Science Discovery

2014; 2(2): 34-42

Published online November 10, 2014 (http://www.sciencepublishinggroup.com/j/sd)
doi: 10.11648/j.sd.20140202.12
ISSN: 2331-0642 (Print); ISSN: 2331-0650 (Online)

Theory of radiative heat exchange in furnaces, fire boxes,

combustion chambers is replenished by four new laws
Anatoly Nikolaevich Makarov
Department of Electrotechnics and Electric Supply, Tver State Technical University, nab. Afanasiya Nikitina 22, Tver, 170026 Russia

Email address:
tgtu_kafedra_ese@mail.ru

To cite this article:

Anatoly Nikolaevich Makarov. Theory of Radiative Heat Exchange in Furnaces, Fire Boxes, Combustion Chambers is Replenished by
Four New Laws. Science Discovery. Vol. 2, No. 2, 2014, pp. 34-42. doi: 10.11648/j.sd.20140202.12

Abstract: Review of radiative heat exchange design procedures in electric arc steel melting and flame furnaces, fire
boxes, combustion chambers is made. Radiative heat exchange is a uniting factor for electric arc and flame furnaces, fire
boxes, combustion chambers. We prove the existence of crisis of heat exchange design procedures in furnaces, fire boxes,
combustion chambers. Laws of radiation emitted by gas layers of electric arc, glowing in metallic vapors at atmospheric
pressure and a flame of furnaces, fire boxes, combustion chambers are discovered and stated. Laws of radiation form a
basis for a new design procedure in electric arc and flame furnaces, fire boxes, combustion chambers, designing new
furnaces, fire boxes, chambers.
Keywords: Theory, Heat Exchange, Radiation, Flame, Electric Arc, Furnaces, Fire Boxes, Discovery

1. Introduction
Radiative heat exchange is the main type of heat transfer chambers has been investigated since the late 19th century.
in furnaces and fire boxes and accounts for 90-98% of the In the early years two methods (analytical in parallel with
total heat exchange in steam boiler boxes [1], arc steel empiric) for solving heat exchange problems were outlined .
melting furnaces[2], [3]plasma arc steel melting [3], flame Analytical method is based on the solution of equations,
heating and melting furnaces [4], [5]. The quantity of heat, describing heat exchange process and allow to determine
which flame gives burner liners by flame accounts for 0.5- effects of separate variable parameters on the process
1% and 99-99.5% by radiation [6]. studied and analyze efficiency possibilities of the process.
Modern science isn’t a dogma and some of its base may The point of the empiric method adds up to link factual
be revised and supplemented with new laws. Since the late data-based variable parameters, affecting heat exchange
19th schedule. Empiric method is applied for validating the
century and throughout the 20th century, heat exchange findings of investigations, obtained analytically and also
calculation in flame furnaces, fire boxes, combustion applied in all cases, when it is impossible to solve heat
chambers has been carried out on the base of the law, exchange problem theoretically. Theoretical analysis is
experimentally obtained by Y. Stefan in 1879 in analyzing used until its application appears fruitful in existing
solid body radiation, and then theoretically proved by learning curve and then experimental material is involved,
Boltzmann in 1884 in studying analytically solid body permitting to solve the problems of analytical solution of
radiation._ In the late 19th – early 20th century, solid bulk equations, describing heat exchange process.
fuel (carbon, shale, turf, fire wood) was burnt in furnaces The further development of heat exchange theory in
on fire grates, and the first descriptions of heat transfer flame furnaces, fire boxes, combustion chambers
processes were essentially descriptions of problems and throughout the 20th century shows, that due to little
calculation of radiant heat transfer between two arbitrarily analytical data on heat exchange and experience miss, heat
located surfaces (a fuel bed and a heating surface) with the exchange problems were solved by crude theory in the
use of Stefan-Boltzmann law. early 20th century. At a later stage, appeared experimental
Heat exchange in flame furnaces, fire boxes, combustion data denote imperfection of the theory and encourage both
 Science Discovery 2014; 2(2): 34-42 35

