The temperature field in a hollow cylinder due to a source moving along a helix

We solve the problem of the temperature distribution in a hollow cylinder due to a source moving along a helix on the outer surface with boundary conditions of the second kind. The solution can be used to calculate temperature fields on a computer for various forms of processing materials.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 20, No. 1, pp. 154–156, January, 1971.     

Solution of a Heat-Conduction Problem for a Finite Cylinder and Semispace under Mixed Local Boundary Conditions in the Plane of Their Contact

With the use of the method of summator–integral equations, an axisymmetric problem has been investigated that deals with the development of spatial temperature fields appearing in a finite cylinder with an arbitrary distribution of initial temperature when the cylinder comes in contact with a semi-infinite body that has a constant initial temperature. The essential feature of the considered thermophysical model of heat exchange is that mixed boundary conditions of the second and fourth kind are assigned in the plane of contact of the finite body with the semispace. The thermophysical properties of the bodies considered are different.     

Application of dirichlet and neumann problems in connection with studies of nonstationary heat conduction

Regularities in the development of three-dimensional nonstationary temperature fields in semi-bounded iso- and orthotropic media are deduced under discontinuous boundary conditions of the first or second kind, given in the most general form.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 58, No. 1, pp. 141–145, January, 1990.     

Heating of a film flowing over the surface of a rotating heat transfer device

The authors have solved the problem of a liquid flow over the surface of a rotating conic heat-transfer device with thermal boundary conditions of the second kind with account of heat losses to the vapor-gas phase. Relations have been obtained for calculation of the mean mass temperature, the Nusselt number, and other characteristics of the heating process of the film.Kazan State Technological Institute, Kazan, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 5, pp. 781–788, September–October, 1995.     

Use of the schlieren method to investigate temperature fields in a solid

The use of the Schlieren method to measure the temperature field and temperature gradients in a solid is considered. The results obtained are compared with a theoretical calculation of the temperature field in a finite cylinder for boundary conditions of the second and third kind.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 20, No. 3, pp. 510–514, March, 1971.     

Quasistatic temperature stresses in a multilayer thermally sensitive cylinder

An approach to the evaluation of nonstationary temperature fields and the thermoelastic state of multilayer hollow long thermally sensitive cylinders based on the use of the Kirchhoff substitution, generalized functions, and Greens functions of the corresponding problems for a hollow cylinder with piecewise constant physicomechanical characteristics is illustrated. The problem of heat conduction is reduced to the solution of a Fredholm-Volterra nonlinear integral equation of the second kind for the Kirchhoff variable. In the problem of thermoelasticity, the coefficients of the equation (continuous inside each layer) are approximated by piecewise constant functions. The boundary conditions at the ends of the cylinder are satisfied in the integral form. Numerical analysis is performed for the case of a three-layer cylinder.Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 40, No. 4, pp. 7–16, July–August, 2004.     

Temperature field of an infinite plate with variable thermophysical characteristics

Nomograms are proposed to compute the temperature fields of simplest kind with a linear change in the thermophysical coefficients for boundary conditions of the third kind, which refine engineering computations of body heating.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol.18, No.1, pp.180–183, January, 1970.     

Temperature distribution at a thermally insulated crack in a plate at various boundary conditions

Integral characteristics are defined for the temperature field of a plate with an open and thermally insulated crack and with boundary conditions of the first, the second, or the third kind at the lateral surfaces.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol, 23, No. 3, pp. 528–532, September, 1972.     

Study of cyclic temperature fields in specimens tested for thermal fatigue

The method is suggested for calculating cyclic temperature fields heated by passing an electric current and cooled by compressed air on the basis of solving the problem of nonsteady state thermal conductivity for a rod with internal heat sources, second order asymmetrical boundary conditions, and nonuniform initial conditions. A method and equipment have been developed for contactless measurement of temperature fields for a specimen by means of a scanning photoresistor, a two-coordinate electronic storage oscillograph, and a photographic attachment. Results of calculating cyclic temperature fields by the suggested method are compared with those obtained by experimental data.60th Year of the USSR Institute of Civil Aviation Engineering, Kiev. Translated from Problemy Prochnosti, No. 9, pp. 36–41, September, 1989.     

