Radiant heat transfer between bodies in a transparent medium (reduced emissivity of the system, calculation of heat transfer, methods of reducing or increasing the intensity of heat transfer).

Screens

In various fields of technology, there are quite often cases when it is required to reduce the transfer of heat by radiation. For example, you need to protect workers from heat rays in workshops where there are surfaces with high temperatures. In other cases, it is necessary to shield the wooden parts of buildings from radiant energy in order to prevent ignition; thermometers should be protected from radiant energy, otherwise they will give incorrect readings. Therefore, whenever it is necessary to reduce the transfer of heat by radiation, they resort to installing screens. Typically, the screen is a thin, highly reflective metal sheet. The temperatures of both screen surfaces can be considered the same.

Let us consider the action of a screen between two flat, infinite parallel surfaces, and the transfer of heat by convection will be neglected. The surfaces of the walls and the screen are assumed to be the same. The wall temperatures T 1 and T 2 are kept constant with T 1> T 2. We assume that the radiation coefficients of the walls and the screen are equal to each other. Then the reduced emissivities between surfaces without a screen, between the first surface and the screen, the screen and the second surface are equal to each other.

The heat flux transferred from the first surface to the second (without a screen) is determined from the equation

The heat flux transferred from the first surface to the screen is found by the formula

and from the screen to the second surface according to the equation

At steady state thermal state q 1 = q 2, therefore

where

Substituting the obtained screen temperature into any of the equations, we obtain

Comparing the first and last equations, we find that the installation of one screen under the accepted conditions reduces the heat transfer by radiation by half:

(29-19)

It can be proved that the installation of two screens reduces the heat transfer by three times, the installation of three screens reduces the heat transfer by a factor of four, etc.

(29-20)

where C "pr is the reduced emissivity between the surface and the screen;

C pr - reduced emissivity between surfaces.

Emission of gases

The radiation of gaseous bodies differs sharply from the radiation of solids. Monatomic and diatomic gases have negligible emissivity and absorption capacity. These gases are considered transparent to heat rays. Triatomic gases (CO 2 and H 2 O, etc.) and polyatomic gases already possess significant emitting and, consequently, absorbing capacity. At high temperatures, the radiation of triatomic gases formed during the combustion of fuels is of great importance for the operation of heat exchange devices. The emission spectra of triatomic gases, in contrast to the emission of gray bodies, have a pronounced selective (selective) character. These gases absorb and emit radiant energy only in certain ranges of wavelengths located in different parts of the spectrum (Fig. 29-6). For rays with other wavelengths, these gases are transparent. When the beam meets

on its way a layer of gas capable of absorbing a ray with a given wavelength, then this ray is partially absorbed, partially passes through the gas column and exits from the other side of the layer with an intensity lower than at the entrance. A very thick layer can practically absorb the entire beam. In addition, the absorption capacity of a gas depends on its partial pressure or the number of molecules and temperature. Emission and absorption of radiant energy in gases occurs throughout the entire volume.

The gas absorption coefficient can be determined by the following relationship:

or the general equation

The thickness of the gas layer s depends on the shape of the body and is determined as the average ray length according to the empirical table.

The pressure of the combustion products is usually taken equal to 1 bar, therefore, the partial pressures of the three-atom gases in the mixture are determined by the equations p co2, = r co2, and P H 2 O = r H 2 O, where r is the volume fraction of the gas.

Average wall temperature - calculated by the equation

(29-21).

where T "st is the temperature of the channel wall at the gas inlet; T" "c t is the temperature of the channel wall at the gas outlet.

The average gas temperature is determined by the formula

(29-22)

where T "g is the gas temperature at the entrance to the channel;

T "" p is the gas temperature at the exit from the channel;

the plus sign is taken in the case of cooling, and the minus sign is taken in the case of gas heating in the channel.

The calculation of heat transfer by radiation between the gas and the channel walls is very complicated and is performed using a number of graphs and tables. A simpler and completely reliable calculation method was developed by Shack, who proposes the following equations that determine the emission of gases into an environment with a temperature of O ° K:

(29-23)

(29-24) where p is the partial pressure of the gas, bar; s is the average thickness of the gas layer, m; T is the average temperature of the gases and the wall, ° K. An analysis of the above equations shows that the emissivity of gases does not obey the Stefan - Boltzmann law. The emission of water vapor is proportional to T 3, and the emission of carbon dioxide is proportional to T 3 "5.

for laminar mode

T
Table 6

T (46) thermal parameters of dry air

at a pressure of 101.3 10³ Pa

for turbulent conditions

where λ m- thermal conductivity of gas, for air the value can be selected from table. 6; N i- coefficient taking into account the orientation of the body surface:

8. Determine thermal conductivity σ k between the surface of the body and

O the surrounding environment:

where S n, S in, S b - areas of the lower, upper and lateral surfaces of the block body, respectively;

S n = S in = L one · L 2 ;S b = 2 L 3 (L 1 +L 2).

