Conductive heat transfer (lat. conduce, conductum to reduce, connect) T. by conducting heat to (or from) the surface of any solid body in contact with the surface of the body.
Large medical dictionary. 2000 .
Heat transfer due to the combined transfer of heat by radiation and thermal conductivity... Polytechnic terminological explanatory dictionary
radiation-conduction heat exchange- - [A.S. Goldberg. English-Russian energy dictionary. 2006] Topics: energy in general EN heat transfer by radiation and conduction ... Technical Translator's Guide
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It is carried out due to the collision of molecules, electrons and aggregates of elementary particles with each other. (Heat moves from a more heated body to a less heated one). Or in metals: gradual transfer of vibrations of the crystal lattice from one particle to another (elastic vibrations of lattice particles - phonon thermal conductivity).
Convective transport;
This transfer is associated with the movement of fluid particles and is caused by the movement of microscopic elements of substances; it is carried out by the free or forced movement of the coolant.
Under the influence of a temperature gradient in the earth's crust, convective flows of not only heat, but also matter arise. A thermohydrodynamic pressure gradient arises.
One can also observe the phenomenon that when a hydrodynamic pressure gradient occurs, oil is retained in the formation without a seal.
3. Heat transfer due to radiation.
A radioactive unit releases heat as it decays, and this heat is released through radiation.
33. Thermal properties of oil and gas formation, characteristics and area of use.
Thermal properties are:
1) Heat capacity coefficient c
2) Thermal conductivity coefficient l
3) Thermal diffusivity coefficient a
1. Heat capacity:
c – the amount of heat required to increase the temperature of a substance by one degree under given conditions (V, P=const).
с=dQ/dТ
Average heat capacity of a substance: c=DQ/DT.
Because Rock samples can have different masses and volumes; for a more differentiated assessment, special types of heat capacity are introduced: mass, volumetric and molar.
· Specific mass heat capacity [J/(kg×deg)]:
С m =dQ/dТ=С/m
This is the amount of heat required to change a unit mass of the sample by one degree.
· Specific volumetric heat capacity [J/(m 3 ×K)]:
С v =dQ/(V×dТ)=r×С m,
where r is density
The amount of heat that must be imparted to a unit to increase it by one degree, in the case of P, V=const.
· Specific molar heat capacity [J/(mol×K)]:
С n =dQ/(n×dТ)=М×С m,
where M – relative molecular weight [kg/kmol]
The amount of heat that must be imparted to a mole of a substance to change its temperature by one degree.
Heat capacity is an additive property of the formation:
С i = j=1 N SC j ×К i , where SC i =1, К – number of phases.
The heat capacity depends on the porosity of the formation: the greater the porosity, the lower the heat capacity.
(s×r)=s sq ×r sq ×(1-k p)+s ×r s ×k p,
where с з – pore filling coefficient;
k p – porosity coefficient.
Thermal conductivity.
l [W/(m×K)] characterizes the property of a rock to transfer kinetic (or thermal) energy from one element to another.
Coefficient of thermal conductivity – the amount of heat passing per unit time through a cubic volume of a substance with a face of unit size, while on other faces a temperature difference of one degree is maintained (DT = 1°).
The thermal conductivity coefficient depends on:
ü mineral composition of the skeleton. The spread of coefficient values can reach ten thousand times.
For example, the largest l for a diamond is 200 W/(m×K), because its crystal has virtually no structural defects. For comparison, l of air is 0.023 W/(m×K), water - 0.58 W/(m×K).
ü degree of fullness of the skeleton.
ü Thermal conductivity of fluids.
There is such a parameter as contact thermal conductivity coefficient
.
Quartz has the highest contact coefficient - 7-12 W/(m×K). Next come hydrochemical sediments, rock salt, sylvite, and anhydrite.
Coal and asbestos have a reduced contact coefficient.
Additivity for the thermal conductivity coefficient is not observed, the dependence does not obey the additivity rule.
