Nonstationary (transient) radiative-conductive heat transfer in a plane layer of gray absorbing medium

The kinetics of the heating of a plane layer of gray absorbing medium by radiative-conductive heat transfer are considered. The nonstationary energy equation is reduced to a nonlinear integral equation by means of a Green's function, and this is solved numerically by the Newton method. The results of the solution are presented in the form of the temperature fields in the layer for various values of the defining parameters (optical thickness, radiative-conductive heat-transfer criterion, heat-transfer criterion at the boundaries).Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 156–159, January–February, 1972.     

Radiative-convective heat transfer in a plane layer of a selectively absorbing mist

This paper deals with the thermal field in a plane layer of selectively absorbing gas which has been injected into a steady turbulent stream of high-temperature gas flowing around a porous plate. The boundary-value problem in terms of the energy equation reduces to a nonlinear integral equation in terms of a dimensionless temperature, and this equation is solved numerically by the Newton-Kantorovich method. The results are presented on graphs of temperature and thermal flux in the absorbing gas layer as functions of the space coordinate. Such a problem has been analyzed in [1] for the case of an injected gray gas.Translated from Zhurnal Prikladnoi Mekhaniki i Technicheskoi Fiziki, No. 3, pp. 179–182, May–June, 1972.     

Transient radiative-conductive heat transfer in a flat layer of a selectively absorbing and radiating medium

Results of a numerical solution of the unsteady boundary-value problem of radiative-conductive heat transfer in a flat layer of a selective nonscattering medium with semitransparent mirrorreflecting boundaries are presented. This problem reduces to a nonlinear integral equation in the unknown temperature with the use of a Green function. The optical properties of the walls are shown to have a strong effect on the formation of a temperature field in the layer. The intensity of heating of the layer depends on the radiative fluxes to a greater extent than on the conductive fluxes. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 1, pp. 105–109. January–February, 1998.     

Spectrally dependent radiative transfer in a heat conducting medium

Coupled thermal radiation and heat conduction has been examined in a medium with a spectrally dependent mass absorption coefficient. This contrasts with prior studies in which semi-empirical total absorption correlations, having no connection with spectral characteristics, have been employed. Two spectral distribution functions were considered; the exponential and the uniform or gray. The former is a realistic model for molecular gases having both theoretical and empirical justification, while the latter is frequently employed despite its artificiality. The formulation is obtained in terms of exact expressions for the one-dimensional radiative transmission and absorption functions; other formulations of similar problems have approximated the angular integrations by the substitute kernel method. Results have been obtained for a wide range of parameters, considerably extending available results. Exponential and gray band results differ considerably in both a qualitative and a quantitative sense.     

Transient two-dimensional radiative and conductive heat transfer in an axisymmetric medium

This work considers transient conductive and radiative heat transfer in a two-dimensional, cylindrical, scattering medium heated or cooled by internal heat source or boundary surface. A finite difference scheme is employed for handling the energy storage and the heat diffusion by conduction, while a discrete-ordinate method is used to analyze the radiative heat transfer. The effects of various parameters, including the conduction-radiation parameter, the scattering albedo and the emissivity of the boundary surfaces, are investigated. Received on 30 April 1997     

Unsteady radiative-conductive heat transfer in a semitransparent selectively absorbing layer

Results of a numerical solution of the boundary-value problem of radiative-conductive heat transfer in a flat layer of a selectively absorbing and radiating medium are presented. The effect of the optical properties of the medium and the walls, the temperature of the source of radiation, and the relationship between the absorption spectra of the medium and the source of radiation on temperature distribution is studied. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 124–129, March–April, 2000.     

Simultaneous radiative and convective heat transfer in a variable porosity medium

 The flow of an incompressible grey fluid through a horizontal channel filled with a saturated medium of variable viscosity has been considered in this paper. Such flows in porous media have several applications in industrial processes. For the radiative effects a two flux model has been used in order to simplify the governing integro-differential equations for which closed-form solutions are not obtainable. The problem has been solved by employing a highly successful tri-diagonal, implicit, iterative, finite difference method. The effects of the pertinent parameters on the velocity and temperature distributions have been shown in several figures. Received on 6 December 1999     

Radiative heat transfer in an emitting,absorbing, and scattering compressed layer

The aim of the paper is to investigate the screening of radiation from the high-temperature part of the compressed layer by the two-phase ablation products of a graphite axisymmetric body moving under the following conditions through a hypersonic air flow: V = 12–18 km/sec, p_s = 10⁵ Pa, R = 1–3 m, and /₀ = (2.54–5.73)·10^–4. Steady and unsteady sublimation regimes of graphite ablation with strong blowing are considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 94–103, March–April, 1984.     

Transient couple heat transfer in an absorbing rectangular medium with one semitransparent diffuse boundary

This paper studies 2-D transient coupled radiative and conductive heat transfer in an absorbing non-scattering rectangular medium. The medium have one diffuse semitransparent boundary, and the other three boundaries are black. The reflectivity of the diffuse semitransparent boundary is determined by integrating the reflected energy over the whole hemispherical space according to the Fresnel’s reflective law and Snell’s refractive law based on assuming each bit of the rough surface to be optically smooth.     

