Spatial nonstationary heat-conduction problem for a prism with a coordinate-dependent heat-transfer coefficient

We present an efficient method for the determination of three-dimensional nonsteady-state fields of bodies of simple shapes, when the heat-transfer coefficient from their surface changes locally.Notation t temperature field - dimensionless temperature field - x, y, and z dimensional coordinates - X, Y, and Z dimensionless cordinates - time - thermal conductivity - a thermal diffusivity Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 42, No. 1, pp. 133–137, January, 1982.     

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.     

Finite-difference solution of conjugate heat-conduction problems

The nonlinear conjugate heat-transfer problem is solved by the method of finite differences. The convergence of the resulting finite-difference scheme is analyzed.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 35, No. 5, pp. 924–929, November, 1978.     

On inverse boundary heat-conduction problems for recovery of heat fluxes to anisotropic bodies with nonlinear heat-transfer characteristics

A closed method is proposed for recovering heat fluxes to anisotropic bodies under conditions of aero-gasdynamic heating from experimental temperature data at spatial-temporal nodes. The thermal protection of a body is made of anisotropic materials with components of thermal-conductivity tensor, which are dependent of temperature, i.e., are nonlinear. The method is based on approximating a spatial dependence of a heat flux by a linear combination of basis functions with sought coefficients (parameters), which are found by minimization of a quadratic functional of the residual (the discrepancy between experimental and theoretical temperature values) using the implicit method of gradient descent, as well as on constructing and numerically solving problems for the determination of sensitivity coefficients. To increase the degree of correctness of an inverse problem, along with a main functional, the regularizing functionals have been constructed and utilized on the basis of smoothness requirements for spatial functions of heat fluxes to have continuous first and second derivatives, which allowed heat fluxes with the coupled heat transfer to be recovered in the form of arbitrary functions: monotonic, nonmonotonic, having extrema, inflection points, etc. Numerous results of recovering heat fluxes to anisotropic bodies are obtained and discussed, with the regularization parameter being selected for every case.     

Duhamel integral and the operational-structural method of solution in nonstationary heat-conduction problems for regions of complicated shape

We propose an analytic method for solving nonstationary heat-conduction problems for regions of complicated shape with nonstationary boundary conditions and energy sources.Notation u temperature - density - thermal conductivity - c specific heat capacity - n number of coordinate functions - Fo=t(/cL) Fourier number - direction of the inner normal to the contour ₂ - L characteristic dimension of the plate - d thickness of the plate - sum of the total heat-transfer coefficients from the surface of the plate - Bi=L²/d=b² Biot number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 5, pp. 901–906, May, 1981.     

On an approximate method of solution of nonlinear heat-conduction problems

An approximate method is presented for the solution of problems of transient heat conduction in solids with thermal conductivity and specific heat linearly dependent on temperature.     

Numerical solution of retrospective heat-conduction problems

The article presents a method of solving heat-conduction problems by determining the initial temperature field or the instant when some physical event occurred.Translated from Inzhenerno-Fizlcheskii Zhurnal, Vol. 45, No. 5, pp. 765–769, November, 1983.     

Analytical solution of heat-conduction problems with a variable initial condition based on determining a temperature perturbation front

With the aid of the integral heat-balance method an analytical solution of the problem of unsteady-state heat conduction has been obtained for an infinite plate with a variable initial condition. To increase the accuracy of solution by the integral method additional boundary conditions are introduced which are determined from the initial differential equation and basic boundary conditions, including those prescribed at the temperature perturbation front. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 80, No. 3, pp. 27–35, May–June, 2007.     

Solution of heat-conduction problems with variable thermophysical properties by the method of nets

The paper presents the numerical solution of a two-dimensional heat-conduction problem for an infinite bar with a square cross-section, temperature-dependent thermophysical properties and radiant heat transfer at the surface.     

Semiempirical solution of heat-transfer problems for nucleate boiling

On the basis of semiempirical turbulent transport theory, with the dynamic velocity expressed in terms of energy dissipation factor controlling the transport process, equations are derived for the heart-transfer coefficient for the nucleate boiling of liquids in the cases of pool boiling and boiling in vertical pipes.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 19, No. 4, pp. 629–636, October, 1970.     

Approximate analytical solution of linear heat-conduction problems in regions with noncanonical boundaries

We present a method for solving linear heat-conduction problems in regions bounded by a noncanonical contour. The method is based on extending the noncanonical contour to a contour imbedded in the grid of classical coordinate systems.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 53, No. 4, pp. 659–662, October, 1987.     

Electrical models for the solution of inverse non steady heat-conduction problems

Analog methods proposed earlier for the solution of inverse nonsteady heat-conduction problems on RC networks are further elaborated with allowance for convective, contact, and radiative heat transfer.     

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.     

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.     

The effectiveness of using one variant of the finite-element method for solving nonlinear nonstationary heat-conduction problems

It is established that the use of a previously proposed variant of the finite-element method for solving nonlinear nonstationary heat-conduction problems is efficient (in the sense of computer time expenditures) when the half-width of the band β of the resulting matrix in the system of linear algebraic equations does not exceed a certain value of β_cr. As a result of a numerical experiment for an axially symmetric case we obtain β_cr ≈ 47, which demonstrates the effectiveness of this variant of the finite-element method for solving a wide range of practical problems of heat-conduction theory. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 70, No. 2, pp. 284–289, March–April, 1997.     

Experimental design of measurements for the solution of coefficient-type inverse heat-conduction problems

A numerical method is proposed for optimization of the spatial placement of a fixed number of temperature sensors in the solution of coefficient-type inverse heat-conduction problems.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 48, No. 3, pp. 490–495, March, 1985.     

Practically achievable accuracy and reliability of the solution of inverse heat-conduction problems

We develop a method of solution of inverse heat-conduction problems which makes it possible to obtain a guaranteed minimum of reliable information in conditions of indeterminacy.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 52, No. 2, pp. 316–323, February, 1987.     

Algorithm of the zonal solution of radiation — conduction heat-transfer problems

A numerical method is proposed to compute the stationary radiation-conduction heat transfer in semitransparent materials on the basis of a zonal approach.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 6, pp. 1094–1102, December, 1981.