For example, the thermal conductivity of minerals can be written as follows:
1gl=Sv i ×1gl i ,
where 1gl i is the logarithm of the l i-th phase with the volumetric content v i .
An important property is the reciprocal of thermal conductivity, called thermal resistance.
Due to thermal resistance, we have a complex distribution of thermal fields. This leads to thermal convection, due to which special types of deposits can form - not an ordinary seal, but a thermodynamic one.
Thermodynamic resistance decreases with a decrease in density, permeability, humidity, and also (in northern regions) the degree of ice content.
It increases when water is replaced by oil, gas or air in the process of thermal pressure changes, with an increase in layered heterogeneity, the phenomenon of anisotropy.
Coals, dry and gas-saturated rocks have the greatest thermal resistance.
When moving from terrigenous rocks to carbonate rocks, the thermal resistance decreases.
Hydrochemical sediments such as halite, sylvite, mirabelite, anhydrite, i.e. have minimal thermal resistance. rocks with a lamellar salt structure.
Clay layers, among all layers, stand out for their maximum thermal resistance.
From all this we can conclude that thermal resistance determines the degree of thermal inertia, thermal conductivity.
Thermal diffusivity.
In practice, a coefficient such as thermal diffusivity, which characterizes the rate of temperature change during an unsteady heat transfer process.
а=l/(с×r), when l=const.
In fact, “a” is not constant, because l is a function of coordinates and temperature, and c is a function of porosity coefficient, mass, etc.
During development, we can use processes in which an internal heat source may occur (for example, acid injection), in which case the equation will look like this:
dТ/dt=а×Ñ 2 Т+Q/(с×r),
where Q is the heat of the internal heat source, r is the density of the rock.
Heat transfer.
The next important parameter is heat transfer.
DQ=k t ×DТ×DS×Dt,
where k t is the heat transfer coefficient.
Its physical meaning: the amount of heat lost to neighboring layers, through a unit of surface, per unit of time when the temperature changes by one degree.
Typically, heat transfer is associated with displacement into the layers above and below.
34. The influence of temperature on changes in the physical properties of an oil and gas reservoir.
The heat that is absorbed by the rock is spent not only on kinetic thermal processes, but also on mechanical work, which is associated with the thermal expansion of the formation. This thermal expansion is associated with the dependence of the bonding forces of atoms in the lattice of individual phases on temperature, in particular appearing in the direction of bonds. If atoms are more easily displaced when moving away from each other than when approaching each other, a displacement of the centers of the fissile atoms occurs, i.e. deformation.
The relationship between temperature increase and linear deformation can be written:
dL=a×L×dТ,
where L is the original length [m], a is the coefficient of linear thermal expansion.
Similarly for volumetric expansion:
dV/V=g t ×dT,
where g t is the coefficient of volumetric thermal deformation.
Since the coefficients of volumetric expansion vary greatly for different grains, uneven deformations will occur during the impact, which will lead to destruction of the formation.
At the points of contact there is a strong concentration of stress, which results in the removal of sand and, accordingly, the destruction of the rock.
The phenomenon of oil and gas displacement is also associated with volumetric expansion. This is the so-called Joule-Thompson process. During operation, a sharp change in volume occurs, and a throttling effect occurs (thermal expansion with a change in temperature). Thermodynamic debitometry is based on the study of this effect.
Let's introduce one more parameter - adiabatic coefficient : h s =dТ/dр.
The differential adiabatic coefficient determines the change in temperature depending on the change in pressure.
The value of h S >0 under adiabatic compression. In this case, the substance heats up. The exception is water, because... in the range from 0¼4° it cools down.
h S =V/(C p ×g)×a×T,
where V is volume, T is temperature, a is linear expansion coefficient, g is gravitational acceleration.
The Joule-Thompson coefficient determines the temperature change during throttling.
e=dТ/dр=V/(Ср ×g)×(1 - a×Т)=V/(Ср ×g) - h S ,
where V/(Ср×g) determines heating due to the work of friction forces
h S – cooling of the substance due to adiabatic expansion.