Convective heat transfer in a locally heated plane incompressible fluid layer

The problem of convection in a plane horizontal layer of incompressible fluid with rigid boundaries when the temperature is constant on the lower boundary and has a parabolic profile on the upper boundary can be reduced to solution of a system of time-dependent one-dimensional equations. An analytic solution of the problem is obtained directly at the extremum point. Together with the wellknown solutions which describe heat transfer for the linear temperature distribution on the boundaries, the results obtained make it possible to calculate the heat flux through a thin slit for an arbitrary given heating of a thin fluid layer between heat-conducting bodies.     

Attenuation of forced weak plane pressure waves in a gas with radiative heat transfer

This paper considers the effect of radiative heat transfer on the propagation of forced plane harmonic pressure waves of small amplitude in an infinite emitting-absorbing inviscid nonconducting gas. The radiative pressure and radiative energy are neglected. The purpose of this paper is: a) to construct a theory based on the exact directional distribution of the total (frequency-integrated) specific intensity and to use this theory to calculate the parameters of the wave motion, b) to compare the exact theory with results obtained on the basis of the direction-averaged equation of radiative transfer [1] so as to estimate the errors introduced by various directional approximations and to demonstrate the importance of the anisotropy of radiation in radiation gasdynamics.In the linear theories of Stokes, Rayleigh, Kirchhoff, and Langevin the problem of wave attenuation is separated into special cases, in each of which only one single process is considered. This separation is admissible when to the first approximation the effects of the different dissipation mechanisms (viscosity, thermal conductivity, radiation, etc.) are additive. When only one factor is considered the problem becomes much simpler and the results are more amenable to physical interpretation, and these results can then be used in the solution of the complete problem.     

Radiative and convective heat transfer in a plane layer of absorbent curtain

An examination is made of the thermal state of a plane layer of gray gas injected into a turbulent stream of high temperature gas flowing over a permeable flat plate.Similarity-type formulations of problems are encountered both in examination of flow near a stagnation point, and also in analysis of the lifting of the boundary layer by intense injection through a porous plate [1]. The examination described relates to the following idealized formulation of the problem (Fig. la).In a plane layer of gray absorbing medium, formed by plane-parallel diffusely radiating surfaces (1-porous plate; 2-boundary of high temperature turbulent gas stream), heat transfer is accomplished by radiation and convection of the layer normal to the surfaces and by molecular heat conduction. All the physical and optical properties of the medium and of the boundary surfaces are assumed to be constant, independent of temperature.The temperature of the wetted surface of the specimen and also that of the fictitious surface determining the upper bound of the lift-off region, are given.Also assumed given is the velocity of the injected medium, which is constant throughout the entire lift-off layer. This idealization appreciably facilitates our examination without in principle changing its features.A very simplified examination of this problem was given in [2]. The special case of a medium with low optical thickness was examined in [3,4].The problem was examined in [5] under the assumption that molecular heat conduction in the medium is negligibly small.In the formulation considered the generalized energy equation has the form     

Combined heat transfer in a boundary layer of a selectiviely absorbing medium on a permeable plate under the conditions of intense radiation heating

Results of a numerical study of unsteady radiative-convective heat transfer in a boundary layer on a thermally thin permeable plate in the presence of intense radiation heating from outside are reported. The conjugate formulation of the problem takes into account the thermal interaction between the plate and an external gas flow. We consider a turbulent flow of an emitting-absorbing medium with the selective character of absorption. Calculation results are analyzed with a view for clarifying the influence of the governing parameters, namely, the relative temperature of an external radiation source, the Stark number, and the injection parameter. The possibility of inversion of a convective heat flux on the plate under the conditions of high-level external radiation is found. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirisk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 5, pp. 126–133, September–October, 1998.     

Boundary layer and heat transfer in a two-phase gas-evaporating droplet medium

An asymptotic model of the flow in the laminar boundary layer of a gas-evaporating droplet mixture is constructed within the framework of the two-continuum approximation. The case of evaporation of the droplets into an atmosphere of their own vapor is examined in detail with reference to the example of longitudinal flow over a hot flat plate. Numerical and asymptotic solutions of the boundary layer equations constructed are found for a number of limiting situations (low droplet concentration, no droplet deposition, significant droplet deposition). The development of the flow with respect to the longitudinal coordinate is studied and it is shown that in the absence of droplet deposition a region of pure vapor may be formed near the surface. Similarity criteria are established and the mechanism of surface heat transfer enhancement is studied for a low evaporating droplet concentration in the boundary layer. In the inertial deposition regime the results of calculating the integral heat transfer coefficient are found to correspond with the experimental data [1].Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 42–50, May–June, 1992.     

The moving, plane heat source in an elastic medium

Summary This note presents an exact solution for the stress and displacement field in an unbounded and transversely constrained elastic medium resulting from the motion of a plane heat source travelling through the medium at constant speed in the direction normal to the source plane.Nomenclature mass density - diffusivity - thermal conductivity - Q heat emitted by plane heat source per unit time per unit area - speed of propagation of plane heat source - shear modulus - Poisson's ratio - T temperature - _x, _y, _z normal stress components - u _x, u_y, u_z displacement components - c speed of irrotational waves - t time - x, y, z Cartesian coordinates - =x–vt moving coordinate