For more efficient heat dissipation, IVEP blocks with finned surfaces are often used. If the designer is tasked with performing a thermal calculation for this type of secondary power supply unit, then he needs to additionally determine the effective heat transfer coefficient α eff i of the finned i-th surface, which depends on the design of the fins and the overheating of the case relative to the environment. Α eff i is determined in the same way as when calculating radiators (see calculation of radiators, p. 5.5).

After determining the effective heat transfer coefficient α eff i, proceed to the calculation of the thermal conductivity of the entire body σ k, which consists of the sum of the conductivities of the non-ribbed σ to 0 and ribbed σ to p surfaces:

G
de σ k 0 is calculated by formula (47), but excluding the ribbed surface;

G
de S pi is the area of ​​the base of the ribbed surface; N i is a coefficient that takes into account the orientation of this surface.

9. We calculate the overheating of the case of the IVEP unit in the second approximation θ k0:

G
de TO KP - coefficient depending on the perforation of the block body TO NS; TOН1 - coefficient taking into account the atmospheric pressure of the environment.

The graph by which you can determine the coefficient TO H1 is shown in Fig. 9, and the coefficient TO KP in Fig. fourteen.

The perforation coefficient is determined according to (11) - (13), and according to the graph shown in Fig. eight.

10. Determine the calculation error:

E
If δ ≤ 0.1, then the calculation can be considered complete. Otherwise, the calculation of the temperature of the housing of the secondary power supply unit should be repeated for a different value. θ k, adjusted to the side θ to 0.

11. We calculate the temperature of the block body:

H
and this completes the first stage of calculating the thermal regime of the IVEP unit.

Stage 2. Determination of the average surface temperature of the heated zone.

1. Calculate the conditional specific surface power q from the heated zone of the block according to the formula (19).

2. From the graph in fig. 7 we find in the first approximation the overheating of the heated zone θ h relative to the temperature surrounding the unit environment.

3. Determine the coefficients of heat transfer by radiation between the lower α PLV, upper α PLV and lateral α PLB surfaces of the heated zone and the body:

where ε P i - reduced emissivity i-th surface of the heated zone and the case:

ε s i and S s
i - emissivity and area i th surface of the heated zone.

R is. fifteen

4. For the determining temperature t m = ( t k + t 0 +θ h) / 2 and determining size h i we find the Grashof number Gr hi and the Prandtl number Pr (formula (43) and Table 6).

5. We calculate the coefficients of convective heat transfer between the heated zone and the body for each surface;

for the bottom surface

for top surface

d for lateral surface

6... Determine the thermal conductivity σ sc between the heated zone and the case:

G
de TOσ - coefficient taking into account conductive heat exchange:

σ - specific thermal reducibility from modules to the block body, depends on the pressing forces to the body (Fig. 15); in the absence of a clamp σ = 240 W / (m 2 K); Sλ is the contact area of ​​the module frame with the block body.

Table 7

Thermophysical properties of materials

7. We calculate the heating of the heated zone θ s0 in the second approximation:

G
de K w - determined by the graph shown in Fig. eleven; K n2 - determined by the graph (Fig. 10).

8. Determine the calculation error

E
if δ< 0,1, то расчет окончен. При δ ≥ 0,1 следует повторить расчет для скорректированного значенияθ h.

9. Calculate the temperature of the heated zone

NS
step 3. Calculation of the surface temperature of the component included in the IVEP circuit

Here is the sequence of the calculation required to determine the temperature of the case of the component installed in the module of the first downscaling level.

1. Determine the equivalent coefficient of thermal conductivity of the module in which the component is located, for example a microcircuit, for the following options:

in the absence of heat-conducting tires λ eq = λ P, where λ P is the thermal conductivity of the board base material;

in the presence of heat-conducting tires

G de λ w - thermal conductivity of the heat-conducting bus material; V P is the volume of the printed circuit board, taking into account the volume of heat-conducting buses; V w is the volume of heat-conducting buses on the printed circuit board; A- surface filling factor of the module board with heat-conducting buses:

G
de S w is the total area occupied by heat-conducting buses on the printed circuit board.