derivation of empirical formulas and improvement, This dependence attracted the title Stefan-Boltzmann law
development of the theory. and under radiation flux density it is of the form:
Е о = с sТ 4 (4)
2. Laws of Heat Surface Radiation
where сs = 5,67×10-8 W/(m2×К) – Stefan-Boltzmann
Planck's law (the Nobel prize of 1918) characterizes constant
spectral irradiance distribution of black body along the For computational convenience Stefan-Boltzman law is
wavelength in the radiation spectrum against the body written in the form
temperature:
Ео = со(Т /100)4 (5)
2π h 3 hν /kT -1 where со = 5,67 W(m2×К4).
E = ν (e − 1) , (1)
2 Integral flux density of real body is determined by
oν c Stefan-Boltzmann law considering total emissivity of ε
o
body:
where h = 6.626×10-34 J×s – Planck's constant; k = Е = ε с s Т 4. (6)
1.381×10-23 J/К, Boltzmann constant; со = 2.998×108 m/s –
vacuum velocity; Еоν ─ monochromatic radiation density of Kirchhoff's law suggests, that ratio between surface
black body, W/(m2×s-1). density of real body radiation and absorption body
Passing from velocity to wavelength, the equation (1.3 b.) coefficient is equal for all the bodies at the same
can then be written: temperature and equals surface density of black body
radiation at the temperature given
c
2 / λ×T −1
E = c λ−5(e − 1) (2)
Е Е Е
oλ 1 1 = 2 =. 0 =Е
. .= . (7)
-16 2 -2
where с1 = 3,742×10 W×m , с2 = 1,439×10 m×К – the А А А 0
first and the second Planck's radiation constants ; Eoλ, 1 2 0
W/(m2×µm).
From Kirchhoff's law follows, that absorption coefficient
Equation (2) is graphically given by Fig.1.
equals the radiation coefficient for the black and gray
bodies, and the coefficient of radiation for define interval of
Е0
10 , W/ (m mcm)
-3 2
wavelengths for selectively radiating bodies and gas spaces:

2000 К А = ε, А =ε . (8)
40 λ λ
1800
30 1600 According to Lambert's law, named also cosine law, the
1400 intensity of surface radiation in any direction, making an α
20 1200 angle with the normal to a surface is directly proportional
to cosine of the angle:
10
I Oα = I ON cos α (9)
0 0,2 0,4 0,6 0,8 , mcm where ION – intensity of surface radiation in the direction of
Fig 1. Radiation flux density of black body v/s wavelength N normal to a surface ; IOα – intensity of surface radiation
in the direction, making an α angle with the N normal to a
Wavelength, µm×К, at which density of black body surface.
radiation attains its maximum value, arises from Wien Absorption and radiation flux leakage are designated by
displacement law (the Nobel prize of 1911): Bouguer-Lambert-Beer law that decrease in surface
radiation intensity in penetration of elementary layer of
λ Т = 2897,8 . (3) absorbent is proportional to substance attenuation factor
М
and beam path length in this layer :
Т≈ 5 800 К for the sun and electric arc, wave length λm =
0,5 µm and peak solar density and electric arc fall at visual I ON1 = I ON e − kl (10)
spectrum. Solar spectrum is similar to black body spectrum.
The fact that black body radiation is a quartic function of where ION1 – intensity of surface radiation at l distance ; k –
its absolute temperature was first determined solid substance attenuation factor; l – beam path length.
experimentally by Stefan, then theoretically by Boltzman. As is evident from the foregoing, laws of radiation,
36 Anatoly Nikolaevich Makarov: Theory of Radiative Heat Exchange in Furnaces, Fire Boxes, Combustion Chambers is
Replenished by Four New Laws