Finite-Element Axially Symmetric Model of the Thermal Regime under Self-Propagating High-Temperature Synthesis of Blanks in a Free-Flowing Shell

By the finite-element method the problem of nonstationary heat conductivity in the system of three bodies of finite sizes with an internal moving source of the first kind (burning front) has been solved. The influence of various factors on the temperature field parameters under HTS pressing of alloys of the Ti–C–Ni system has been investigated. It has been found that in the synthesis products internal cooling conditions under which the contact surface temperature behind the burning front remains constant are realized and temperature equalization throughout the blank volume occurs. Under internal cooling conditions the material has the highest plasticity and compactability.     

Temperature distribution in a planar body with circular boundary and thermally insulated cracks

Stationary heat-conduction problems are analyzed for infinite plates with a circular hole or for a circular disk weakened by straight-line thermally insulated cracks of arbitrary direction if boundary conditions of the first or second kind are specified on the domain boundary.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 32, No. 2, pp. 350–353, February, 1977.     

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.     

A method of constructing a solution of the heat-conduction equation with complex boundary conditions

It is proposed to solve the heat conduction equation with complicated boundary conditions using the notion of R-functions. A solution which satisfies exactly mixed boundary conditions or boundary conditions of the first, second, or third kind is constructed.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol.21, No. 5, pp.909–913, November, 1971.     

Approximate calculation of thermoelastic stresses under nonstationary conditions

An analytical method of calculating thermal stresses for mixed boundary conditions of the second and third kind is proposed. Problems are solved for arbitrary time-variations of the temperature of the ambient medium.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 16, No. 1, pp. 117–124, January, 1969.     

Freezing of a liquid at a flat wall

The single-phase Stefan problem is considered with boundary conditions of the second and of the third kind. An iteration scheme is developed for solving the nonlinear integrodifferential equation.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 21, No. 3, pp. 537–546, September, 1971.     

Temperature distribution in a rotating hollow cylinder

The temperature distribution in a hollow cylinder rotating with a given angular velocity is found for steady-state boundary conditions of the first kind.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 4, pp. 705–711, October, 1979.     

Analysis of the temperature of a circular electrode

Results are presented of numerical computations of the temperature fields in the circular electrode of a plasmotron. Taken into account in the model proposed are the nonlinearity in the boundary conditions, the dependence of the electrode material properties on the temperature, the heat of phase transformation, etc.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 58, No. 2, pp. 307–311, February, 1990.     

Some effects related to the finite velocity of propagation of heat

The hyperbolic heat-conduction equation is solved for periodic boundary conditions of the second kind. The amplitude, phase, and damping factor of the temperature oscillations turn out to depend on the relaxation time. The possibility of determining the velocity of propagation of heat experimentally is analyzed.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 22, No. 1, pp. 129–135, January, 1972.     

Temperature in a wedge due to a source of variable size and strength

A derivation is given of the temperature equation for a wedge with arbitrary included angle and boundary conditions of the second kind, on the surface of which there acts a strip source of variable dimensions and intensity. An example of the calculation of dimensionless temperature is examined, and its distribution over the boundary surfaces of the wedge is given.     

Calculation of the temperature field associated with the injection of a heat-transfer agent into an oil stratum in the linear case

Equations are obtained for determining the temperature field of an oil stratum and the surrounding rock when a heat-transfer agent is pumped into the stratum. These equations are derived on the basis of a boundary condition of the third kind at the point where the fluid enters the bed, which corresponds more closely to the actual pumping conditions than the usual boundary condition of the first kind.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 19, No. 6, pp. 1088–1093, December, 1970.