For liquid V/Ср×g>>hS Þ Liquids heat up.
For gases e<0 Þ Газы охлаждаются.
In practice they use noise metry wells - a method based on the phenomenon when gas, when the temperature changes, releases vibrational energy, causing noise.
35. Changes in the properties of an oil and gas reservoir during the development of a deposit.
1. In their natural state, the layers are located at great depths, and, judging by the geothermal steps, the temperature in these conditions is close to 150°, so it can be argued that the rocks change their properties, because when we penetrate into the layer We disrupt the thermal balance.
2. When we pumping water into the reservoir, this water has a surface temperature. Once water enters the formation, it begins to cool the formation, which will inevitably lead to various unfavorable phenomena, such as waxing of oil. Those. If there is a paraffin component in the oil, then as a result of cooling, paraffin will fall out and clog the formation. For example, at the Uzen field, the temperature of oil saturation with paraffin is Tn = 35° (40°), and during its development these conditions were violated, as a result the formation temperature decreased, the paraffin fell out, blockage occurred and the developers had to pump in hot water for a long time and warm up the formation until all the paraffin has dissolved in the oil.
 |
3. High-viscosity oils.
To liquefy them, a coolant is used: hot water, superheated steam, as well as internal heat sources. So, a combustion front is used as a source: oil is ignited and an oxidizer is supplied.
The following projects are also being implemented in Switzerland, France, Austria, and Italy:
A method for reducing the viscosity of oils using radioactive waste. They are stored for 10 6 years, but at the same time heat highly viscous oil, making it easier to extract.
36. Physical state of hydrocarbon systems in oil and gas formations and characteristics of these states.
Let's take a simple substance and consider the state diagram:
R
Point C is the critical point at which the difference between properties disappears.
Pressure (P) and temperature (T), which characterize the formation, can be measured in a very wide range: from tenths of MPa to tens of MPa and from 20-40° to more than 150°C. Depending on this, our deposits containing hydrocarbons can be divided into gas, oil, etc.
Because at different depths, pressures vary from normal geostatic to abnormally high, then hydrocarbon compounds can be in gaseous, liquid or in the form of gas-liquid mixtures in the deposit.
At high pressures, the density of gases approaches the density of light hydrocarbon liquids. Under these conditions, heavy oil fractions can dissolve in compressed gas. As a result, the oil will be partially dissolved in the gas. If the amount of gas is insignificant, then with increasing pressure the gas dissolves in oil. Therefore, depending on the amount of gas and its condition, deposits are distinguished:
1. pure gas;
2. gas condensate;
3. gas and oil;
4. petroleum containing dissolved gas.
The boundary between gas-oil and oil-and-gas deposits is arbitrary. It developed historically, in connection with the existence of two ministries: the oil and gas industries.
In the USA, hydrocarbon deposits are divided according to the value of the gas-condensate factor, density and color of liquid hydrocarbons into:
1) gas;
2) gas condensate;
3) gas and oil.
The gas condensate factor is the amount of gas in cubic meters per cubic meter of liquid product.
According to the American standard, gas condensates include deposits from which lightly colored or colorless hydrocarbon liquids with a density of 740-780 kg/m 3 and a gas condensate factor of 900-1100 m 3 /m 3 are extracted.
Gas deposits may contain adsorbed bound oil, consisting of heavy hydrocarbon fractions, constituting up to 30% of the pore volume.
In addition, at certain pressures and temperatures, the existence of gas hydrate deposits, where gas is in a solid state, is possible. The presence of such deposits is a large reserve for increasing gas production.
During the development process, initial pressures and temperatures change and technogenic transformations of hydrocarbons into deposits occur.
Somehow, gas may be released from the oil during a continuous development system, as a result of which there will be a decrease in phase permeability, an increase in viscosity, a sharp decrease in pressure occurs in the bottomhole zone, followed by the loss of condensate, which will lead to the formation of condensate plugs.
