Solution of nonautomodeled problems of boundary-layer theory taking into account nonstationary conjugate heat exchange and blowing

The results of an investigation of conjugate heat exchange when a supersonic flow of gas flows around a spherical shell when gas blows from the surface of the material are presented.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 38, No. 3, pp. 543–550, March, 1980.     

Interface integral BEM for solving multi-medium heat conduction problems

In this paper, a new and simple boundary element method, called interface integral boundary element method (IIBEM), is presented for solving heat conduction problems consisting of multiple media. In the method, the boundary integral equation is derived by a degeneration technique from domain integrals involved in varying heat conductivity problems into interface integrals in multi-medium problems. The main feature of the presented technique is that only a single boundary integral equation is used to solve heat conduction problems with different material properties. The effect of nonhomogeneity between adjacent materials is embodied in the interface integrals including the material property difference between the two adjacent materials. Comparing with conventional multi-domain boundary integral equation techniques, the presented method is more efficient in computational time, data preparing, and program coding. Numerical examples are given to verify the correctness of the presented technique.     

A meshless method for conjugate heat transfer problems

Mesh reduction methods such as boundary element methods, method of fundamental solutions, and spectral methods all lead to fully populated matrices. This poses serious challenges for large-scale three-dimensional problems due to storage requirements and iterative solution of a large set of non-symmetric equations. Researchers have developed several approaches to address this issue including the class of fast-multipole techniques, use of wavelet transforms, and matrix decomposition. In this paper, we develop a domain decomposition, or the artificial sub-sectioning technique, along with a region-by-region iteration algorithm particularly tailored for parallel computation to address the coefficient matrix issue. The meshless method we employ is based on expansions using radial-basis functions (RBFs).An efficient physically based procedure provides an effective initial guess of the temperatures along the sub-domain interfaces. The iteration process converges very efficiently, offers substantial savings in memory, and features superior computational efficiency. The meshless iterative domain decomposition technique is ideally suited for parallel computation. We discuss its implementation under MPI standards on a small Windows XP PC cluster. Numerical results reveal the domain decomposition meshless methods produce accurate temperature predictions while requiring a much-reduced effort in problem preparation in comparison to other traditional numerical methods.     

Use of generalized diffusion coefficients in solving conjugate problems

A numerical method is used to solve the conjugate problem of the heating of a graphite body in a high-temperature gas flow.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 6, pp. 1001–1006, December, 1977.     

Applicability of boundary-layer theory to calculation of heat transfer under separation conditions

The conditions are examined under which methods and relations developed for attachment flow are applicable to regions of separation flow.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 43, No. 3, pp. 397–401, September, 1982.     

Use of methods of solving inverse problems of heat conduction to establish the coefficient of heat transfer in jet cooling

The problem of determining the coefficient of heat transfer is analyzed as an inverse problem for the heat-conduction equation. The results of a calculation of the coefficient of heat transfer on the basis of experimental data on the jet cooling of metal plates are presented.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 34, No. 5, pp. 903–909, May, 1978.     

A new method of solving the integral equations of radiation heat transfer

We present a method for calculating the radiation heat transfer between bodies and a new approach to the solution of the corresponding integral equations. We show, in fact, that the first approximation describes the solution of these equations with sufficiently high accuracy and is, in some cases, exact.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 51, No. 6, pp. 1031–1040, December, 1986.     

Methods of solving nonstationary problems in the theory of radiative heat exchange

The generalized zonal method of Surinov and the method of successive approximations are applied to the study of nonstationary radiative heat exchange.     

Application of integral equations to heat conduction problems in which the heat transfer coefficient varies

The problem of heat conduction with a variable heat transfer coefficient is reduced to the solution of a Volterra integral equation of the second kind with a kernel having a singularity.     

Finite integral transforms for heat and mass transfer problems in nonstationary and inhomogeneous media

Several boundary-value problems of heat and mass transfer are solved for equations with varying coefficients.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 1, pp. 149–157, July, 1981.     

Numerical method of solving certain nonlinear boundary-value problems in heat and mass transfer

The gist of a numerical method of solving certain nonlinear boundary-value problems in heat- and mass-transfer theory is illustrated on an example of a one-dimensional such problem.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 24, No. 4, pp. 756–760, April, 1973.     

Proper Generalized Decomposition model reduction in the Bayesian framework for solving inverse heat transfer problems

In this paper, the proper generalized decomposition (PGD) is used for model reduction in the solution of an inverse heat conduction problem within the Bayesian framework. Two PGD reduced order models are proposed and the approximation Error model (AEM) is applied to account for the errors between the complete and the reduced models. For the first PGD model, the direct problem solution is computed considering a separate representation of each coordinate of the problem during the process of solving the inverse problem. On the other hand, the second PGD model is based on a generalized solution integrating the unknown parameter as one of the coordinates of the decomposition. For the second PGD model, the reduced solution of the direct problem is computed before the inverse problem within the parameter space provided by the prior information about the parameters, which is required to be proper. These two reduced models are evaluated in terms of accuracy and reduction of the computational time on a transient three-dimensional two region inverse heat transfer problem. In fact, both reduced models result on substantial reduction of the computational time required for the solution of the inverse problem, and provide accurate estimates for the unknown parameter due to the application of the approximation error model approach.     

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.     

Use of the method of integral relations to solve problems in ignition theory

The method of integral relations is used to solve an unsteady system of equations of thermal explosion. With the help of this method several problems of ignition theory are solved.     

Applicability of a one-dimensional conjugate scheme for solving nonstationary convection problems

A calculation of the nonstationary temperature of one-dimensional thermal sensors washed by a laminar water flow is performed on the basis of a numerical one-dimensional conjugate scheme. Results of the calculation are compared with experimental data for sensors of different thickness and different material.Ufa State Aeronautical Technical University. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 66, No. 3, pp. 281–285, March, 1994.     

Iterative approach to solving boundary-value problems of heat and mass transfer in reactive media

One possible approach is considered to simplifying the procedure of solving heat and mass transfer problems in reacting media.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 58, No. 5, pp. 836–842, May, 1990.     

An approximate method for solving the integral equation of transport theory

An approximate solution is given for one of the integral equations of transport theory, using the Pade method.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol.31, No.1, pp.111–115, July, 1976.