Solution of the two-dimensional inverse heat-conduction problem in a cylindrical coordinate system

The two-dimensional inverse heat-conduction problem is considered. An algorithm of the solution and the results of a trial computation are presented.     

Solution of a two-dimensional heat-conduction problem for a geometrically complex domain by an integrointerpolation method

A methodology is proposed for the construction of an algorithm to solve heat transfer problems for spatial domains of complex geometric shape.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 3, pp. 464–471, March, 1989.     

A mixed two-dimensional stationary heat-conduction problem for a cylinder

We investigate the exact solution to the problem of calculating the stationary thermal field external to a cylinder on a portion of the surface of which the thermal flow density is constant and on the remaining portion of which the temperature is constant.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 21, No. 3, pp. 476–479, September, 1971.     

Solution of heat-conduction problem with variable heat-exchange coefficient

Exact solution is obtained in the form of an infinite series of the heat-conduction equation with boundary condition of the third kind and time-variable heat-exchange coefficient.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol.18, No.1, pp. 133–138, January, 1970.     

Solution of two-dimensional heat-conduction problems by the Z transform method

The Z-transform (discrete Laplace transform) is used to solve heat-conduction problems in axisymmetric bodies of arbitrary shape for different types of boundary conditions.     

Formulation of the two-dimensional transient heat-conduction problem for the bladed disk of a gas turbine

A system of differential equations is derived for the transient heat conduction associated with a cooled gas turbine disk equipped with shrouded blades on a shank.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 21, No. 2, pp. 257–264, August, 1971.     

Analysis of the accuracy of solutions of the two-dimensional heat-conduction problem

The accuracy of solutions of the two-dimensional inverse heat-conduction problem is investigated. Exact and perturbed values of the temperature on the inner boundary are used as initial data.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 49, No. 6, pp. 966–970, December, 1985.     

Steady heat-conduction problem for a double cylinder

An analytical solution of the problem stated in the title is obtained for various conditions at the ends of the cylinder. The method of asymptotic solution of boundary-value problems for elliptic equations in thin domains is translated to the case of boundary conditions of the third kind.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 26, No. 2, pp. 339–348, February, 1974.     

Algorithms and results of solving the inverse heat-conduction boundary problem in a two-dimensional formulation

The effectiveness of gradient algorithms for solving the inverse problem which are regulated in terms of the number of iterations is investigated.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 48, No. 4, pp. 658–666, April, 1985.     

Generalization of Sommerfeld heat-conduction problem for a ring

A solution is obtained for the problem of heat conduction in a one-dimensional ring consisting of two sections with different lengths, heat sources, and thermophysical parameters.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 35, No. 1, pp. 150–154, July, 1978.     

Solution of the nonlinear inverse problem for a generalized heat-conduction equation in a region with moving boundaries

In an analysis of the numerical solution of the nonlinear inverse heat-conduction problem in a region with moving boundaries, a regularization method is used to construct an algorithm for smoothing the experimental data in a compilation of the input data for the inverse problem.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 29, No. 1, pp. 151–158, July, 1975.     

A heat-conduction problem

A heat-conduction problem is posed with a branching of the heat flux at the boundaries, leading to a system of Volterra integral equations of the second kind; the system is transformed to a form which can be solved by the operator series method.     

Solution of the steady-state heat-conduction problem for thin filament heaters of arbitrary geometry

The temperature distribution for thin filaments heated by an electric current in vacuo is found, and simple analytical expressions are derived for calculations of the fundamental variables characterizing the thermal mode of the heater. The results of calculations according to these expressions are compared with the experimental data.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 21, No. 4, pp. 707–712, October, 1971.     

Solution of nonlinear heat-conduction problems for a semitransparent body

We solve the nonlinear heat-transfer problem in a semitransparent optically thick body by the finite-differences method in combination with the small-parameter method.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 38, No. 3, pp. 522–527, March, 1980.     

Determination of external thermal load parameters by solving the two-dimensional inverse heat-conduction problem

A method is proposed for recovering the space-time behavior of an external unsteady heat load to a cylindrical body by solving the two-dimensional inverse heat-conduction boundary problem.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 4, pp. 581–586, October, 1981.     

Variational formulation of a nonstationary heat-conduction problem

Belorus Polytechnic Academy, Minsk. Translated from Inzhenerno-fizicheskii Zhurnal, Vol. 62, No. 1, pp. 130–139, January, 1992.     

Solution of the linear one-dimensional inverse heat-conduction problem on the basis of a hyperbolic equation

The linear problem of determining the temperature in an infinite one-dimensional plate with a stationary heat sensor and a stationary boundary is solved. The allowable approximation time steps in the calculations can be diminished by using a hyperbolic heat-conduction equation with a suitably chosen hyperbolicity parameter.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 6, pp. 1093–1098, June, 1981.     

Solution of a nonlinear heat-conduction equation for volume heat sources

Solutions of a nonlinear heat-conduction equation which are self-similar or self-similar in the limit are discussed for a given total input power.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 18, No. 5, pp. 927–930, May, 1970.     

Coefficient inverse heat-conduction problem

The computational algorithm and the results are given for the solution of the inverse problem of determining the total set of coefficients of the inhomogeneous quasilinear heat-conduction equation.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 53, No. 3, pp. 474–480, September, 1987.