In addition, phase transformations of the gas may occur during gas transportation.
38. Phase diagrams of single-component and multicomponent systems.
Gypsum phase rule (shows the variability of the system - the number of degrees of freedom)
N - number of system components
m is the number of its phases.
Example: H 2 O (1 set) N=1 m=2 Þ r=1
When jammed R only one T
One-component system.
Compress from A to B - the first drop of liquid (dew point or condensation point P=P us)
At point D the last bubble of steam remains, the point of vaporization or boiling
Each isotherm has its own boiling and vaporization points.
Two-component system
Changes R And T, i.e., the condensation onset pressure is always less than the vaporization pressure.
Related information.
Among the processes of complex heat transfer, a distinction is made between radiation-convective and radiation-conductive heat exchange.
is divided by their sum. Radiation-conduction heat transfer in a flat layer for other initial conditions is considered in [L. 5, 117, 163]; for a cylindrical layer - in [L. 116].
So why, in the region classified as fluidized beds of large particles, do the maximum heat transfer coefficients increase with increasing diameter? It's all about gas-convective heat exchange. In layers of small particles, gas filtration rates are too low for the convective component of heat transfer to “manifest” itself. But with increasing grain diameter it increases. Despite the low conductive heat transfer, in a fluidized bed of large particles, the growth of the convective component compensates for this disadvantage.
Chapter fourteen Radiation-conduction heat transfer
14-2. Radiation-conduction heat transfer in a flat layer of a gray absorbing medium without heat sources
14-3. Radiation-conduction heat exchange in a flat layer of a selective and anisotropically scattering medium with heat sources
Thus, based on the above and some other, more specific works, it becomes obvious that radiation-conduction heat transfer in systems containing volumetric heat sources has clearly not been sufficiently studied. In particular, the influence of the selectivity of the medium and boundary surfaces and the influence of the anisotropy of volume and surface scattering have not been clarified. In connection with this, the author undertook an approximate analytical solution to the problem of radiation-coductive heat transfer in a flat layer.
thermal and convective heat transfer. Special cases of this guide to heat transfer are: radiation heat transfer in a moving medium (in the absence of conductive transfer), radiation-conductive heat transfer in a stationary medium (in the absence of convective (transfer) and purely “convective heat transfer in a moving medium, when there is no radiative transfer. The complete system of equations describing the processes of radiation-convective heat transfer was considered and analyzed in IB Chapter 12.
In equation (15-1), the total heat transfer coefficient from the flow to the channel wall can be found based on (14-14) and (14-15). For this purpose, we will consider, within the framework of the adopted scheme, the process of heat exchange between the flowing medium and the boundary surface as radiation-conduction heat exchange between the flow core and the channel wall through a boundary layer of thickness b. Let us equate the temperature of the flow core with the average calorimetric temperature of the medium in a given section, which can be done taking into account the small thickness of the boundary layer compared to the diameter of the channel. Considering the flow core as one of the boundary surfaces [with the temperature in a given section of the channel T(x) and absorption capacity ag], and as another - the channel wall (with temperature Tw and absorption capacity aw), we consider the process of radiation-conduction heat transfer through the boundary layer. Applying (14-14), we obtain an expression for the local heat transfer coefficient a in a given section: Problems of radiation-convective heat transfer, even for simple cases, are usually more difficult than the problem of radiation-conductive heat transfer. Below is an approximate solution [L. 205] of one common problem of radiation-convective heat transfer. Significant simplifications allow us to complete the solution.
As shown in [L. 88, 350], the tensor approximation under certain conditions is a more accurate method that opens up new opportunities in the study of heat transfer processes by radiation. In (L. 351] the proposed tensor approximation (L. 88, 350] was used to solve the combined problem of radiation-conductive heat transfer and gave good results. Subsequently, the author generalized the tensor approximation “and the case of spectral and total radiation for arbitrary indicatrices volumetric and surface scattering in radiating systems [L. 29, 89].