discovered in the 19th – early 20 century explain solid exchange (MIF-2000), the existing procedure for
radiation. Solid fuel was the main fuel in furnaces, fire- calculating radiative heat exchange in furnaces, fire boxes
boxes in the 19th – early 20 century. Heat exchange design with gaseous ,fuel, pulverized torch with which torch is
in furnaces , fire boxes under lump firing on feed grate is simulated by equivalent gas hemisphere , isothermal
carried out by Stefan-Boltzmann law : volume or bulk bands with i- parameters were criticized in
series of reports [10]. At the I International Symposium on
 T1  4  T2  4  radiant heat exchange in 1995 it was noted, that there isn’t
q = c Sε rrc   −  ϕ12 (11) sufficiently safe and effective procedure for calculating
 100   100  
radiative heat exchange, every existing method has its
where q – radiant-flux density of fuel to the heating surface; imperfection and restricted range of application [11].
cS – coefficient of black body radiation; εrrc – reduced At present many facts, proving the need of updating the
radiation coefficient; Т1, Т2 – temperatures of fuel bed and existing procedure for calculating radiative heat exchange
heating surface accordingly; φ12 – angular radiation in flame furnaces, fire boxes, combustion chambers are
coefficient of fuel bed to the heating surface. accumulated.
The calculated results by equation (11) give a good fit Rise of flame temperature without its expansion doesn't
with measured results of heating surface temperatures reduce to increase in furnace efficiency. Determining
while solid fuel burning. influence on radiation torch flux density incident on heating
In the 20th and 21st centuries fluid, gas, powder fuel is surfaces has its power and not a temperature. At the same
used with the flaring formation of gas radiative torch. torch temperature but different power, generated in it,
Throughout the 20th century heat exchange design in flame radiant flux, incident on heating surface and net flux are
furnaces, fire boxes, combustion chambers have been different. The distribution of incident radiant flux on
accomplished by Stefan-Boltzmann law. Calculating heating surfaces depends on power distribution along the
radiative heat exchange in flame furnaces, fire boxes, torch length. In some sources [12] the data for a slight drop
combustion chambers, we made an assumption, that gas in in power under the existing reduction of its temperature are
volume doesn’t involve in heat exchange in space but cited, that proves weak influence of torch temperature on
imaginary solid surface, restricted it [7]-[9]. It is assumed, processes of its heat exchange with heating surfaces.
that radiation of this surface is equivalent to gas space Torch power and hence, item-heating capacity may be
radiation. However, flame is not a solid body, but a large arised by increase in fuel consumption or using fuel with a
radiative gas volume under oil burning, gas – fuel burning, more high heat value and also by previously heating fuel
pulverized-fuel burning. In gas burning a torch consists of and air , as evident from equation:
triatomic products of combustion process and hot smoke
Р f = Qvh В fc + QshVac + Q fsh В fc (12)
particles. In oil burning a luminous torch is formed,
consisted of triatomic gases, smoke particles, free carbons.
A flame, containing triatomic gases, carbon, ash, ash - where Рf – torch power; Qh , В − heat value and fuel
v fc
subliming products is obtained by solid pulverized-fuel
consumption; Qsh, Vac – sensible heat and air consumption;
burning. Radiation emitted by triatomic gases, carbon Qfsh – fuel sensible heat .
dioxide and water vapours doesn’t follow Stefan-
Boltzmann law. Radiation emitted by carbon dioxide is
In [13] characteristics of 7 MW injection burner torch in
proportional to the temperature to the 3.5 power and water
the antechamber of a calcining machine, operating in
vapour radiation to the temperature to the 3 power.
technological mode under changes of gas flow from 100 to
Throughout the 20th century heat exchange design
500 m3/h are listed. As investigations show, gas discharge
procedure in torch furnaces, fire boxes, combustion
changing doesn’t practically affect torch temperature but
chambers has been perfected ,temperature modifying
furnace efficiency arises with fuel rate increasing and torch
factors were inserted into formula (11) effective
capacity.
emissivities of gas, radiative gas space were divided into a
From [14] it is know, that combustion product recycling
variety of radiative zones. However, review of centenary
is made to decrease the yield of nitric oxide. Incorporation
operating experience, design of torch furnaces, fire boxes,
of recycling gases in fire chambers provides torch
combustion chambers theoretical and experimental data
temperature decrease and temperature field correction
shows incorrect heat exchange theory for exploitation
without decrease in boiler capacity. It only goes to show the
practice.
determining influence of heat value and fuel rate rather
than torch temperature on radiative heat exchange in torch
3. Crisis of the Existing Heat Exchange furnaces.
Water injection or steam injection in fuel combustion
Design Procedure in Furnaces, Fire zone (gas,fuel) is also used for thermal nitric oxide
Boxes, Combustion Chambers suppression [14].
Decrease in nitric oxide formation is a result of
At the IV Minsk International Forum on heat-mass
 Science Discovery 2014; 2(2): 34-42 37