Table 7 shows the thermophysical parameters of some materials.

2. Determine the equivalent radius of the microcircuit case:

G
de S o IC - the area of ​​the base of the microcircuit.

3. We calculate the coefficient of heat flow propagation:

G
de α 1 and α 2 - heat transfer coefficients from the first and second sides of the printed circuit board; for natural heat exchange

δ P
- the thickness of the printed circuit board of the module.

4... Determine the desired overheating of the surface of the microcircuit case:

where IN and M- conditional values ​​introduced to simplify the recording form: with one-sided arrangement of microcircuit cases on a printed circuit board IN= 8.5π R 2 VT / K, M= 2; with double-sided housing IN= 0,M= 1;TO- empirical coefficient: for microcircuit cases, the center of which is spaced from the ends of the printed circuit board at a distance of less than 3 R,TO= 1.14; for microcircuit cases, the center of which is spaced from the ends of the printed circuit board at a distance of more than 3 R,TO= 1;TOα - the heat transfer coefficient from the microcircuit cases is determined according to the graph shown in Fig. sixteen; TO 1 and TO 0 - modified Bessel functions; N - number i-x cases of microcircuits located at a distance of no more than 10 / m, i.e r i ≤ 10 m; Δ t c - average volume overheating of air in the unit:

Q
ims i - power dissipated i th microcircuit; S ims i - total surface area i th microcircuit; δ z i is the gap between the microcircuit and the board; λ z i is the coefficient of thermal conductivity of the material filling this gap.

5. Determine the surface temperature of the microcircuit case:

NS
The above algorithm for calculating the temperature of the microcircuit can be applied to any other discrete component that is part of the secondary power supply unit. In this case, the discrete component can be considered like a microcircuit with a local heat source on the plate, and the corresponding values ​​of the geometric parameters can be entered into equations (60) - (63).

Purpose of work

Acquaintance with the method of conducting experiments to determine the degree of blackness of the body surface.

Developing experimentation skills.

The task

Determine the emissivity ε and emissivity from the surfaces of 2 different materials (painted copper and polished steel).

Establish the dependence of the change in the degree of emissivity on the surface temperature.

Compare the emissivity values ​​of painted copper and polished steel with each other.

Theoretical introduction

Thermal radiation is the process of transferring thermal energy through electromagnetic waves. The amount of heat transferred by radiation depends on the properties of the radiating body and its temperature and does not depend on the temperature of the surrounding bodies.

In the general case, the heat flux falling on the body is partially absorbed, partially reflected and partially passes through the body (Fig. 1.1).

Rice. 1.1. Radiant energy distribution scheme

(2)

where - heat flux falling on the body,

- the amount of heat absorbed by the body,

- the amount of heat reflected by the body,

- the amount of heat passing through the body.

We divide the right and left parts into the heat flow:

The quantities
are called respectively: absorption, reflectivity and transmittance of the body.

If
, then
, i.e. all heat flux falling on the body is absorbed. Such a body is called absolutely black .

Bodies that have
,
those. all the heat flux falling on the body is reflected from it, are called white . Moreover, if the reflection from the surface obeys the laws of optics, the body is called mirrored - if the reflection is diffuse – absolutely white .

Bodies that have
,
those. all the heat flux falling on the body passes through it, are called diathermic or completely transparent .

Absolute bodies do not exist in nature, but the concept of such bodies is very useful, especially about an absolutely black body, since the laws governing its radiation are especially simple, because no radiation is reflected from its surface.

In addition, the concept of an absolutely black body makes it possible to prove that in nature there are no such bodies that emit more heat than black ones.

For example, in accordance with Kirchhoff's law, the ratio of the emissivity of a body and its absorbency is the same for all bodies and depends only on temperature, for all bodies, including absolutely black, at a given temperature:

(3)

Since the absorption capacity of an absolutely black body
but and etc. is always less than 1, then it follows from Kirchhoff's law that the limiting emissivity possesses a completely black body. Since there are no absolutely black bodies in nature, the concept of a gray body is introduced, its emissivity ε, which is the ratio of the emissivity of a gray and an absolutely black body:

Following Kirchhoff's law and considering that
can be written
where
those ... the degree of blackness characterizes both the relative emissivity and the absorption capacity of the body ... The basic law of radiation reflecting the dependence of the radiation intensity
referred to this wavelength range (monochromatic radiation) is Planck's law.

