Begell House Inc.
Heat Transfer Research
HTR
1064-2285
32
1-3
2001
Use of the Method of Relative Correspondence in Heat and Mass Transfer and Combustion
7
10.1615/HeatTransRes.v32.i1-3.10
V. P.
Motulevich
Moscow Power Institute (Technical University), Russia
V. I.
Gudkov
Elektrogorsk Scientific Research Center on the Safety of Atomic Power Stations of the All-Russian Scientific Research Institute on Exploitation of Atomic Electric Power Stations, Elektrogorsk, Russia
Examples of an analysis of thermophysical processes accompanied, in particular, by chemical reactions are given on the basis of the method of relative correspondence. The method is based on the fact that use can be made of less accurate physical and mathematical models of the phenomenon can be used in determining relative values with the assigned degree of reliability than in determining absolute values. A furnace process of dust-like solid fuel (antracite dust coal) combustion in a flow with enrichment of primary air by oxygen and the process of fuel gasification by oxygen at atmospheric pressure are considered. Experimental and calculated data are compared.
Mathematical Simulation of Limiting Conditions of Material Burning under Microgravitation
8
10.1615/HeatTransRes.v32.i1-3.20
A. N.
Kirkorov
Moscow Physico-Technical Institute, Russia
Sergey G.
Cherkasov
Keldysh Research Center, Russian Space Agency Moscow, Russia
A model of homogeneous burning in the vicinity of a critical point of a combustible body in a free-stream flow containing an oxidizer is developed. The boundary-layer equations with account for kinetics of the reaction with the boundary conditions of balance of mass and energy on the surface of the burning body and with account for losses to radiation are used. The problem was reduced to the system of ordinary differential equations by the Howarth-Dorodnitsyn transforms. The system of equations "without regard for kinetics" of the reaction (diffusion burning) was obtained by the Schwab-Zeldovich transform. The systems of equations were solved numerically by the grid method. Limiting modes of burning "with account for kinetics" are compared to the results of calculation "without regard for kinetics" of the reaction. It is shown that a simplified system of equations can be used at small velocities of a free-stream flow. The dependence of the curve of limiting modes of burning for the problem "without regard for kinetics" of the reaction on determining parameters is studied and the relationship between these parameters is found.
Dynamics of Explosive Boiling of Toluene
8
10.1615/HeatTransRes.v32.i1-3.30
V. V.
Ovchinnikov
Kutateladze Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
B. P.
Avksentyuk
Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
We carried out experimental investigations of the dynamics of heterogeneous pool boiling of toluene. A platinum wire of diameter 100 μ;m and length 68 mm served as a working section. Nonstationary heating of the working section was used to attain high levels of the metastability of liquid. The working section was also used as a resistance thermometer to determine the temperature of the heat transfer surface. High-speed motion-picture photography of the processes investigated was made. The experiments were carried out at a pressure in the working volume from 1.6 kPa to 76 kPa and subcoolings from 4 K to 83 K. Comparison was made between the experimental data for the speed of the evaporation front with calculations made by the model suggested by the present authors earlier. The discrepancy did not exceed 15%.
Bubble Boiling of Emulsions with a Low-Boiling Disperse Phase
9
10.1615/HeatTransRes.v32.i1-3.40
N. V.
Bulanov
Institute of Thermophysics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
V. G.
Baidakov
Institute of Thermophysics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
B. M.
Gasanov
Institute of Thermophysics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
We suggest a model of the process of heat transfer from a solid surface to emulsions. On the basis of this model we obtained formulas for describing the heat flux density and bubble boiling crisis of emulsions. The formulas are checked on a multitude of experimental data on heat transfer from wires to water - oil and Freon-113 - water emulsions.
Impulse Superheating of the Solutions of Ethyl Alcohol with Water at Negative Pressures
7
10.1615/HeatTransRes.v32.i1-3.50
V. E.
Vinogradov
Institute of Thermophysics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
Pavel A.
