Nonstationary Heat Conduction Research Articles

Eddy current loss calculation in thin rectangular plates at cryogenic temperatures and its experimental verification

Eddy current losses in conducting plates placed in a non-uniform alternating magnetic held at cryogenic temperatures have been calculated taking into account temperature dependencies of resistivity, heat capacity and heat-transfer coefficient. The calculation method is based on a coupled solution of a quasi-stationary electromagnetic problem and a non-stationary heat-conduction equation. A simplification of the task is achieved by neglecting eddy current reaction and free space charge. In this case the problem is solved in two stages: (1) the calculation of electromagnetic field; (2) the determination of a temperature distribution in the plate. As the first boundary condition for heat-conduction equation it is assumed that the heat transfer from edges of the plate equals zero. The second boundary condition is determined as a solution of the integral equation describing the law of conservation of energy relevant to the plate. The nonlinear two-dimensional heat conduction equation has been solved using partition of coordinates, implicit difference approximation and modified Thomas algorithm for obtained finite-difference equations. The numerical results remain in good agreement with data obtained by means of an experimental model of the cryogenic device, while neglecting thermal processes results in substantial errors amounting up to several hundreds percent. >

Nonstationary heat transfer in multilayer anisotropic shells of revolution

On the basis of the variational principle of “least scattering” in nonequilibrium thermodynamics we obtain an approximate equation and boundary conditions describing the process of nonstationary heat conduction in multilayer anisotropic shells of arbitrary shape. The structure of the equation obtained is independent of the number of layers and the types of boundary conditions. We give an example of the computation of a one-dimensional nonstationary temperature field for an infinite hollow homogeneous cylinder.

The Green's function method in stationary and nonstationary nonlinear heat-conduction problems

By constructing the Green's function we reduce quasilinear boundary-value problems for second-order parabolic and elliptic equations to nonlinear integral equations of second kind. The method is illustrated using the examples of the stationary and nonstationary heat-conduction problems in the case of radiant heat transfer.

Application of thermal potentials to solving heat conduction problems in a layer

We solve the boundary-value problem of nonstationary heat conduction in a layer between parallel planes by joint application of Fourier-Laplace integral transforms and thermal potentials. A relationship is established between the original multidimensional problem and some special one-dimensional problem of nonstationary heat conduction, which is solved numerically. As a result, we obtain a solution of the original multidimensional problem of heat conduction which can be conveniently used in practical calculations.

Calculation of nonstationary heat conduction in multilayer objects with boundary conditions of the third kind

Some aspects of the calculation of nonstationary heat conduction in multilayer objects with boundary conditions of the third kind are considered. The homogeneous problem with inhomogeneous boundary conditions is solved for the one-dimensional case. The proposed solution has an explicit form and may be useful in numerical calculations due to the recurrence representation of the basic relations.

The inverse coefficient problem of heat conduction for an isotropic body

We discuss a method for determining the complex of thermophysical characteristics of isotropic materials based on the solution of the two-dimensional nonstationary heat conduction problem for a layer subject to a narrow-band heating by a heat flow. We take account of the finite speed of thermal action of an annular heater.

Method of analysis of stochastic nonstationary heat conduction equations

A method is proposed for determination of nonstationary fields of mathematical expectation, second moments, and dispersion of a stochastic nonstationary temperature field for inhomogeneous bodies of an arbitrary form and dimension with arbitrary stochastic boundary conditions.

Theoretical fundamentals of the method for thermal diffusivity measurements from auto-oscillation parameters in a system with a thermal feedback

Theoretical fundamentals of the method to determine thermal diffusivity from auto-oscillation parameters in a control system, CS, with thermal feedback through the test specimen, are developed. The equation of a CS with a flat specimen and proportional controller (nonlinear boundary value problem of nonstationary heat conduction) is considered. Periodic solutions of the boundary value problem, which is linearized in the vicinity of the stationary solution, are analyzed. It is proved that, with a certain value of CS gain factor, excitation of auto-oscillations occurs. Their frequency ωc is related to the thermal diffusivity α as α = Cωc, where C is constant. By nonlinear analysis, it is revealed that the auto-oscillation excitation mode is soft and the frequency depends on the gain factor to a very weak degree. Formulas for calculation of the thermal diffusivity and the specimen temperature field are obtained.

The isotherms migration method in the theory and practice of heat and mass transfer investigation—II. Numerical-analytical determination of temperature fields

The equation of the process of non-stationary heat conduction in solid bodies—a new equation of mathematical physics—is found for a multidimensional case of the migration of isothermal surfaces. The analysis of the existence and of the uniqueness of the solution of the first boundary value problem for the above equation is given. The application of the method of perturbations in the kinematic description of heat conduction to the solution of problems with temperature-dependent thermophysical properties of the medium is shown. The finite difference approximation of the new heat conduction equation by the boundary value and explicit schemes is found and the stability condition of the latter is substantiated. Using these schemes an algorithm is developed to determine the temperature fields and location of the interface between new and old phases by a computer.