(4)

where - wavelength, [m];

;

and are the first and second Planck constants.

In fig. 1.2 this equation is presented graphically.

Rice. 1.2. Graphical representation of Planck's law

As you can see from the graph, a blackbody radiates at any temperature in a wide range of wavelengths. With increasing temperature, the maximum radiation intensity shifts towards shorter wavelengths. This phenomenon is described by Wien's law:

Where
is the wavelength corresponding to the maximum radiation intensity.

With values
instead of Planck's law, you can apply the Rayleigh-Jeans law, which is also called the "law of long-wave radiation":

(6)

The radiation intensity referred to the entire wavelength interval from
before
(integral radiation) can be determined from Planck's law by integrating:

where is the emissivity of an absolutely black body. The expression is called the Stefan-Boltzmann law, which was established by Boltzmann. For gray bodies, the Stefan-Boltzmann law is written in the form:

(8)

- the emissivity of the gray body. Heat transfer by radiation between two surfaces is determined on the basis of the Stefan-Boltzmann law and has the form:

(9)

If
, then the reduced emissivity becomes equal to the emissivity of the surface , i.e.
... This circumstance forms the basis of the method for determining the emissivity and emissivity of gray bodies, which have insignificant dimensions in comparison with bodies exchanging radiant energy with each other.

(10)

(11)

As can be seen from the formula, determining the degree of emissivity and emissivity WITH gray body, you need to know the surface temperature test body, temperature environment and radiant heat flux from the body surface
... Temperatures and can be measured by known methods. And the radiant heat flux is determined from the following considerations.

The spread of heat from the surface of bodies into the surrounding space occurs through radiation and heat transfer during free convection. Full stream from the surface of the body, thus, will be equal to:

, where
;

- the convective component of the heat flux, which can be determined by the Newton-Richmann law:

(12)

In turn, the heat transfer coefficient can be determined from the expression:

(13)

the defining temperature in these expressions is the temperature of the boundary layer:

Rice. 2 Diagram of the experimental setup

Legend:

B - switch;

Р1, Р2 - voltage regulators;

PW1, PW2 - power meters (wattmeters);

NE1, NE2 - heating elements;

IT1, IT2 - temperature meters;

T1, T2, etc. - thermocouples.

Study of thermal radiation. determination of the degree of blackness of a tungsten incandescent lamp

3.1 Thermal radiation and its characteristics

Bodies heated to sufficiently high temperatures are capable of emitting electromagnetic waves. The glow of bodies associated with heating is called thermal radiation. This radiation is the most common in nature. Thermal radiation can be in equilibrium, i.e. can be in a state of thermodynamic equilibrium with matter in a closed (heat-insulated) system. The quantitative spectral characteristic of thermal radiation is the spectral density of the radiant luminosity (emissivity):

where is the spectral density of the radiant luminosity; - the energy of electromagnetic radiation emitted per unit of time from a unit of body surface area in the wavelength range from to;

The characteristic of the total power of thermal radiation from a unit surface area of ​​the body in the entire range of wavelengths from to is the energy luminosity (integral energy luminosity):

3.2. Plank formula and laws of thermal radiation of a black body

Stephan-Boltzmann's law

In 1900, Planck put forward a hypothesis according to which atomic oscillators emit energy not continuously, but in portions-quanta. In accordance with Planck's hypothesis, the spectral density of the radiant luminosity is determined by the following formula:

. (3)

From Planck's formula, one can obtain an expression for the energetic luminosity. Substitute the value of the spectral density of the radiant luminosity of the body from formula (3) into expression (2):

(4)

To calculate the integral (4), we introduce a new variable. From here; ... Formula (4) is then transformed to the form:

As , then expression (5) for the radiant luminosity will have the following form:

. (6)

Relation (6) is the Stefan-Boltzmann law, where the Stefan-Boltzmann constant W / (m 2 K 4).

Hence the definition of the Stefan-Boltzmann law follows:

The energy luminosity of an absolutely black body is directly proportional to the fourth degree of absolute temperature.

In the theory of thermal radiation, along with the black body model, the concept of a gray body is often used. A body is called gray if its absorption coefficient is the same for all wavelengths and depends only on temperature and surface conditions. For a gray body, the Stefan-Boltzmann law has the form:

where is the emissivity of the thermal emitter (emissivity).

The first law of wine (the law of displacement of Wine)

Let us examine relation (3) for an extremum. To do this, we define the first derivative of the spectral density with respect to the wavelength and equate it to zero.