Pavlov
Institute of Thermophysics, Ural Branch of the Russian Academy of Sciences, Amundsen Street
107a, Ekaterinburg, 620016, Russia
We carried out an experimental study of the boiling-up of ethyl alcohol, water, and of their solutions on impulse overheating on a thin platinum wire in the field of temperatures from 100 to 310°C and negative pressures of up to −10 MPa. We obtained the dependences of the temperature of the limiting overheating of liquid over a wire on the magnitude of the negative pressure. In the case of a pure alcohol (with the concentration of 96 vol. %) the limit of the attainable overheating of liquid (Tov(P)) continually passes from the region of positive to the region of negative pressures. The additions of water into ethanol cause a discontinuity of Tov(P) in transition to negative pressures towards a decrease in the temperature of the limiting overheating of liquid.
Experimental and Theoretical Investigation of the Process of Initiation of Vapor Explosion on a Solid Hemispherical Model. Part 1. Experiment
8
10.1615/HeatTransRes.v32.i1-3.60
Vasilii V.
Glazkov
Moscow Power Engineering Institute (Technical University), Russia
Vyacheslav G.
Zhilin
Incorporated Institute of High Temperatures (IIHI) of the Russian Academy of Science, 13/19 Igorskaya str., Moscow, Russia
Yurii P.
Ivochkin
Moscow Power Engineering Institute; and Joint Institute for High Temperatures of the Russian Academy of Sciences, Moscow, Russia
V. S.
Igumnov
Institute for High Temperatures, Russian Academy of Sciences, Moscow, Russia
Oleg A.
Sinkevich
Science Technological Center of Associated Institute for High Temperature, Russian Academy of Science and Moscow Power Engineering Institute (Technical University), Russia
Vladimir R.
Tsoi
Elektrogorsk Research and Engineering Center on Nuclear Plants Safely (ENIT's),Bezymyannaya ul., 6, Elektrogorsk, Moscowoblas t, 142530, Russia
V. G.
Shvets
Elektrogorsk Scientific-Research Center, Elektrogorsk, Russia
On a small-scale setup, we carried out investigations of the process of interaction of a heated solid hemispherical surface with water. We studied the processes of the development of instability and rupture of a vapor layer. As a measuring system we used fiber-optical transducers of pressure and of vapor-film thickness. Video filming of the process of the destabilization and rupture of a vapor film was made with subsequent computer processing of pictures.
Experimental and Theoretical Investigation of the Process of Initiation of Vapor Explosion on a Solid Semispherical Model. Part 2. Experiment
8
10.1615/HeatTransRes.v32.i1-3.70
Vasilii V.
Glazkov
Moscow Power Engineering Institute (Technical University), Russia
Vyacheslav G.
Zhilin
Incorporated Institute of High Temperatures (IIHI) of the Russian Academy of Science, 13/19 Igorskaya str., Moscow, Russia
Yurii P.
Ivochkin
Moscow Power Engineering Institute; and Joint Institute for High Temperatures of the Russian Academy of Sciences, Moscow, Russia
V. S.
Igumnov
Institute for High Temperatures, Russian Academy of Sciences, Moscow, Russia
Oleg A.
Sinkevich
Science Technological Center of Associated Institute for High Temperature, Russian Academy of Science and Moscow Power Engineering Institute (Technical University), Russia
Vladimir R.
Tsoi
Elektrogorsk Research and Engineering Center on Nuclear Plants Safely (ENIT's),Bezymyannaya ul., 6, Elektrogorsk, Moscowoblas t, 142530, Russia
V. G.
Shvets
Elektrogorsk Scientific-Research Center, Elektrogorsk, Russia
On the basis of the analysis of the experimental data, a physical model of the initiation of a vapor explosion has been developed. The following stages of the process of an explosion-like transition from a film to a bubble boiling on a semi-spherical model immersed in water are calculated: the incipience of the Kelvin-Helmholtz instability of a vapor film; growth of the instability amplitude and the collision of the crests of liquid waves with a surface; extension of the region of collisions due to the propagation of capillary waves generated in recoil; the cooling of the model of the temperature below the critical one and collapse of the vapor film; superheating of the surface layer of liquid that came in contact with the model and the expansion of the formed vapor layer resulting in the generation of a descending liquid jet. The estimates obtained demonstrate the qualitative and quantitative agreement with experimental results.