Non-stationary heat conduction of a porous medium

The thermal diffusion process is examined for a porous sample with idealized arrangement and form of the pores, when its surface is illuminated by a modulated light. A formula for the frequency dependence of the average surface temperature is derived. It is shown that it depends on the porosity, the form of the pores, and the ratio between a characteristic pore size and the thermal wavelength. In the limiting cases of low frequency of modulation and low porosity the results agree well with those quoted in the literature. The frequency dependence of the surface temperature of a microporous rubber sample, glass filtering crucibles, and leather samples have been measured by a PA cell and compared with the analytical results. The influence of various processes on the heat diffusion in porous media is discussed.

Variational formulation of a nonstationary heat-conduction problem

Variational formulation of a nonstationary heat-conduction problem

Computational coupled non-associative thermo-plasticity

Computationally oriented formulation of the isothermal, rate-independent theory of non-associative elasto-plasticity is extended in this paper to describe coupled thermo-elastic-plastic and thermo-elastic-visco-plastic behaviour of materials. This is done by additionally considering thermal strains, assumming all material properties to be temperature dependent and accounting for the mechanical coupling terms in the non-stationary heat conduction equation. The finite deformation effects are included in the analysis. The theory is employed for the analysis of thermo-mechanical response of ductile metals with damage effects modelled by a generalization of the so-called Gurson approach. This constitutive model is known to generate equations typical of non-associative plasticity and hence it can be consistently incorporated into the present more general considerations. The finite element assessment of combined thermal and damage effects on the axisymmetric necking process illustrates the paper. Numerical aspects such as a ‘tangent’ stiffness for rate-dependent thermo-plasticity and the algorithmic (or consistent) tangent stiffness matrix for non-associative plasticity are discussed as well.

Application of dirichlet and neumann problems in connection with studies of nonstationary heat conduction

Regularities in the development of three-dimensional nonstationary temperature fields in semi-bounded iso- and orthotropic media are deduced under discontinuous boundary conditions of the first or second kind, given in the most general form.

Estimation of the solidification front occuring on resin molding of IC and the evaluation of warping of the moldings.

The state-dependent variable a was introduced to the formula of the rate of heat evolution deduced from the thermal analysis of the molding compounds. The a was determined by the inverse solution of the FEM for temperatures measured. The variation of a is expressed as a function of time after the end of the filling process on the basis of the conversion of resin. The temperature profiles in the mold cavity after the end of filling were calculated using the FEM coupled with the a. Making use of the a in the calculations, the solidification front is estimated by the analysis of non-stationary heat conduction. The relationship between molding temperature and warping of the moldings was evaluated on the basis of the variation mode of a. The fundamental data used to estimate the relation between molding temperature, soldification front and warping of the moldings were obtained.

Solution of a two-dimensional equation of nonstationary heat conduction for orthotropic cylindrically bounded media

Analytical relationships are presented to determine two-dimensional (2-D) nonstationary thermal fields in a bounded orthotropic cylinder for various boundary conditions. The solution obtained generalizes a wide class of eighty boundary-value problems of nonstationary heat conduction in studies of heat exchange in the bodies being considered.

ＩＣ樹脂封止材の凝固解析 金型キャビティ内充てん後の温度解析

This report describes a method for the estimation of the curing process of thermosets used for plastic-encapsulated ICs. This method consists of a thermal analysis by the differential scanning calorimetry (DSC) and an analysis of non-stationary heat conduction using the finite element method (FEM) coupled with the rate of heat evolution. The formula of the rate of heat evolution deduced from the DSC data could not be directly applied to the analysis because the thermodynamic conditions in DSC were not exactly the same as that in molding process, so that a state-dependent variable α were newly introduced to correct the formula. The temperature profiles at four positions in the cavity during cure were measured with CA-thermocouples. The α was determined by inverse solution of the FEM with the measured temperatures. The obtained variation of α is expressed by a function of time after the end of filling process and the conversion of resin. With making use of the α in the calculations of temperature, the predicted temperature profiles compare reasonably well with the experimental results. It is found that this method gives propriety of curing analysis including the effect of process parameters of α to estimate the solidification front.

Heat transfer in intensive nonstationary processes

A theory is exposed of intensive nonstationary heat-conduction processes, based on energy transfer mechanisms by means of carriers, emitted and absorbed by particles of the material. Results are provided of solving the integrodifferential transport equation by a difference method.

Exact solution of a nonstationary convective heat-exchange problem in a two-dimensional channel

Degenerate hypergeometric functions are employed to give an exact solution of a nonstationary convective heat-conduction problem for an established laminar flow of a viscous incompressible fluid in a plane-parallel layer.

Local heating of an anisotropic body by a circular heat source

The solution and analysis of the two-dimensional nonstationary heat-conduction problem are presented for an anisotropic (orthotropic) body heated by a circular heat source.

The well-posed nature of the problem of determining an unknown boundary of a domain in a similarity regime

The necessary and sufficient algebraic conditions are found for the existence of a solution of the boundary value problem for the quasilinear, non-stationary heat conduction equation with an unknown moving domain boundary under the condition that it is a similarity process. A uniqueness theorem is proved and the convergence of the iterational method is established.