Stability of a supersonic boundary layer on a permeable surface with heat transfer

The effect of cooling of a permeable surface on the stability of a supersonic boundary layer on it is investigated. As distinct from the case of an impermeable surface, deep cooling can reduce the critical Reynolds number. Common points of the continuous and discrete spectra are found in the region of the disturbance parameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 41–46, January–February, 1977.The work was carried out at the Department of Applied Mathematics of the University of Western Ontario in Canada. I am grateful to the Head of the Department Professor J. Blackwell for suggesting the investigation of this problem.     

On radiative heat transfer in a plane layer of an absorbing medium

Recently there has arisen increased interest in the study of radiative heat transfer between geometrically simple systems, both as autonomous problems and as elements of more complex problems.Problems of this kind have been treated by many authors [1–111 who have considered gray, diffusely emitting and absorbing boundaries and gray nonscattering media. In most cases these investigations were restricted either to the derivation of approximate formulas for the net radiative flux, without an exact analysis of the temperature distribution in the layer [5–7], or to numerical computation [1–4], In the latter case, with the exception of [8], which contains a numerical analysis for the case of optical symmetry, no attempt was made to analyze the effect of the optical properties of the boundaries on the temperature field in the layer.These papers can be divided into two groups according to the method of analysis used. The first group includes papers based on the integral equations of radiative transfer, with the corresponding integral analytical methods [1, 2], Similar in nature are [3, 4] which use the slab method, applicable to electrical-analog computation, as well as a recent paper [8] based on probability methods.The second group of papers [5–7] is based on the so-called differential methods. Of particular interest is [7], which develops these methods to an advanced degree. In several papers the problem of radiative transfer is analyzed in conjunction with more complex problems (cf., e.g. [10, 11]).In the present work we shall attempt to carry out an approximate analytical study of problems connected with radiative heat transfer in a plane layer of an absorbing, emitting, nonscattering gray medium with temperature-independent optical properties. The layer is bounded by two parallel, diffusely emitting and diffusely reflecting, isothermal, gray planes.The paper presents the fundamental formulation of the problem, which consists in: (a) the determination of the net heat flux on the basis of given temperature distribution (direct formulation), and (b) the determination of the temperature distribution on the basis of given distribution of the net radiative heat source per unit volume and boundary temperatures (inverse formulation). The analysis is based on integral methods appropriate to the integral equations which represent the net total and hemispherical radiation flux densities [12].The author would like to thank S. S. Kutateladze for his interest in this work.     

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.     

Turbulent heat transfer in a flat plate boundary layer disturbed by a cylinder

Augmentation of heat transfer from a flat plate using a turbulence promoter has been studied. A circular cylinder 8 mm in diameter was placed in the turbulent boundary layer detached from the flat plate. It was located parallel to the plate and perpendicular to the flow direction. Clearance, c, between the cylinder and the flat plate was varied in nine steps: c=0, 1, 2, 3, 4, 6, 11, 20 and 29.5 mm. Measurements were made of the local heat transfer coefficients, mean velocity profiles, turbulence intensity profiles, static pressure and skin friction. Experimental results showed that the heat transfer deterioration which occurs just downstream of the cylinder at c=0 mm can be removed by displacing the cylinder a small distance from the wall. The improvement in heat transfer is mainly due to the unsteadiness of the recirculating flow on the plate and the effect of intense turbulence arriving at the near wall region from the lower shear layer of the cylinder wake. Heat transfer augmentation is most effective when c=4 mm and becomes less effective when c is increased more than 6 mm. The enhancement disappears far downstream from the cylinder.     

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.     

Displacement in the turbulent boundary layer on a permeable plate with supercritical injection

The displacement thickness in a turbulent boundary layer is determined for supercritical injection parameters. Experimental relations between the displacement thickness and the injection parameter are obtained for air, helium, and freon-12 injected into air.     