Evolution of a Vapor Cavity in Boiling of a Superfluid Helium
7
10.1615/HeatTransRes.v32.i1-3.80
A. A.
Gorbunov
Institute of the Problems of Mechanics, Russian Academy of Sciences, Moscow
I. M.
Dergunov
Moscow Power Engineering Institute, Russian Academy of Sciences, Moscow, Russia
Alexei P.
Kryukov
National Research University, Moscow Power Engineering Institute, Moscow 111250, Russia
We consider the growth and collapse of a vapor film in boiling of a superfluid helium (He-II). A mathematical description of the process is formulated. Examples of numerical solution of a system of conservation equations for liquid are given. Then the phenomena of transfer on the interphase surface are described by the methods of the molecular-kinetic theory. The effect of the magnitude of heat load, of the immersion depth of a heater and of the degree of account for dissipation processes in He-II on the results obtained is analyzed.
Heat Transfer in Boiling of Nonazeotropic Mixtures of Refrigerating Agents within a Horizontal Tube
7
10.1615/HeatTransRes.v32.i1-3.90
G. N.
Danilova
St. Petersburg State Academy of Cold and Foodstuff Technologies, Russia
V. G.
Bukin
Astrakhan State Technical University, Russia
V. F.
Shurshev
Astrakhan State Technical University, Russia
We present the results of an experimental investigation of heat transfer in boiling of the nonazeotropic mixture R22/R142b in the interior of a horizontal tube. The regimes of flow of a liquid-vapor stream in a tube are elucidated. It is found that the intensity of heat transfer depends on the regimes of flow and is determined by the mutual effect of bubble boiling and forced convection. The characters of the dependences of the heat transfer coefficients on the basic regime parameters in boiling of a mixture and of its components are qualitatively the same. The greatest discrepancies are observed in the region where bubble boiling prevails. It is found that a substantial effect on bubble boiling is exerted by mass transfer, with its maximum falling on the region with the concentration of R22 in liquid 0.30−0.40 kg/kg. The generalization of the obtained experimental results on heat transfer is made with account for the specific features of the bubble boiling of mixtures.
Experimental Investigation of Heat Transfer in a Cylindrical Tube Heated on One Side by Highly Dense Energy Beams
6
10.1615/HeatTransRes.v32.i1-3.100
Aleksey V.
Dedov
National Research University "Moscow Power Engineering Institute", Russia, 111250 Moscow, Krasnokazarmennaya str., 14
Alexander N.
Varava
National Research University "Moscow Power Engineering Institute", Russia, 111250 Moscow, Krasnokazarmennaya str., 14
Alexander T.
Komov
National Research University "Moscow Power Engineering Institute", Russia, 111250 Moscow, Krasnokazarmennaya str., 14
V. K.
Naumov
Russian Scientific Center "The Kurchatov Institute" Instituteof Nuclear Synthesis Moscow, Russia
S. A.
Shcheglov
Moscow Power Engineering Institute (Technical University), Moscow, Russia
We present the results of experimental investigations of heat exchanging in a cylindrical tube heated on one side by beams of charged particles (electrons) with a high density of thermal energy. Heat removal is made by a water stream, twisted by a screw insert, having the mass velocities in the range ρw = 1870−8900 kg/(m2·sec). The experiments were carried out on a fragment of the tube in the receiver of the beams of deviated ions in the system of injection of a T-15 tokamak. The bank of experimental data includes 510 points. It is shown that under the conditions of heat removal by the twisted flow with the coefficient of twisting k = 0.897 and subcooling ~170°C the density of the flux removed can attain ~100 MV/m2 in the case of long-pulse heating. It is noted that with the number of cycles of about 70 the fatigue destruction of the surface occurs.