Using an iterative method for solving problems of complex heat transfer, one should first specify the values of Qpea.i for all zones and determine on an electrical integrator of the described type the resulting temperature field for the accepted distribution Qpea.i (i=l 2,..., n), on the basis of which the temperature field is calculated second approximation of all quantities
Radiation-conduction heat transfer is considered in relation to a flat layer of an attenuating medium. Two problems have been solved. The first is an analytical consideration of radiation-conduction heat transfer in a flat layer of a medium without any restrictions regarding the temperatures of the surfaces of the layer. In this case, the medium and boundary surfaces were assumed to be gray, and there were no internal heat sources in the medium. The second solution relates to the symmetric problem of radiation -conductive heat exchange in a flat layer of a selective and anisotropically dissipating medium with heat sources inside the layer. Results of solving the first problem
As special cases, from the system of complex heat transfer equations follow all the individual equations considered in hydrodynamics and heat transfer theory: the equations of motion and continuity of the medium, the equations of purely conductive, convective and radiation heat transfer, the equations of radiation-conductive heat transfer in a stationary medium and, finally, the equations of radiative heat transfer in a moving but non-heat-conductive medium.
Radiation-conduction heat exchange, which is one of the six types of complex heat exchange, takes place in various fields of science and technology (astro- and geophysics, metallurgical and glass industries, electrovacuum technology, production of new materials, etc.). The need to study the processes of radiation-conduction heat transfer also leads to problems of energy transfer in the boundary layers of flows of liquid and gaseous media and problems of studying the thermal conductivity of various translucent materials.
but to calculate the process of radiation-"conductive heat transfer IB those conditions for which the obtained solutions are valid. Numerical solutions of the problem provide a clear picture of the process under study for (specific cases, without requiring the introduction of many restrictions inherent in approximate analytical studies. Both analytical and Numerical solutions are undoubtedly a well-known (progress in the study of radiative-tonductive heat transfer processes, despite their limited and private nature.
This chapter discusses two analytical solutions performed by the author to the problem of radiation-conduction heat transfer in a flat layer of a medium. The first solution considers the problem in the absence of restrictions regarding temperatures, absorption abilities of boundary surfaces and optical thicknesses of the medium layer [L. 89, 203]. This solution was carried out by the iteration method, and the medium and boundary surfaces are assumed to be gray, and there are no heat sources in the volume of the medium.
Rice. 14-1. Scheme for solving the problem of radiation-conduction heat transfer in a flat layer of an absorbing and heat-conducting medium in the absence of internal heat sources in the medium.
The most detailed analytical study was carried out on the above-considered problem of radiation-conductive heat transfer through a layer of gray, purely absorbing medium when the temperatures of the gray boundary surfaces of the layer are specified and in the absence of heat sources in the medium itself. The problem of radiation-conduction heat exchange between a layer of radiating and heat-conducting medium with boundary surfaces in the presence of heat sources in the volume has been considered in a very limited number of works with the adoption of certain assumptions.
For the first time, an attempt to take into account internal heat sources in the processes of “radiation-conduction heat transfer” was made in [L. 208], where the problem of heat transfer by radiation and thermal conductivity through a layer of gray, non-scattering medium with a uniform distribution of sources throughout the volume was considered. However, a mathematical error made in the work negated the results obtained.
This type of heat exchange occurs between contacting body particles located in the temperature field
T = f ( x , y, z , t ), characterized by a temperature gradient grad T. The temperature gradient is a vector directed along the normal n 0 to the isothermal surface in the direction of increasing temperature:
gradT = P o dT/dn = P o T
There are thermal fields: one-dimensional, two-dimensional and three-dimensional; stationary and non-stationary; isotropic and anisotropic.