. (8)

Let's introduce a variable. Then from equation (8) we get:

. (9)

The transcendental equation (9) is generally solved by the method of successive approximations. Since for real temperatures, a simpler solution to equation (9) can be found. Indeed, under this condition, relation (9) is simplified and takes the form:

which has a solution for. Consequently

A more accurate solution of equation (9) by the method of successive approximations leads to the following dependence:

, (10)

where mK.

The definition of Wien's first law (Wien's displacement law) follows from relation (10).

The wavelength corresponding to the maximum spectral density of the radiant luminosity is inversely proportional to body temperature.

The quantity is called the constant of Wien's displacement law.

The second law of wine

Substitute the value from equation (10) into the expression for the spectral density of the radiant luminosity (3). Then we get the maximum spectral density:

, (11)

where W / m 2 K 5.

The definition of Wien's second law follows from relation (11).

The maximum spectral density of the radiant luminosity of an absolutely black body is directly proportional to the fifth power of the absolute temperature.

The quantity is called the constant of Wien's second law.

Figure 1 shows the dependence of the spectral density of the radiant luminosity on the wavelength for a certain body at two different temperatures. With an increase in temperature, the area under the spectral density curves should increase in proportion to the fourth power of temperature in accordance with the Stefan-Boltzmann law, the wavelength corresponding to the maximum spectral density should decrease in inverse proportion to the temperature according to Wien's displacement law, and the maximum value of the spectral density should increase in direct proportion to the fifth power of the absolute temperature in accordance with the second law of Wien.

Picture 1

4. INSTRUMENTS AND ACCESSORIES. UNIT DESCRIPTION

In this work, the filament of electric lamps of various powers (25, 60, 75 and 100 W) is used as the emitting body. To determine the temperature of the filament of electric bulbs, the volt-ampere characteristic is taken, according to which the value of the static resistance () of the filament is determined and its temperature is calculated. Figure 2 shows a typical current-voltage characteristic of an incandescent lamp. It can be seen that at low current values, the current linearly depends on the applied voltage and the corresponding straight line passes through the origin. With a further increase in the current, the filament heats up, the resistance of the lamp increases, and a deviation of the current-voltage characteristic from the linear dependence passing through the origin is observed. To maintain the current with a higher resistance, more voltage is required. The differential resistance of the lamp decreases monotonically, and then takes on an almost constant value, and the current-voltage characteristic as a whole is non-linear. Assuming that the power consumed by an electric lamp is dissipated by radiation, it is possible to determine the emissivity of the lamp filament or estimate the Stefan-Boltzmann constant using the formula:

, (12)

where is the area of ​​the lamp filament; - degree of blackness; is the Stefan-Boltzmann constant.

From formula (12), you can determine the emissivity of the filament of an electric lamp.

. (13)

Figure 2

Figure 3 shows the electrical diagram of the installation for taking the current-voltage characteristics of the lamp, determining the resistance of the filament, its temperature and studying the laws of thermal radiation. Keys K 1 and K 2 are designed to connect electrical measuring instruments with the required limits for measuring current and voltage.

Variable resistance is connected to an alternating current circuit with a voltage of 220V according to a potentiometric circuit that provides a smooth voltage change from 0 to 220 V.

The determination of the temperature of the filament is based on the known dependence of the resistance of metals on temperature:

where is the resistance of the filament at 0 0 С; - temperature coefficient of resistance of tungsten, 1 / deg.

Figure 3

Let us write expression (14) for room temperature.

. (15)

Dividing expression (14) by (15) term by term, we get:

From here we determine the temperature of the filament:

. (17)

Thus, knowing the static resistance of the filament in the absence of current at room temperature and the resistance of the filament when the current flows, the filament temperature can be determined. When performing work, the resistance at room temperature is measured by a digital electrical meter (tester), and the static resistance of the filament is calculated according to Ohm's law

6. ORDER OF PERFORMANCE OF WORK

1. Unscrew the incandescent lamp from the socket and use a digital electric meter to determine the resistance of the filament of the electric lamp under test at room temperature. Record the measurement results in Table 1.

2. Screw the lamp into the socket, read the current-voltage characteristic of the lamp (the dependence of the current strength on the voltage). Measure the current strength every 5 mA after a short exposure for 2-5 minutes. Record the measurement results in table 1.