Investigation of the Dynamics of Transition to Film Boiling of Nitrogen on High-Temperature Superconductors
8
10.1615/HeatTransRes.v32.i1-3.110
V. I.
Deev
Moscow Engineering and Physics Institute (State University), Moscow
K. V.
Kutsenko
Moscow Engineering and Physics Institute (State University), Moscow
A. A.
Lavrukhin
Moscow Engineering and Physics Institute (State University), Moscow
V. S.
Kharitonov
Moscow Engineering and Physics Institute (State University), Moscow
V. N.
Novikov
Moscow State Engineering Physics Institute (Technical University), Russia
Experimental data are given on a critical heat flux and dynamics of the development of heat transfer crisis in boiling of nitrogen on the surface of a cylindrical specimen made from high-temperature super conducting (HTSC) ceramics. On the basis of an approximate analytical model estimation of the velocity of propagation of film boiling over a heat generating surface of a current carrying element is made. The results of theoretical calculations are compared with experimental data.
The Interaction of a Liquid Nitrogen Jet with a Surface in Boiling
7
10.1615/HeatTransRes.v32.i1-3.120
Guenrikh A.
Dreitser
Department of Aviation-Space Thermal Techniques,
Moscow Aviation Institute, Volokolamskoe shosse, 4, Moscow, 125993, Russia
V. P.
Firsov
Moscow Aviation Institute (Technical University), Moscow, Russia
I. V.
Antyukhov
Moscow Aviation Institute (Technical University), Moscow, Russia
D. A.
Morozov
Moscow State Aviation Institute (Technical University), Russia
The work presents the results of experimental investigation of heat transfer in interaction of a liquid nitrogen jet 3 mm and 4 mm in diameter (the jet velocity is from 1.5 m/sec to 16.5 m/sec, the angle of flow impingement is 90°C) with a preliminarily heated (up to 450 K) copper and steel surface. The temperature of the liquid in the experiment was maintained equal to 77.4 K at atmospheric pressure. The results of visual observations showed that a jet before its incidence on a surface is continuous and the region of the interaction of the jet with a surface is stable and forms a spot of contact of diameter from one to five diameters of the jet.
The Kinetics of Boiling and the Limit of Attainable Overheating of a Well-Degassed n-Pentane
8
10.1615/HeatTransRes.v32.i1-3.130
G. V.
Ermakov
Institute of Thermophysics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
E. V.
Lipnyagov
Institute of Thermophysics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
B. M.
Smolyak
Institute of Thermophysics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
S. A.
Perminov
Institute of Thermophysics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
L. A.
Mikhalevich
Institute of Thermophysics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
R. B.
Nurbaev
Institute of Thermophysics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
The paper presents experimental data on the temperature dependence of the mean expectation time of the boiling-up of a strongly superheated liquid subjected to preliminary degassing. Basic parameters of the kinetic theory of homogeneous nucleation and the character of statistical distribution of the expectation time are estimated from experimental data. A conclusion is drawn about the inhomogeneous character of the boiling-up of a strongly superheated liquid and the necessity to improve the theory.
Experimental and Computational Investigations of Heat Transfer and Stability of Boiling Liquid Metal in a Model of an Array of the Fast-Neutron Reactor Fuel Elements
9
10.1615/HeatTransRes.v32.i1-3.140
A. D.
Efanov
State Scientific Center of the Russian Federation - Physical and Power Engineering Institute, 1 Bondarenko Sq., 249033, Obninsk, Russia
E. F.
Ivanov
State Scientific Center of the Russian Federation - Physical and Power Engineering Institute, Obninsk, Russia
V. P.
Kolesnik
State Scientific Center of the Russian Federation - Physical and Power Engineering Institute, Obninsk, Russia
O. A.
Korkhov
State Scientific Center of the Russian Federation - Physical and Power Engineering Institute, Obninsk, Russia
V. L.
Mal'kov
State Scientific Center of the Russian Federation - Physical and Power Engineering Institute, Obninsk, Russia
D. E.
Martsinyuk
State Scientific Center of the Russian Federation - Physical and Power Engineering Institute, Obninsk, Russia
K. S.
Rymkevich
State Scientific Center of the Russian Federation - Physical and Power Engineering Institute, Obninsk, Russia
