Nonstationary Heat Conduction Research Articles

Kinetic derivation of nonstationary general relativistic thermodynamics

Chernikov, who generalized Grad’s thirteen-moment method for an approximate formal solution of the Boltzmann equation to the case of the general relativistic Boltzmann equation (applicable also to a photon gas), did not exploit his formalism completely but developed the last eight moment equations for dissipation phenomena no further than a stationary theory. However, this stationary theory results in the possibility of the dissipation processes propagating with infinite speed, which is not acceptable. In this paper the complete Chernikov thirteen-moment approximation is developed to obtain nonstationary transport equations, providing linearized collision integrals, for heat and viscous stresses which lead only to finite dissipation speeds. The flux, density and entropy production and therefore the entropy-balance equation representing the second law of thermodynamics is approximated in terms of moments (and microscopic quantities) at the nonstationary level. An expression for entropy production is also deduced as a linear function of the collision integrals. Furthermore, the Gibbs equation, free energy and chemical potential are given in a nonstationary form. A linearized nonstationary heat-conduction equation is derived for a system in mechanical equilibrium without viscous stresses.

Some variational principles pertaining to non-stationary heat conduction and coupled thermoelasticity

In the first part of this paper, some restricted variational formulations for non-stationary and non-linear heat conduction are presented. The principles proposed are shown to be valid for isotropic as well as anisotropic solids with temperature dependent density, heat conductivity and specific heat. In the second part, two new variational principles for coupled thermoelasticity are proposed: these differ essentially from each other by the functions selected to be varied and by their range of application. The first principle is an extension of a general principle for purely dissipative processes, as presented by the authors in a previous paper, and uses, as functions to be varied, the temperature, the heat flux vector and the velocity field. This formulation is quite general in that the thermal and elastic coefficients may depend on the temperature. The second principle presented is inspired by the principle ofBiot: the functions to be varied are the temperature, the displacement field and the total heat flux vector ofBiot. The range of application of this formulation is limited to the case of constant thermal and elastic properties.

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.

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

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.

The investigation of nonstationary heat transfer by electric models

A device is discussed which can extend the potentialities of existing models and permit the solution of problems in nonstationary heat conduction with time-dependent boundary conditions of the third kind.

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.

Nonstationary heat conductivity of moist bodies

The temperature field of moist bodies in the form of a plate, a hollow cylinder, and a hollow sphere is analyzed for general boundary conditions of the third kind at the inner and outer surfaces.

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.

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.

One Problem in Nonstationary Heat Conduction

straight-through flow combustion chamber, can be extended, with some reservations, to include the process occurring in a ramjet combustion chamber. The presence of a set of stabilizers used in a real combustion chamber, stabilizers operating under identical conditions, does not prevent us from considering one of the elements, with a single stabilizer, as a simple straight-through combustion chamber. The most suitable scheme will indeed involve just such a flat element, for if the chamber has a row of concentric stabilizers, the ratio of the cross section of one chamber element to the length of the stabilizer periphery is quite small, and the curvature of the stabilizer can be neglected. The conclusions remain valid also in the case of a combustion process distributed in depth, although the calculation becomes more complicated in this case.