Turbulent boundary layer with positive pressure gradient on a permeable surface under nonisothermal conditions

It is known that the longitudinal pressure gradient can exert a strong influence on the friction law and the characteristics of a dynamic turbulent boundary layer. The thermal and diffusion boundary layers are more conservative to the effect of the pressure gradient, and, hence, methods of analyzing them are based, in the majority of cases, on the hypothesis of conservativity of the heat- and mass-transfer laws to the longitudinal pressure gradient [1]. This hypothesis is verified by experimental results [2, 3] on heat transfer on an impermeable surface in a turbulent stream with positive pressure gradient under almost isothermal conditions. However, such investigations under nonisothermal conditions are practically nonexistent. An approximate theoretical analysis of the heat transfer in a turbulent boundary layer of a nonisothermal stream with a positive pressure gradient is given in this paper. Experimental results are presented. The experimental investigation was conducted in a burned-out graphite diffuser both with and without injection of an inert gas through the wall.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 43–49, July–August, 1976.     

Visco-elastic boundary layer flow past a stretching plate with suction and heat transfer

In this paper the study of visco-elastic (Walters' liquid B model) flow past a stretching plate with suction is considered. Exact solutions of the boundary layer equations of motion and energy are obtained. The expressions for the coefficient of skin friction and of boundary layer thickness are obtained.     

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.     

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.     

Effect of heat flux on boundary layer flow under rotating conditions

The boundary layer flow behaviour in a smooth rotating channel with heated walls is measured by particle image velocimetry (PIV). To simulate the real operation environment of an internal coolant channel in a turbine blade, airflow is analysed in a rotating channel, whose four walls are uniformly heated by Indium Tin Oxide (ITO) glass. The flow is measured in the middle plane of the rotating channel with a Reynolds number equal to 10000 and rotation numbers ranging from 0 to 0.52. The results are presented for the boundary layer flow behaviour with and without heated thermal boundary conditions. The buoyancy force generated by the heated walls influences the flow behaviour under rotating conditions. Separated flow occurs, which substantially influences the turbulent flow behaviours. Sometimes, this buoyancy force can determine the flow behaviours. The results also showed that the displacement thickness and the momentum loss thickness present new changes at different radius positions due to the heated thermal boundary conditions. The displacement thicknesses of both the leading and trailing sides with heated walls are both thicker than those of the leading and trailing sides without heated walls. Then, the difference of the boundary layer thickness between these two cases increases with the increase of rotation number. For momentum loss thickness, a sharp drop happens when the rotation number increases to a certain value. At the large radius position, the drop in momentum loss thickness is much greater than that in the small radius position.     

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.     

Similarity conditions for heat transfer in incompressible two-dimensional laminar boundary layer flow

Summary Similarity conditions are presented for the solution of some problems of heat transfer in incompressible two-dimensional boundary layer flow. The treatment holds for forced convection as well as for free convection. For free convection no a priori restriction is made with respect to geometry or temperature distribution of the solid surface. For forced convection the treatment is restricted to uniform bulk flow parallel to a flat surface of non-uniform temperature or heat flux. The results are summarized in some tables that facilitate comparison with older work.     

Turbulent boundary layer on a permeable surface

Several theoretical [1–4] and experimental [5–7] studies have been devoted to the study of the effect of distributed injection of a gaseous substance on the characteristics of the turbulent boundary layer. The primary study has been made of flow past a flat plate with gas injection. The theoretical methods are based primarily on the semiempirical theories of Prandtl [1] and Karman [2].In contrast with the previous studies, the present paper proposes a power law for the mixing length; this makes it possible to obtain velocity profiles which degenerate to the known power profiles [8] in the case of flow without blowing and heat transfer. This approach yields analytic results for flows with moderate pressure gradient.Notation x, y coordinates - U, V velocity components - density - T temperature - h enthalpy - H total enthalpy - c mass concentration - , , D coefficients of molecular viscosity, thermal conductivity, diffusion - c_p specific heat - adiabatic exponent - r distance from axis of symmetry to surface - boundary layer thickness - U velocity in stream core - friction - c_f friction coefficient - P Prandtl number - S Schmidt number - S_t Stanton number - M Mach number - j=0 plane case - j=1 axisymmetric case The indices 1 injected gas - 2 mainstream gas - w quantities at the wall - core of boundary layer - 0 flow of incompressible gas without injection - v=0 flow of compressible gas without injection - ^* quantities at the edge of the laminar sublayer - quantities at the initial section - turbulent transport coefficients