temperature reduction in fuel combustion zone by 10-12 %. 4. Laws of Radiation Emitted by Gas
Damp injection is directly effected to the center of
combustion, torch temperature decreases without decrease Layers of Flame and Electric Arc
in its power and boiler capacity. To reduce torch On 23/05/2011 International Academy of Authors of
temperature and repress nitric oxide emission in steam Scientific Discoveries and Inventions (IAASDI, Russia)
boiler boxes OFA combustion of fuel is applied, when fuel registered scientific discovery of laws of radiation of large
with air deficiency is feeded to furnace through main gas volumes, formed in gas , fluid, pulverized fuel flaring
burners, and the rest of the air is directed further along the and arc glowing in metallic vapors at atmospheric pressure.
torch through specific nozzle or lighted off high-level Discovery priority: 21.04.1983. – in statement component
burners. [22], [23], [24]; 19.03.1987 – in theoretical foundation [25],
In [15] the data are cited, that plant load, fuel rate [26], [27]; 1.05.2001. – in experimental verification [28],
reduction accompanying air ratio increase result in reduce [29], [30]. The title of discovery «A Regular correlation
of luminous part of torch with simultaneous temperature between the parameters characterizing radiation from
increase .In this case in accord with Stefan-Boltzmann law isothermalcoaxial cylindrical gas layers generated during
(11), heat flux on water-cooled surfaces increase and boiler torch combustion of fuel and during the burning of electric
capacity grows, that conflicts with common sense and arc in metal vapors at atmospheric pressure» (Makarov’s
energy conservation law. Steam supply to torch root was regularities).Regularities, laws are synonyms, estimating
used in Martin furnaces, with this torch temperature relationships between some phenomenons.
decreased by 35-60 0С, fuel combustion process improved, Discovered formula:« A Regular correlation between the
sooting diminished , heat transfer with a bath increased and parameters characterizing radiation from isothermal coaxial
furnace capacity rised [16]. cylindrical gas layers generated during torch combustion of
It is known, that with the increase in the temperature fuel and during the burning of electric arc in metal vapors
difference between item and torch ,the net radiation flux on at atmospheric pressure, that has previously been unknown
heated body rises. However, as exploitation practice of is determined. It involves invariance of radiation
torch furnaces and fire boxes shows, with the decreasing parameters which characterize electric, geometric and heat
the torch temperature by 10-20 % without fuel rate indices (angular coefficients of radiation, beam path length,
reduction, furnace capacity and fire boxes remain at radiation flux density and others) ».
previous level i.e. radiative heat exchange doesn’t decline. In the 17th– 20th centuries in the scientific world there
Calculation by the formula (11) shows, that , with was a good tradition to name the law after the author,
decreasing the torch temperature by − 20 %, the net flux on discovered it. It is evident nowadays, that the scientific
heated item declines 1.5-2 times. ethic binds the researchers to mention the author's name
From equation (12) follows, that torch power may be when they follow his law in their studies. The point of the
increased at the expense of air heating. Thus, for instance, discovery is thus the following:
when air is heated by 600 0С , torch power increased by Torch made by single burner in furnaces and combustion
17 %, and torch temperature increases from 1300 0С to chambers represents a large gas volume in the form of
2000 0С, i.e. 1.5 times [17]. By equation (11) net flux spheroid where fuel combustion occurs and combustion
density to calculating zone from torch must increase 5 products are ejected from spheroid in portions of fuel and
times, heating rate must also increase 5 times that conflicts oxidizer. Radiative and absorbing cylinder gas spaces are
with energy conservation law. Under actual operating inscribed in spheroid , which torch is simulated by (Fig.2).
conditions of furnaces, when air is heated and torch power In steam boilers boxes torch represents a large gas volume
increases by 17 %, heat flux density and heating rate in the form of elliptic gas cylinder in which several tens of
increase by 12-15 % , i.e varies directly as torch power right circular cylinder gas spaces are inscribed (Fig.3).
multiplication rather than temperature in the 4th power.
[17].
Thus, despite the fact that heat exchange theory in torch
furnaces, fire boxes, combustion chambers, based on laws
of black body radiation has been improved for the 20th
century[18]-[21], it turned out to be approximate and need
to be updated. It doesn’t fit the requirements of modern
exploitation practice of torch furnaces, fire boxes,
combustion chambers, doesn’t show the real pattern of heat
flux distribution on heating surfaces, doesn’t meet modern Fig 2. Fuel torch pattern and its structure with distribution of isotherms by
cases of calculation and selection of rational thermal its volume. 1 – burner; 2 – torch; 3 – combustion products
conditions of furnaces, fire boxes, combustion chambers,
providing economy of fuel and energy resources.
38 Anatoly Nikolaevich Makarov: Theory of Radiative Heat Exchange in Furnaces, Fire Boxes, Combustion Chambers is
Replenished by Four New Laws