The analytical description of the process of conductive heat transfer is based on the fundamental Fourier law, which relates the characteristics of a stationary heat flow propagating in a one-dimensional isotropic medium, geometric and thermophysical parameters of the medium:
Q =λ(T 1 –T 2 )S/l t or P = Q /t =λ (T 1 –T 2 )S/l
Where: - Q - the amount of heat transferred through the sample over time t , feces;
λ - coefficient of thermal conductivity of the sample material, W/(m-deg.);
T 1 , T 2 - temperatures of the “hot” and “cold” sections of the sample, respectively, degrees;
SS - cross-sectional area of the sample, m2;
l - sample length, m;
R - heat flow, W.
Based on the concept of electrothermal analogy, according to which thermal quantities R AndT match electric current I and electric potential U , Let's present Fourier's law in the form of "Ohm's law" for a section of the thermal circuit:
P = ( T 1 –T 2 )/l/ λS = (T 1 –T 2 )/R T (4.2)
Here, according to the physical meaning, the parameter R T There is thermal resistance of the thermal circuit section, and 1/ λ - specific thermal resistance. This representation of the conductive heat transfer process makes it possible to calculate the parameters of thermal circuits represented by topological models and known methods for calculating electrical circuits. Then, just as for an electric circuit, the expression for the current density in vector form has the form
j = – σ gradU ,
for a thermal circuit, Fourier's law in vector form will have the form
p = - λ grad T ,
Where R - heat flux density, and the minus sign indicates that the heat flux propagates from the heated to the colder section of the body.
Comparing expressions (4.1) and (4.2), we see that for conductive heat transfer
a= a cd = λ / l
Thus, to improve the efficiency of the heat transfer process, it is necessary to reduce the length l thermal circuit and increase its thermal conductivity λ
A generalized form of describing the process of conductive heat transfer is the differential equation of thermal conductivity, which is a mathematical expression of the laws of conservation of energy and Fourier:
Wed dT / dt = λ x d 2 T / dx 2 + λ y d 2 T / dy 2 + λ z d 2 T / dz 2 + W v
Where With - specific heat capacity of the medium, J/(kg-K);
p - density of the medium, kg/m3;
W v - volumetric density of internal sources, W/m 3 ;
λ x λ y λ z - specific thermal conductivities in the directions of the coordinate axes (for an anisotropic medium).
This type of heat exchange is a complex physical process in which the transfer of heat from the surface of a heated body to the surrounding space occurs due to its washing by a flow of coolant - liquid or gas - with a temperature lower than that of the heated body. In this case, the parameters of the temperature field and the intensity of convective heat transfer depend on the nature of the movement of the coolant, its thermophysical characteristics, as well as on the shape and size of the body.
Thus, the movement of the coolant flow can be free and forced, which corresponds to the phenomena natural And forced convection. In addition, there are laminar And turbulent th modes of flow movement, as well as their intermediate states, depending on the ratio of the forces that determine these flow movements - the forces of internal friction, viscosity and inertia.
Simultaneously with convective heat exchange, conductive heat exchange occurs due to the thermal conductivity of the coolant, but its efficiency is low due to the relatively low values of the thermal conductivity coefficient of liquids and gases. In the general case, this heat transfer mechanism is described by the Newton-Richmann law:
P = a K.B. S ( T 1 - T 2 ), (4.3)
Where: a K.B. - heat transfer coefficient by convection, W/(m 2 -deg.);
T 1 - T 2 2 - wall and coolant temperatures, respectively, K;
S - heat exchange surface, m2.
Despite the apparent simplicity of the description of the Newton-Richmann law, the difficulty of quantitatively assessing the efficiency of the convective heat transfer process lies in the fact that the value of the coefficient a K.B. depends on many factors, i.e. is a function of many process parameters. Find the dependency explicitly a K.B. = fA 1 , a 2 , ..., A j , ..., A n ) often impossible, since the process parameters also depend on temperature.
