On the solution of stationary problems for the thermal conductivity of heat-sensitive bodies in contact

Popovich, V. S.

doi:10.1007/bf01097230

Cited by 6 publications

(5 citation statements)

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“…Let us construct the solution of the problem of heat conduction (1), ( 3), (4) by the method proposed in [8,10,12,13]. It assumes the following: 1°.…”

Section: Construction Of the Solution Of The Problem Of Heat Conductionmentioning

confidence: 99%

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Quasistatic thermal stresses in a thermosensitive layer under convective heat exchange with media of time-varying temperature

Popovych

Yanishevsky

2012

J Math Sci

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We have tested the method of linearizing parameters for the determination of temperature fields in thermosensitive structural elements by the example of the determination of a temperature field in a thermosensitive layer through the surfaces of which convective heat exchange with an environment of timevarying temperature occurs. The components of the stress-strain state caused by the found temperature distribution have been determined and investigated.

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“…Let us construct the solution of the problem of heat conduction (1), ( 3), (4) by the method proposed in [8,10,12,13]. It assumes the following: 1°.…”

Section: Construction Of the Solution Of The Problem Of Heat Conductionmentioning

confidence: 99%

“…To solve problem ( 8)- (10) with the linear boundary condition (11) (instead of the nonlinear condition ( 9)), we use Laplace transformation [20] with respect to the variable Fo .…”

Section: Construction Of the Solution Of The Problem Of Heat Conductionmentioning

confidence: 99%

Quasistatic thermal stresses in a thermosensitive layer under convective heat exchange with media of time-varying temperature

Popovych

Yanishevsky

2012

J Math Sci

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“…On s It was shown in [5][6][7][8] that when the coefficient of thermal conductivity depends linearly on the temperature…”

Section: ~0[ +Cl(t(o)ls_tm)=omentioning

confidence: 99%

“…Numerical computations carried out for a layer of U12 steel with t~ = 20"C, t m = 700"C, t o = 700"C, Bi = 1, L, (t) = 475(1 -0.37 T) W/m-deg [8] are shown in the table. The solution of the system (20) is denoted t .…”

Section: [9]mentioning

confidence: 99%

Solution of nonstationary heat-conduction problems for thermosensitive bodies under convective heat exchange

Popovich¹,

Garmatii²

1998

J Math Sci

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We propose a technique for solving nonstationary heat-conduction problems for thermosensitive bodies with simple nonlinearity (the coefficients of thermal conductivity and the heat capacity per unit volume depend on temperature, but the coefficient of thermal diffusivity is constanO heated by convective heat exchange from the surrounding medium.Nonlinear heat-conduction problems for thermosensitive structural elements made of materials whose coefficient of thermal conductivity ~,, and heat capacity per unit volume c, depend on temperature in such a way that their ratio, the coefficient of thermal diffusivity a, is constant, can be completely linearized using the Kirchhoffvariable [lO] in the case when the temperature or heat flux is prescribed on the surface. We consider a method of solving nonstationary problems when convective heat exchange occurs across the entire surface or part of it and the Kirchhoff variable linearizes the heat-conduction problem only partially.Suppose a thermosensitive body is heated by sources arbitrarily distributed over its volume with density W(x, y, z, "0, and by the surrounding medium, from which heat exchange across the boundary S of the body occurs according to Newton's law. Then the temperature of the body is determined from the heat equation Here t,. is the temperature of the medium surrounding the surface S, or, is the coefficient of thermal emission from this surface, t i is the initial temperature of the body, and n is the exterior normal to the surface.We introduce the notation T = t/t o , and we write the coefficient of thermal conductivity and the heat capacity per unit volume of the material of the body in the form L, (t) = ~o L; (T), c,(t) o . = c, c, (T). Here t o isthe base temperature, Z~ and c o are quantities having dimensions, and the superscript 9 denotes the corresponding dimensionless quantities F = ~,;(T)dT.(3) ri We reduce the problem (1), (2) to the forms.where T(0) is the temperature expressed in terms of the Kirchhoff variable (3). Hence, the original problem has been partially linearized: the heat-exchange condition (5) contains the nonlinear expression for the temperature T(0) on the surface S. Let us assume that the value of the temperature

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“…As a result, the nonlinear convective heat exchange condition on  becomes linear. However, it has been shown in (Kushnir & Popovych, 2009;Popovych, 1993b;Popovych & Harmatiy, 1996) that this unsubstantiated linearization leads to the numerically or physically incorrect results. In our case, when we take into account the radiation constituent (which is nonlinear even for a non-thermosensitive material) and dependence of the heat transfer coefficient and emittance on the temperature, the considered substitution does not provide the complete linearization of the condition (11).…”

Section: Introductionmentioning

confidence: 99%

Heat Conduction Problems of Thermosensitive Solids under Complex Heat Exchange

Кушнір¹,

Popovych²

2011

Heat Conduction - Basic Research

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On the solution of stationary problems for the thermal conductivity of heat-sensitive bodies in contact

Cited by 6 publications

References 0 publications

Quasistatic thermal stresses in a thermosensitive layer under convective heat exchange with media of time-varying temperature

Quasistatic thermal stresses in a thermosensitive layer under convective heat exchange with media of time-varying temperature

Solution of nonstationary heat-conduction problems for thermosensitive bodies under convective heat exchange

Heat Conduction Problems of Thermosensitive Solids under Complex Heat Exchange

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