Problem Of Nonstationary Heat Conduction Research Articles

Nonstationary nonlinear heat-conduction problems

An exact analytical solution is constructed for the one-dimensional nonlinear nonstationary problem of heat conductivity with boundary conditions of the third kind.

Identification of time-variable coefficients of heat transfer by solving a nonlinear inverse problem of heat conduction

The solution of the inverse nonstationary problem of nonlinear heat conduction by using the method of optimal dynamic filtering is considered.

The localization of temperature perturbations in media with volume absorption of heat

THE SOLUTIONS of some non-stationary problems of non-linear heat conduction when there is volume absorption of heat, temperature dependent with a time-dependent coefficient, are considered. Conditions are found for which the effect of stopping of the temperature wavefront occurs, leading to the spatial localization of the temperature perturbations. The properties of the solutions obtained are investigated.

Nonstationary heat conduction in a half-space with an infinite number of cylindrical heat sources

The problem of nonstationary heat conduction is treated for a half-space containing an infinite number of cylindrical heat sources, and a boundary condition of the first kind at the surfaces. It is assumed that the radii of the sources are small in comparison with their spacing and the ordinate of the center.

On further development of the “method of large λ” in the theory of mixed prOBLEMS: PMM vol. 40, n≗ 3, 1976, pp. 561–565

The method of large λ [1], when the solution of the integral equations is represented as an asymptotic expansion in negative powers of some dimensionless parameter λ is used extensively, among the asymptotic methods of investigating the integral equations of the theory of mixed problems. As a rule only several terms of such an asymptotic expansion are constructed successfully. Certain types of integral equations of the second kind, for which a method is proposed for the construction of all terms of the asymptotic expansion, are investigated below by the method of large λ. The coefficients and expansions of the required solution in negative powers of λ are represented as polynomials in the main argument and recursion formulas are obtained for the coefficients of these polynomials. Considered as examples are the axisymmetric mixed nonstationary problem of heat conduction for a homogeneous half-space and the axisymmetric problem of elasticity theory for the torsion of a truncated sphere by a press.

An effective approach to the solution of two-dimensional heat-conduction problems for multiconnected composite bodies of complex shape

An algorithm to solve two-dimensional nonstationary heat-conduction problems for multiconnected bodies of complex shape, constructed on the basis of potential theory methods with preliminary application of the Rothe method in the time variable, is described. Results of computations are presented for a single- and multilayer strip with holes of arbitrary outline.

Results of numerical solutions of nonlinear problems of heat conduction in cases of annealing in liquid media

The paper gives the results of numerical solutions of nonlinear, partly linearized, and completely linearized nonstationary problems of heat conduction in a plate annealed in a liquid medium.

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.

Variational method of calculating a nonstationary temperature field

Varlational formulation is given of the nonstationary heat conduction problem for two bodies; its numerical solution by the finite-element method (FEM) reduces to the solving of simultaneous linear algebraic equations.

Inverse problem of heat conduction

We consider the one-dimensional inverse problem of nonstationary heat conduction and we analyze the physical and mathematical causes of instability in various forms of its solution.

Non-stationary problems of non-linear heat conduction with volume heat absorption

Non-stationary problems of non-linear heat conduction with volume heat absorption

The problem of the three-dimensional localization of thermal perturbations in the theory of non-linear heat conduction

SOLUTIONS are found for some non-stationary problems of non-linear heat conduction with volume absorption of heat. It is shown that in the cases considered an effect of the stopping of the temperature wave front occurs leading to a three-dimensional localization of the thermal perturbations.

On the solution of nonstationary heat-conduction problems with variable heat-transfer coefficient

The article describes an exact method for calculating the temperature field in solids when they are heated in a medium with a variable heat-transfer coefficient and a nonuniform initial temperature distribution.

Heat conduction with a temperature-dependent thermal conductivity coefficient

A variational method is employed to solve stationary and nonstationary heat conduction problems when the thermal conductivity coefficient is temperature-dependent and the heat generation function of the medium is arbitrary.

Application of a differential-difference method to the solution of a one-dimensional nonstationary two-layer heat conduction problem with a moving boundary

Application of a differential-difference method to the solution of a one-dimensional nonstationary two-layer heat conduction problem with a moving boundary

Application of a differential-difference method to the solution of one-dimensional nonstationary heat conduction problems with a moving boundary

We apply a differential-difference method to obtain an approximate solution of a nonstationary heat conduction problem with a moving boundary for a medium consisting of an unbounded plate (0≤x≤l) and a halfspace (l, <x<∞), possessing various thermophysical properties.

A solution of direct and converse two-dimensional problems of nonstationary heat conduction with variable boundary conditions using the method of transfer functions

A procedure is developed for determining transfer functions and by employing them to solve direct and converse two-dimensional problems of nonstationary heat conduction with variable boundary conditions for a hollow cylinder.

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.

Nonstationary heating of a conical rod

The Galerkin-Kantorovich method is used to obtain an approximate solution of the nonstationary problem of heat conduction for a thin conical rod.

The thermoelastic stresses in the walls of a reactor housing with internal sources of heat in nonstationary states

In nonstationary processes, the thermoelastic stresses arising at various critical points and parts of a reactor, working over a wide range of change in heat load, can exceed the stresses arising under stationary conditions. Therefore, to ensure reliable operation with changing loads, the rate at which these processes takes place should be limited. The geometric form of a number of the critical points may be reduced to the two usual configurations of plane and cylindrical walls. By solving the nonstationary heat conduction problem for plane and cylindrical reactor walls with internal heat sources, comparative results have been obtained for the thermoelastic stresses arising in walls of this sort during transitional processes.