It helps to solve this problem for each specific case similarity theory, studying the properties of similar phenomena and methods for establishing their similarity. In particular, it has been proven that the course of a complex physical process is determined not by its individual physical and geometric parameters, but by dimensionless power-law complexes composed of parameters essential for the course of this process, which are called similarity criteria . Then the mathematical description of a complex process is reduced to compiling from these criteria, one of which contains the desired value a q, criterion equation , the form of which is valid for any of the varieties of this process. If it is not possible to draw up similarity criteria, this means that either some important parameter of the process is omitted from consideration, or some parameter of this process can be removed from consideration without much damage.
Real conditions of transfer of mass and energy in various types of thermal processes and natural phenomena are characterized by a complex set of interrelated phenomena, including the processes of radiation, conduction and convective heat exchange. Radiation-conduction heat transfer is one of the most common types of heat transfer in nature and technology
The mathematical form of the problem of radiation-conduction heat transfer follows from the energy equation, supplemented with appropriate boundary conditions. In particular, when studying radiation-conduction heat transfer in a flat layer of an absorbing and radiating medium with opaque gray boundaries, the problem is reduced to solving the energy equation
(26.10.2)
with boundary conditions
Here is the dimensionless flux density of the resulting radiation; - criterion of radiation-conduction heat transfer; - criterion for the dependence of the thermal conductivity of the medium on temperature; - dimensionless temperature in the section of the layer with thickness .
Equation (26.10.1) is a nonlinear integro-differential equation, since in accordance with equation (26.9.13) it is described by an integral expression, and the desired temperature value is presented in equation (26.10.1) both explicitly and implicitly through the equilibrium value of the radiation flux density:
In Fig. 26.19 gives the results of solving equation (26.10.1), obtained by N.A. Rubtsov and F.A. Kuznetsova by reducing it to an integral equation followed by a numerical solution on a computer using Newton’s method. The presented results on the temperature distribution in a layer of an absorbing medium with a frequency-averaged value of the volumetric absorption coefficient indicate the fundamental importance of taking into account the joint, radiation-conductive interaction in the transfer of total thermal energy.
Rice. 26.19. Temperature distribution in a layer of absorbing medium of optical thickness at
Noteworthy is the sensitivity of interaction effects to the optical properties of boundaries (especially for small values of the radiation-conduction heat transfer criterion: .
A decrease in the emissivity of a hot wall (see Fig. 26.19) leads to a redistribution of the roles of the radiative and conductive components of the thermal energy flow. The role of radiation in the heat transfer of a hot wall decreases, and the surrounding medium is heated due to conduction from the wall. The subsequent transfer of thermal energy to the cold wall consists of conduction and radiation due to the medium’s own radiation, while the temperature of the medium decreases compared to the value that the medium would have in the case of conductive heat transfer alone. A change in the optical properties of boundaries leads to a radical restructuring of temperature fields.
In recent years, due to the widespread introduction of cryogenic technology, the problem of heat transfer by radiation at cryogenic temperatures (studies of optical properties, thermal insulation efficiency in superconducting devices and cryostats) has become fundamentally important. However, even here it is difficult to imagine the processes of radiative heat transfer in a refined form. In Fig. 26.20 shows the results of experimental studies carried out by N. A. Rubtsov and Ya. A. Baltsevich and reflecting the kinetics of temperature fields in a system of metal screens at temperatures of liquid nitrogen and helium. It also presents the calculation of the steady-state temperature field using equations (26.4.1) under the assumption that the main mechanism of heat transfer is radiation. The discrepancy between experimental and calculated results indicates the presence of an additional, conductive mechanism of heat transfer associated with the presence of residual gases between the screens. Consequently, the analysis of such a heat transfer system is also associated with the need to consider interconnected radiation-conduction heat exchange.
The simplest example of combined radiation-convective heat transfer is the transfer of heat in a flat layer of absorbing gas blown into a turbulent flow of high-temperature gas flowing around a permeable plate. Problem formulations of this kind have to be encountered both when considering the flow in the vicinity of the frontal point and when analyzing the displacement of the boundary layer by intense injection of absorbing gas through a porous plate.
