The principles of data processing based on the numerical solution of the nonlinear heat-conduction problem Pt. 2. The coefficient functional optimization problem in a variational formulation

The solution of the coefficient heat-conduction problem when a linear pulsed heat source acts in the plane of contact of two semibounded bodies, obtained using variational-iterational calculus methods, is presented. The results of tests on a number of heat-insulating materials are given. __________ Translated from Izmeritel’naya Tekhnika No. 2, pp. 48–50, February, 2008.     

A method for the solution of the problem of heat conduction for temperature peaks

The solution of the heat conduction equation with boundary conditions of the second kind obtained in the form of Wiener integrals is reduced to Lebesgue integrals. We analyze the behavior of this solution for different models of heat generation and heat transfer in the process of friction. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 34, No. 2, pp. 97–104, March–April, 1998.     

The detection of defects in materials using thermography

A three-dimensional solution of the direct problem of heat conduction for a semi-bounded isotropic body with a defect when it is heated by pulsed thermal radiation and cools due to convective heat transfer to the surroundings is presented. The results of modeling and experiment are given. __________ Translated from Izmeritel’naya Tekhnika, No. 4, pp. 49–53, April, 2008.     

Analytical solutions of the problems of heat transfer during liquid flow in plane-parallel channels by determining the temperature perturbation front

Based on the integral method of heat balance, an analytical solution of the problem of heat transfer in stabilized liquid flow in a plane tube is obtained. To increase the accuracy of solution, the approximation of the temperature function is made by polynomials of higher degrees. To determine their coefficients, supplementary boundary conditions are introduced that are found from the basic differential equation and given boundary conditions including conditions at the temperature perturbation front. In the second approximation the obtained analytical solution in the range of the longitudinal coordinate 10⁻⁶ ≤ x ≤ ∞ already virtually coincides with the exact one. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 80, No. 5, pp. 176–186, September–October, 2007.     

Temperature shock waves in a moving medium with allowance for the relaxation of the heat flux

The solution of the gasdynamic equation with allowance for the heat transfer in the relaxation of the heat flux is analyzed. The relations expressing the laws of conservation on the front of strong discontinuity of the quantities sought, including the discontinuity of the temperature and the heat-flux density, are discussed. The possibility of existence of two shock waves with fixed initial data is shown using the self-similar solution of the problem on gas motion ahead of the piston. The occurrence of two strong discontinuities is due to the presence of different velocities of propagation of gasdynamic and thermal disturbances — the velocity of sound and the finite rate of heat transfer at a nonzero time of relaxation of the heat flux. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 79, No. 4, pp. 57–68, July–August, 2006.     

An analysis of the temperature field of the workpiece in dry continuous grinding

The recent model for heat transfer during intermittent grinding described in Skuratov, Ratis, Selezneva, Pérez, Fernández de Córdoba and Urchueguía (Appl Math Model 31:1039–1047, 2007) is considered. This model is particularized to the case of continuous dry grinding, where an alternative solution is obtained in the steady state. This alternative solution is analytically equivalent to the well-known formula of Jaeger (Proc R Soc NSW 76:204–224, 1942) for the steady–state temperature field created by an infinite moving source of heat and proves to be very useful for evaluating the maximum point of the temperature.     

The systematic errors in determining the nonstationary heat-exchange conditions with parametric identification

A universal method of estimating the accuracy of the results of a solution of the optimum planning of the realization of the inverse boundary-value problem of heat conduction from the establishment of the input peak flux density q(τ) is proposed for different heat-flux converters. The method is based on the construction of combined confidence regions or intervals for optimum estimates of the parameters, which realize a piecewise-linear spline-approxmation of q(τ). __________ Translated from Izmeritel’naya Tekhnika, No. 8, pp. 54–58, August, 2007.     

Application of group theory to the analysis of the equations of stationary heat conduction and static thermoelasticity

Similarity transformations are constructed and used to obtain an exact solution of the axially symmetric boundary-value problem of static thermoelasticity for a half space whose free surface is heated by a continuous point heat source. It is shown that this solution agrees with the solution obtained earlier by the method of thermoelastic potentials. Franko L'viv State University, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 35, No. 3, pp. 69–73, May–June, 1999.     

Non-equilibrium Thermodynamic Model for the Estimation of the Soret Coefficient in Dilute Polymer Solutions

In the present work a theoretical model based on linear non-equilibrium thermodynamics and the concept of Eyring’s activation energy of viscous flow is developed to estimate the Soret coefficient in dilute polymer solutions. The model is capable of predicting a sign change in the Soret coefficient, when the polymer molecular weight changes. The key part of the model is the way that the net heat of transport of the polymer molecules is simulated. Employing the Mark–Houwink equation, which correlates the polymer solution intrinsic viscosity with its molecular weight, the net heat of transport of the polymer is correlated with the activation energy of viscous flow of the polymer’s monomer in the liquid state, the Mark–Houwink solution parameter, and the polymer molecular weight. The model is evaluated against the experimental data, where qualitative and in some cases quantitative agreement is found.     

The use of an explicit method of identifying objects to solve problems of nonstationary heat conduction

The theoretical principles of an explicit method of identifying multidimensional objects with nonstationary thermal conductivity are described. The solution of problems of measuring nonstationary heat flux and thermal conductivity in the range λ = 0.03–800 W/(m·K), the thermal conductivity of one of the materials of a double-layer system, the temperature dependence of the thermal conductivity, and the combined “thermal conductivity and volume heat capacity” are presented. The results of investigations on thermal models are given. __________ Translated from Izmeritel’naya Tekhnika, No. 6, pp. 32–38, June, 2008.     