A. P.
Sorokin
State Scientific Center of the Russian Federation - Physical and Power Engineering Institute, Obninsk, Russia
Galina Pavlovna
Bogoslovskaya
SSC RF "Institute of Physics and Power Engineering" Bondarenko sq. 1, Obninsk, Kaluga Region, 249033, Russia
The paper presents and analyzes experimental and calculated data on the boiling of a sodium-potassium heat carrier in an array of simulators of fuel elements in a loop with natural circulation which models the conditions of operation of a fast reactor in the regime of accidental cooling. At different mass flow rates of a heat carrier, three regimes of boiling were obtained: a stable (bubble) regime at the initial stage of boiling, then a pulsing (slug) regime which, on increase in the power supply, passed into the second stable (mist) regime of boiling.
A Table for Heat Transfer Coefficients in the Postcritical Region in the Case of Water Flow in a Tube (The Version of the Year 1997)
7
10.1615/HeatTransRes.v32.i1-3.150
A. D.
Efanov
State Scientific Center of the Russian Federation - Physical and Power Engineering Institute, 1 Bondarenko Sq., 249033, Obninsk, Russia
P. L.
Kirillov
State Scientific Center of Russian Federation−Institute for Physics & Power Engineering, 249033 Obninsk, Kaluga Region, Russian Federation
I. P.
Smogalev
State Scientific Center of the Russian Federation - Physical and Power Engineering Institute Obninsk, Russia
A. A.
Ivashkevich
State Scientific Center of the Russian Federation - Physical and Power Engineering Institute Obninsk, Russia
V.N.
Vinogradov
State Scientific Center of the Russian Federation - Physical and Power Engineering Institute Obninsk, Russia
V. V.
Sergeev
State Scientific Center of the Russian Federation - Physical and Power Engineering Institute Obninsk, Russia
The 1997-year version of the look-up table of the heat transfer coefficient values in the postcritical region in forced flow of water in uniformly heated tubes is presented for the following range of the parameters; pressure 4−20 MPa, mass velocity 250−2000 kg/(m2·sec), relative enthalpy (vapor content) −0.2−2.2, heat flux 0.2−1 MW/m2, diameter of a tube 10 mm.
Heat Transfer in Boiling of Liquid Films
8
10.1615/HeatTransRes.v32.i1-3.160
S. A.
Efimova
Moscow Power Engineering Institute (Technical University), Russia
Yu. M.
Pavlov
Moscow Power Engineering Institute (Technical University), Russia
The work is devoted to the heat transfer in boiling of films of various liquids formed by wetting a heat generating surface from a sprayer in the form of a capillary tube. A physical model of the incipience of a vapor phase in thin layers of liquid in the absence of thermal gravitational convection is presented and on its basis a computational relation is given for the temperature head in boiling-up ΔTs.b.. An interpolation dependence of ΔTs.b. on the height of the column (layer thickness) of liquid on a heat generating surface is suggested which makes it possible to estimate this parameter in the layers of liquid in which there is nondeveloped gravitational convection.
Specific Features of Hydrodynamics in Unsteady Boiling of Nitrogen in a Channel
7
10.1615/HeatTransRes.v32.i1-3.170
I. L.
Yarmak
Institute for High Temperatures of the Russian Academy of Sciences, Moscow
We present the results of photographic recording of a stepwise influence of a heat flux on liquid nitrogen in a vertical channel. We show that nonstationary boiling is accompanied by the formation and growth of vapor locks in the channel. The mechanism of the crisis of heat transfer is associated with the evaporation of a microlayer of liquid on the heat transfer surface under a growing vapor slug.
Boiling Crisis of Nitrogen in a Channel at Low Flow Rates and High Pressures
6
10.1615/HeatTransRes.v32.i1-3.180
Alexander V.
Klimenko
Moscow Power Engineering Institute (Technical University), Russia
Alexander M.