The problem as a whole comes down to considering the following boundary value problem:
under boundary conditions
Here is the Boltzmann criterion, which characterizes the radiation-convective ratio of the components of the heat flow in a medium with constant thermophysical properties - the characteristic values (in the undisturbed region or at the boundary of a nonequilibrium system) of speed and temperature, respectively; - dimensionless velocity distribution function in the region of boundary layer displacement.
In Fig. 26.21 presents the results of the numerical solution of problem (26.10.3) - (26.10.4) for a special case: ; degree of emissivity of the permeable plate; free-stream emissivity for different values of B0. As can be seen, in the case of low B0, which characterizes the low intensity of gas supply through the porous plate, the temperature profile is formed due to radiation-convective heat exchange. As B increases, the role of convection in the formation of the temperature profile becomes dominant. As the optical thickness of the layer increases, the temperature increases slightly at low Bo and correspondingly decreases as Bo increases.
In Fig. 26.22 the dependence characterizing the injection of absorbing gas, which is necessary to maintain the thermally insulated state of the plate, is plotted depending on the optical thickness of the displacement layer. There is a pronounced dependence of the B0 criterion on at small , when the insignificant presence of the absorbing gas component makes it possible to significantly reduce the flow rate of the injected gas. It is effective to create a highly reflective surface, provided that the optical thickness of the injected gas is small. Taking into account the selective nature of radiation absorption under the conditions under consideration does not introduce fundamental changes to the nature of the temperature profiles. This cannot be said about radiation fluxes, the calculation of which without taking into account optical transparency windows leads to serious errors.
Rice. 26.21. Temperature distribution in the curtain layer with optical thickness
Rice. 26.20. Calculated and experimental kinetics of temperature fields in a system of metal screens at temperatures of liquid nitrogen and helium ( - screen number; time, h)
Rice. 26.22. Dependence of B0 on the optical thickness of the layer at and, respectively
The fundamental importance of taking into account the selectivity of radiation in thermal calculations is repeatedly noted in the works of L. M. Biberman, devoted to solving complex problems of radiation gas dynamics.
In addition to direct numerical methods for studying combined radiation-convective heat transfer, approximate calculation methods are of certain practical interest. In particular, considering the limiting law of heat transfer in a turbulent boundary layer under relatively weak influence of thermal radiation
(26.10.5)
We believe that it is a dimensionless complex of radiation-convective heat transfer, where is the total Stanton criterion, reflecting the turbulent-radiation heat transfer to the wall. In this case, Est, where is the total heat flow on the wall, which has convective and radiation components.
Turbulent heat flow q is approximated, as usual, by a polynomial of the third degree, the coefficients of which are determined from the boundary conditions:
where E is the dimensionless density of the hemispherical resulting radiation at the internal boundary points of the boundary layer.
The boundary conditions (26.10.6) include an energy equation compiled respectively for the conditions of the near-wall region and at the boundary of the undisturbed flow. Considering that , the dimensionless parameter required for the calculation is written as follows:
Note that the boundary conditions (26.10.6) were determined by the accepted condition for the formation of a thermal boundary layer near the surface flown around by the radiating medium. This significant circumstance allowed us to believe
What is done under prevailing conditions?
Convection.
The values of and are determined from the analysis of solutions regarding the density of the resulting radiation in relation to the condition of a closed system that makes up the boundary layer. The turbulent boundary layer is considered as a gray absorbing medium with an absorption coefficient independent of temperature. The streamlined surface is a gray, optically homogeneous isothermal body. The undisturbed part of the flow, outside the boundary layer, radiates as a volumetric gray body that does not reflect from its surface and is at the temperature of the undisturbed flow. All this allows us to use the results of the previous consideration of radiation transfer in a flat layer of an absorbing medium with the significant difference that here only a single reflection from the surface of a streamlined plate can be taken into account.
