a hollow cylinder with quasi-steady heating (constant heating rate) for a boundary condition of the second kind at the inner surface of the cylinder, and boundary conditions of the third or first kind at the outer surface. The effect of axial heat flux on the temperature field of the hollow cylinder is estimated.     

Steady-state temperature field of a finite cylinder in a housing

An analytic solution has been obtained for the steady-state temperature field of two coaxial finite cylinders, the inner of which is a rotor. Two cases corresponding to different conditions of cooling of the outer cylinder, or housing, are considered.     

Residual and thermoelastoplastic stress distributions in a heat treated solid cylinder

An important consideration in design is the determination of residual stresses developed during heat treatment of steel. By selecting an appropriate heat treatment technique, one can control the level of residual stresses in the components. Obviously beneficial residual stresses in the material increase the life of components. On the other hand, the unexpected failure of components that is later attributed to detrimental residual stresses is not uncommon.

In this paper, residual stress distribution in a quenched long solid cylinder with temperature dependent properties is evaluated. Using three different speeds of cooling, the level of residual stresses for each speed was determined and compared with the others. From the stresses calculated, it was found that the tensile and tangential residual stresses are more sensitive to the speed of cooling than the radial one. For theoretical analysis a quasi-static uncoupled thermoelastoplastic analysis, based on incremental theory of plasticity, is developed and a numerical procedure for successive elastic solution approximation is formulated.     

Transient solution of temperature field in functionally graded hollow cylinder with finite length using multi layered approach

In this paper by using a multi-layered approach based on the theory of laminated composites, the solution of temperature in functionally graded circular hollow cylinders subjected to transient thermal boundary conditions are presented. The material properties are assumed to be temperature-independent and radially dependent. The cylinder has finite length and is subjected to axisymmetric thermal loads. It is assumed that the functionally graded circular hollow cylinder is composed of N fictitious layers and the properties of each layer are assumed to be homogeneous and isotropic. Employing Laplace transform techniques and series solving method for two-dimensional heat conduction equation in the cylinder, solutions for the variation of temperature with time as well as temperature distribution through the cylinder are obtained.     

Steady-state temperature field of a disc with convective heat transfer at its surface

The mixed problem with axial symmetry is solved approximately, with boundary conditions of the third kind specified at the disc surface.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 23, No. 3, pp. 533–540, September, 1972.     

Effect of skewed heat generation and nonuniform heat transfer at the surface of a heat emitting rod on its temperature field

Analytical solutions are obtained to problems concerning the temperature field of heat emitting rods with skewed sectional heat generation profiles and with an angular dependence of the heat transfer coefficient.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 24, No. 6, pp. 1118–1123, June, 1973.     

The temperature field of a hollow cylinder for small fourier number

An approximate solution is given for the problem of the temperature distribution in an infinite hollow cylinder at small Fourier numbers.     

Laminar heat transfer in a two-dimensional channel with a nonuniform temperature field at the entrance

Heat transfer is investigated, on the basis of the linearized energy equation, in the initial section of a two-dimensional channel with laminar flow of an incompressible fluid and a nonuniform temperature field at the entrance. Results of calculations of the temperature field and Nusselt number Nu are given for various cross sections along the channel.     

Temperature field in a hollow finite-length cylinder with an arbitrarily moving heat source

An analytical solution is obtained to the problem of heating a hollow cylinder from an arbitrary heat source. The asymptotic of the characteristic equation is derived and the eigen-values of the corresponding Sturm-Liouville equation are tabulated.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 22, No. 3, pp.537–543, March, 1972.     

Calculation of the nonstationary temperature field in a composite (three-layer) cylinder

A method of calculating the nonstationary temperature field of a composite hollow cylinder when its external surface is heated asymmetrically is described.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 32, No. 4, pp. 729–733, April, 1977.     

Choosing a calculation scheme for the temperature field in pulse microwelding

Thermal processes in pulsed methods of microwelding in a solid phase during semiconductor assembly are investigated. Expressions determining the choice of the temperature-field calculational scheme are subjected to numerical analysis. It is shown that the calculated and experimental data are in qualitative agreement.     

Asymmetric temperature field of an unbounded cylinder with a moving heating line

The temperature distribution in an unbounded hollow cylinder, a portion of whose inner surface is asymmetrically heated, is obtained under the assumption that the heating line moves at a certain speed toward the cylinder axis.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 15, No. 6, pp. 1080–1085, December, 1968.     

Temperature field of a two-layer cylinder with volumetric heat sources and nonstationary boundaries

A numerical-analytical solution of a differential heat-conduction equation is suggested. Analytical expressions relating the initial and boundary conditions of heat transfer to parabolic temperature distributions in the layers of the cylinder are obtained for the end of the calculated interval of time. The calculation of the temperature field is reduced to the solution of a system of two ordinary differential equations. The error of the solution is analyzed. Ivanovo State Power Engineering University, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 72, No. 1, pp. 76–79, January–February, 1999.     

Heat exchange at the critical point of a cylinder with intense injection

The results of a study of the heat exchange and structure of the zone of stream mixing at the front critical point of a porous cylinder transverse to the flow in the presence of intense injection are presented.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 1, pp. 5–10, July, 1977.     

The calculation of the thermal stresses in a cylinder and a sphere with variable surface temperature

The calculation of the thermal stresses at the surface and at the center of a cylinder and a sphere is suggested to be carried out with the use of the integral-mean temperature and the temperature of the center, computed through the multiplication of a piecewise-linear approximating surface temperature by specific coefficients.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 17, No. 5, pp. 944–950, November, 1969.     

Investigation of the instantaneous temperature field in a fluid stream around a heated cylinder

Temperature fields in a fluid stream are investigated by a pulse holographic interferometry method at low Reynolds numbers.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 58, No. 6, pp. 899–905, June, 1990.     

Mathematical simulation of temperature field in a hollow rotating cylinder with nonlinear boundary conditions

An analytical solution is obtained of the nonlinear problem on heat conduction in a hollow infinite cylinder in view of the temperature dependence of its thermophysical characteristics. Results are given of calculations of temperature field for the roll of machine for continuous casting of slabs.     

Simplified methods for the calculation of partial pressure using the relative ionization cross-section

Two simplified methods for the calculation of partial pressure are discussed theoretically in conjunction with the ionization probability of producing the most characteristic ion of molecules. Ionization probabilities for twenty molecules, usually encountered in many vacuum systems, are determined from the relative ionization cross section by using a correction factor. Partial pressure values calculated from these methods are compared with those from the usual mass spectrometric method. The value can be evaluated within an accuracy of less than 10% for many molecules. The method of calculation using the ionization gauge correction factor is also developed. By these methods the partial pressure evaluation becomes possible without doing troublesome calibrations of the residual gas analyser.     

On the calculation of the temperature field in solids with variable heat-transfer coefficients

A method is presented for the approximate determination of the temperature field in solids with variable heat-transfer coefficients.