Sudarchikov
Moscow Power Engineering Institute (Technical University), Russia
V. V.
Klimenko
Moscow Power Engineering Institute (Technical University), Russia
We carried out an experimental investigation of the boiling crisis of nitrogen in a channel under the conditions of forced convection. The experiments were carried out at pressures of from 2.8 to 7.7 bar and comparatively moderate flow rates of the heat carrier. We investigated the effect of the channel diameter on the critical density of the heat flux. It is shown that an increase in the channel diameter leads to a decrease in the magnitude of the critical heat flux density qcr. Using the experimental data obtained for qcr, a modification of a fragment for the pressure of 7 bar in the table of recommended values of the critical heat flux density is made for boiling of a forced nitrogen flow in a vertical 8 mm-diameter channel for the region of high values of critical mass flow rate vapor content.
The Stability of Boiling Regimes on a Rod as a Function of Local Temperature Perturbations
8
10.1615/HeatTransRes.v32.i1-3.190
S. V.
Usatikou
Kuban' State Technological University, Krasnodar, Russia
S. A.
Kovalev
Institute of High Temperatures of the Russian Academy of Sciences, Moscow, Russia
We analyze the critical conditions for the initiation of the bubble boiling - film boiling replacement by a local site prescribed by a Π-like (finite) profile of temperature at the initial time instant. Using the direct Lyapunov method we obtained analytical expressions for the critical dimensions of the site and of the magnitude of perturbations in it for a one-dimensional problem. A satisfactory agreement of the obtained relations with numerical calculations and experimental data is shown.
Burnout Heat Transfer at Low Mass Velocities
8
10.1615/HeatTransRes.v32.i1-3.200
The paper considers the occurrence of burnout heat transfer in vertical channels at low mass velocities and pressures in a wide range of vapor contents. The change in the intensity of the pulsations of the working section wall temperature in the region of the burnout heat transfer is analyzed. The influence of the mass velocity and liquid subcooling on the characteristics of burnout heat transfer is discussed.
The Appearance of the Region of Deteriorated Heat Transfer for Water Solutions of Na2SO4 at Low Mass Velocities
6
10.1615/HeatTransRes.v32.i1-3.210
A. S.
Sedlov
Moscow Power Engineering Institute (Technical University), Russia
A. I.
Abramov
Moscow Power Engineering Institute (Technical University), Russia
Yu. A.
Shkondin
Moscow Power Engineering Institute (Technical University), Russia
D. V.
Buyakov
Moscow Power Engineering Institute (Technical University), Russia
P. V.
Serbin
Moscow Power Engineering Institute (Technical University), Russia
In recent time a greater attention is paid to the development of new technological processes of the preparation of additional water which makes it possible to repeatedly use waste water in the cycle of water preparation with the application of evaporators. This trend can be considered as the most important one in creation of wasteless technologies of water preparation at thermal electric stations [1, 2].
The Propagation Velocity of the Front of Film Boiling Center in Critical Regimes
7
10.1615/HeatTransRes.v32.i1-3.220
M. O.
Lutset
S. S. Kutateladze Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
Based on a nonlinear heat conduction equation with the temperature-dependent coefficients, a one-dimensional process of the propagation of the boundary of the center of a new boiling regime is considered in two limiting cases: for a maximum and for a minimum critical heat fluxes. The form of the heat transfer curve was assumed to be arbitrary in a reasonable degree. An accurate solution is obtained for the velocity of the propagation of the boundary. It turned out that there is a rigid coupling between the velocity of the motion of the boundary and intensity of heat transfer in a transient region. This means that the form of the heat transfer curve of transient boiling near critical heat fluxes determined the velocity for the motion of the boundary where the change of the regimes occurs. This is an interesting object for experimental investigation.
Regular Structures and Critical Heat Flux in Freely Falling Liquid Films
8
10.1615/HeatTransRes.v32.i1-3.230
Aleksandr N.
Pavlenko
Kutateladze Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences,
Novosibirsk, Russia
Viatcheslav Vladimirovich
Lel'
Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences, Russia
Experimental investigation is made of the conditions of the appearance and development of "dry" spots, critical heat fluxes and of heat transfer in film boiling of liquid nitrogen on a vertical heated surface of a plate. Experimental data are obtained for a variable Reynolds number in the incident liquid film at saturation within the range of from 10 to 2000. The limits of regime parameters are determined that separate the zones of liquid flow with different mechanisms of the occurrence of "dry" spots and of burnout heat transfer.