Analytical methods of investigation of the thermal state of a region with a moving boundary under the conditions of nonstationary heat transfer to the external medium

An analytical method of solution of combined problems of nonstationary heat conduction for a region with a boundary moving according to a known law and with a time-variable coefficient of heat transfer is developed. The idea of splitting the kernel of the obtained generalization of a singular integral Fourier transform with respect to a space variable provides a basis for the method. Theoretical results are used in mathematical simulation of heat transfer processes in the region with a moving boundary under the conditions of nonstationary heat transfer to the external medium. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 73, No. 1, pp. 125–130, January–February, 2000.     

Use of integral boundary-layer theory for solving conjugate problems of heat transfer in channels of high-power plants

The solution of the conjugate problem of convective-conductive heat transfer in the channels of power plants is presented. The problem of convective heat transfer in the gas phase is solved by the integral theory of heat transfer. A one-dimensional problem of conductive heat transfer in the material of the wall is solved by the finite-difference method. Relative laws of heat and mass transfer and friction are obtained by numerical integration with respect to the boundary-layer thickness. The effect of the material and geometry of the wall on the level of problem “conjugation” is studied. Translated from Inzhenemo-Fizicheskii Zhurnal, Vol. 73, No. 1, pp. 131–137, January–February, 2000.     

Calculation of radiative-conductive heat transfer in a system closed by a semitransparent envelope

A compact analytical solution of the one-dimensional problems of heat conduction is obtained for bodies of canonical shape with constant thermophysical properties and internal heat sources (sinks), whose power is generally coordinate-dependence. The solution includes, as partial cases, numerous known and new problems of stationary and nonstationary heat conduction, excluding the case of simultaneous assignment of second-second kind conditions on boundary surfaces. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 73, No. 1, pp. 107–112, January–February, 2000.     

End Effects in the Three-Omega Method to Measure Gas Thermal Conductivity

A two-dimensional analytical solution is derived for the three-omega method for measurement of thermal conductivity of materials with a fine wire. The analytical solution includes the wire heat capacity and the effect of heat losses from the ends of the wire. To derive the solution, finite Fourier transforms are applied in the direction parallel to the wire axis. The solution is compared with a one-dimensional solution and experimental data. It is found that heat losses from the wire ends have a significant effect on the 3ω components at low frequency and tend to be less important at high frequency. Moreover, it is shown that two-dimensional effects will be severe for nano-scale wires, even if the wire length-to-diameter ratio is very large.     

A review of one aspect of the thermal-explosion theory

The historical development of the thermal-explosion theory is examined and reviewed, It is shown that the original formulation of the problem by Semenov accurately defines the phenomenon and explains the reason for the explosion. He showed that, when the heat generation within the solid exceeds the heat dissipation to the surroundings, explosion occurs. Frank-Kamenetskii’s disapproval of Semenov’s logic theorized that the difference between the temperatures at the center of the solid and its surface is the cause of the explosion. His famous and ingenious small-temperature model and the solution to the differential equation that resulted from that distorted the problem and delayed the progress to a full understanding of the problem. He concluded that explosion occurs when no solution to the problem exists. The exact solution to the problem by Shouman, Donaldson and Tsao reaffirmed the validity of the Semenov formulation. Further examination of the effect of reactant consumption on the problem produced full understanding of the physics of the problem.     

Diffusion model of longitudinal agitation in heat and mass transfer processes. problems of the 2nd level

The paper is a continuation of [1] on systematization of the employment of a diffusion model (DM) for describing heat and mass transfer processes. The object of consideration is a heat exchanger (a mass exchanging apparatus) with two flows moving in the DM regime, ideal displacement, and ideal agitation. All possible combinations of them are found. The problems are distributed according to three levels of complexity. The solution of problems of the 2nd level is considered. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 70, No. 5, pp. 724–733, September-October, 1997.     

Identification of the thermal properties of materials using methods of the calculus of variations

A solution of the heat-conduction problem when a linear pulsed source of heat acts in the plane of contact of two semibounded bodies, obtained using methods of the variational-iterational calculus, is presented. The results of tests of a number of heat-insulating materials are given. __________ Translated from Izmeritel’naya Tekhnika, No. 7, pp. 34–36, July, 2007.     

Friction-induced formation of heat with account for heat transfer through the contact surface between homogeneous and piecewise-homogeneous semispaces

An analytical solution of the boundary-value heat conduction problem is obtained for a tribosystem consisting of a homogeneous semispace sliding with a constant velocity along the surface of a plane-parallel strip applied to a semi-infinite foundation. The tribosystem is heated as a result of the frictional heat formation on the sliding surface. It is assumed that the thermal contact of the semispace with the strip is not full. With the aid of the Duhamel theorem, a solution for the considered tribosystem, with sliding at a constant deceleration, is also constructed that models heat formation from friction in disk brakes. For the materials of the friction pair "pig iron semispace (disk)–metal-ceramic strip (lining)–steel foundation (frame)," the influence of the coefficient of thermal conductivity of the contact (Biot number) on the temperature distribution was investigated.     

Temperature and stresses in the vicinity of friction contacts of microasperities in the process of braking

We develop an approach to the solution of heat problems of friction simulating the operation of brake systems. The thermal and stressed state of an element of the friction pair is estimated by using the criterion of octahedral tangential stresses. Franko L'viv State University, L'viv State Agricultural University, State University “L'vivs'ka Politekhnika,” L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 32, No. 6, pp. 72–80, November–December, 1996.     

Variety of the representation of the nonstationary temperature of fuel elements depending on the form of the distribution of the heat sources

The author proposes a representation of the solution of the heat-conduction equation in the form of expansions in basis functions that are selected depending on the form of the distribution of the internal heat sources. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 73, No. 4, pp. 761–772, July–August, 2000.