Variational principles for nonstationary heat conduction problems

Integral variational principles are proposed for nonstationary heat conduction problems. These lead to integration of the wave equation of heat conduction or the Fourier heat conduction equation with the initial and boundary conditions.     

Nonlinear heat conduction with nonstationary boundary conditions

We study the one-dimensional nonstationary temperature field in a solid when the thermal conductivity and heat capacity depend linearly on the temperature.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 19, No. 5, pp. 880–885, November, 1970.     

Method of paired integral equations withL-parameter in problems of nonstationary heat conduction with mixed boundary conditions for an infinite plate

For solving a nonstationary equation of heat-conduction in cylindrical coordinates with mixed discon-tinuous boundary conditions prescribed on one of the surfaces (z=0) of an infinite plate, a method of paired integral equations with L-parameter is used. Moreover, on the other surface (z=h) of the plate the boundary conditions are prescribed unmixed. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 73, No. 5, pp. 902–906, September–October, 2000.     

Additional boundary conditions in nonstationary problems of heat conduction

The integral method of thermal balance, with determining the front of temperature disturbance and introducing additional boundary conditions, is used to obtain analytical solutions of heat conduction problems for plate, cylinder, and sphere at the boundary conditions of the third kind. The distribution of isotherms and the velocities of their motion are analyzed.     

Nonideal contact problem of nonstationary heat conduction for two half-spaces

A nonideal contact problem of nonstationary heat conduction for two half-spaces with arbitrary initial conditions is considered. By introducing unknown conjugate functions and subsequent Laplace transformation, an integral representation for the problem solution has been found; equations in the region of transforms are solved with the aid of Green’s functions. In the particular case of exponential distributions of initial temperatures an accurate solution of the problem has been achieved. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 2, pp. 373–383, March–April, 2008.     

Application of fourier-series methods and integral equations for solving nonstationary nonaxisymmetric heat conduction problems for bodies of revolution

We consider the problem of determining nonstationary nonaxisymmetric temperature fields in bodies of revolution appearing on heating by internal heat sources through and due to convective heat exchange with an external medium. The solution of the problem is represented in the form of a Fourier series in an angular coordinate with coefficients being determined by a method of boundary elements. We consider the general case and particular cases of the nonstationary nonaxisymmetric heat conduction problem and determine the asymptotic temperature distributions with a linear variation in time of the heating medium temperature and with heating by moving heat sources.Ya. S. Podstrigach Institute of Applied Problems of Mechanics and Mathematies, Academy of Sciences of Ukraine, L'vov. Translated from Inzhenerno-Fizicheskii Zhurnal. Vol. 68, No. 6, pp. 1023–1030, November–December, 1996.     

A method of determining nonstationary heat flux and heat conduction using parametric identification

The formulation and solution of the combined (boundary and coefficient) inverse heat-conduction problem of the simultaneous determination of the thermal characteristics of a material and the heat flux density entering the heat receiver are considered. The solution is based on a parameterization of this problem and the use of an extended digital Kalman filter. The results of a simulation of the simultaneous reestablishment of the heat flux and the heat conduction in a single experiment to measure the temperature of a surface are presented.     

Iterative approximation method for solving heat conduction equations

Convergence analysis is given for solving equations of heat conduction in the threedimensional space on an electronic computer under involved boundary conditions; an iterative approximation method is used in which the sought function is determined by successive approximations with a subsequent approximation by Chebyshev polynomial of the same degree.     

A class of integral transformations for the generalized equation of nonstationary heat conduction

Integral transformations for finding analytical solutions of the boundary-value problems of nonstationary heat conduction for the generalized equation of transfer in an infinite region bounded on the inside by a plane, cylindrical, or spherical surface have been constructed. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 1, pp. 123–130, January–February, 2008.     

Application of a variational method for the solution of nonstationary heat conduction problems

We present an application of a variational principle due to Ainola, compatible with Kantorovich's method, for the solution of the first and second boundary value problems.     

Solution of integral equations of inverse problems of heat conduction

A solution is given of integral equations of inverse problems of heat conduction by the method of successive approximations and also by means of expansions in orthogonal systems of functions. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 29, No. 1, pp. 120–123, July, 1975.     

Solution of a two-dimensional equation of nonstationary heat conduction for orthotropic cylindrically bounded media

Analytical relationships are presented to determine two-dimensional (2-D) nonstationary thermal fields in a bounded orthotropic cylinder for various boundary conditions. The solution obtained generalizes a wide class of eighty boundary-value problems of nonstationary heat conduction in studies of heat exchange in the bodies being considered.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 6, pp. 1014–1021, June, 1989.     

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.     

A method of paired integral equations in the region of laplace transforms for solving nonstationary heat conduction problems with mixed discontinuous boundary conditions

On the basis of the method developed, the solutions of four problems of mathematical physics are obtained for an infinite plate (a plane layer of thickness z = h) with assignment of mixed discontinuous boundary conditions (BC) on one of the surfaces z = 0 of the plate and unmixed BC on the other surface z = h. Belarusian State University, Minsk, Belarus. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 72, No. 3, pp. 555–571, May–June, 1999.     

Exact solution of the problem of nonstationary heat conduction for two semispaces in nonideal contact

An exact solution of the nonideal-contact problem of nonstationary heat conduction for two semispaces with constant initial temperatures has been obtained. It is shown that the problem at hand is similar in thermal action to the third boundary-value problem for a semispace bordering on a medium of constant temperature that has a certain value. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 79, No. 5, pp. 86–87, September–October, 2006.     

Calculation of nonstationary heat conduction in multilayer objects with boundary conditions of the third kind

Some aspects of the calculation of nonstationary heat conduction in multilayer objects with boundary conditions of the third kind are considered. The homogeneous problem with inhomogeneous boundary conditions is solved for the one-dimensional case. The proposed solution has an explicit form and may be useful in numerical calculations due to the recurrence representation of the basic relations.V. P. Goryachkin Moscow Institute of Agricultural Production Engineers. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 65, No. 2, pp. 249–251, August, 1993.     

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.     

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.