3. Calculate by the formula (18) and (17) the resistance and temperature of the thread in 0 C and K.

4. Calculate the emissivity of the filament using formula (13). Write down the calculation results in table 1.

Experimental data for calculating the emissivity

Table 1

5. According to table 1, build the current-voltage characteristic of the lamp, the dependence of resistance and emissivity on temperature and power.

Planck's law. The radiation intensities of a black body I sl and any real body I l depend on the wavelength.

An absolutely black body at a given one emits rays of all wavelengths from l = 0 to l = ¥. If you somehow separate the beams with different wavelengths from each other and measure the energy of each beam, then it turns out that the distribution of energy along the spectrum is different.

As the wavelength increases, the energy of the rays increases, at a certain wavelength it reaches a maximum, then decreases. In addition, for a ray of the same wavelength, its energy increases with an increase in the body emitting rays (Figure 11.1).

Planck established the following law for the change in the intensity of radiation from an absolutely black body depending on and wavelength:

I sl = s 1 l -5 / (e s / (l T) - 1), (11.5)

Substituting Planck's law into equation (11.7) and integrating from l = 0 to l = ¥, we find that the integral radiation (heat flux) of an absolutely black body is directly proportional to the fourth power of its absolute (Stefan-Boltzmann law).

E s = C s (T / 100) 4, (11.8)

where C s = 5.67 W / (m 2 * K 4) is the emissivity of an absolutely black body

Noting in Fig. 11.1 the amount of energy corresponding to the light part of the spectrum (0.4-0.8 microns), it is easy to see that it is very small for low ones in comparison with the energy of integral radiation. Only when the sun is ~ 6000K, the energy of light rays is about 50% of the total energy of black radiation.

All real bodies used in technology are not absolutely black and, with the same, emit less energy than a completely black body. The radiation of real bodies also depends on the wavelength. So that the laws of blackbody radiation can be applied to real bodies, the concept of a body and radiation is introduced. Radiation is understood to be one that, similarly to blackbody radiation, has a continuous spectrum, but the intensity of the rays for each wavelength I l for any is a constant fraction of the intensity of the black body radiation I sl, i.e. there is a relationship:

I l / I sl = e = const. (11.9)

The value e is called the emissivity. It depends on the physical properties of the body. The degree of blackness of bodies is always less than one.

Kirchhoff's law. For any body, the emissivity and absorptivity depend on the wavelength. Different bodies have different values ​​of E and A. The relationship between them is established by Kirchhoff's law:

E = E s * A or E / A = E s = E s / A s = C s * (T / 100) 4. (11.11)

The ratio of the emissivity of a body (E) to its absorbency (A) is the same for all bodies that are at the same and is equal to the emissivity of an absolutely black body at the same.

It follows from Kirchhoff's law that if a body has a low absorptive capacity, then it simultaneously has a low emissivity (polished). An absolutely black body, which has the maximum absorption capacity, also has the highest emissivity.

Kirchhoff's law remains valid for monochromatic radiation as well. The ratio of the radiation intensity of a body at a certain wavelength to its absorptive capacity at the same wavelength is the same for all bodies if they are at the same, and is numerically equal to the radiation intensity of an absolutely black body at the same wavelength and, i.e. is a function of wavelength only and:

E l / A l = I l / A l = E sl = I sl = f (l, T). (11.12)

Therefore, a body that emits energy at any wavelength is capable of absorbing it at the same wavelength. If the body does not absorb energy in some part of the spectrum, then it does not radiate in this part of the spectrum.

It also follows from Kirchhoff's law that the degree of emissivity of a body e for the same is numerically equal to the absorption coefficient A:

e = I l / I sl = E / E sl = C / C sl = A. (11.13)

Lambert's law. Radiant energy emitted by the body spreads in space in different directions with different intensities. The law that establishes the dependence of the radiation intensity on the direction is called Lambert's law.

Lambert's law establishes that the amount of radiant energy emitted by a surface element dF 1 in the direction of an element dF 2 is proportional to the product of the amount of energy emitted along the normal dQ n by the value of the spatial angle dsh and cosc, compiled by the direction of radiation with the normal (Fig. 11.2):

d 2 Q n = dQ n * dw * cosj. (11.14)

Consequently, the largest amount of radiant energy is emitted in the direction perpendicular to the radiation surface, i.e., at (j = 0). With an increase in j, the amount of radiant energy decreases and at j = 90 ° is equal to zero. Lambert's law is completely valid for an absolutely black body and for bodies with diffuse radiation at j = 0 - 60 °.

Lambert's law does not apply to polished surfaces. For them, the emission at j will be greater than in the direction normal to the surface.