spaces to surface element amounted to 5.2 m. Assume, that

radiation of inner layers of cylinder gas spaces is absorbed
by neighbor layers and radiation only of outer surface
layers go outside. In this case radiation of isothermal
coaxial cylinder gas layers can be exemplified by radiation
of three cylinder layers. Element angular radiation
coefficients of 1 – 3 coaxial cylinder gas layers on dF are
determined by the following way [12]:

ϕ dFF FdF
1 0.23 × 0.25
ϕ F dF = = = 0.0003815
1 F1 3.14 × 4.8 × 10

ϕ dFF FdF
2 0.188 × 0.25
ϕ F dF = = = 0.0003815 (13)
Fig 3. Torch and distribution of isotherms in steam boiler box. 1 – burner; 2 F 3.14 × 3.92 × 10
2
2 – furnace; 3 – torch; 4 – water-cooled surfaces
ϕ dFF FdF
Let observe steam boiler box of TGMP-314 plant of 300 3 0.133 × 0.25
ϕ F dF = = = 0.0003815
MW which presents rectangular parallelepiped 35 m high, 3 F3 3.14 × 2.78 × 10
14 m wide and 7 m deep (Fig. 3). Torch and combustion
products fill all the space of furnace chamber. Torch is where ϕdFF ,ϕdFF ,ϕdFF – angular radiation coefficients
shaped as elliptic cylinder gas space along the height of 1 2 3
furnace, in which two or several circle cylinder gas spaces of surface element on cylinder spaces accordingly 1 − 3;
may be inscribed. Isotherms divide circle cylinder gas FdF – square of dF surface element; F1 − F3 –lateral
surface platforms of 1 − 3 cylinders.
spaces into several isothermal circle cylinder or several tens
From calculated data (13) follows the first law of
of isothermal circle cylinder gas spaces along the height.
radiation emitted by gas layers of electric arc and torch: «
Let observe the radiation of one isothermal circle cylinder
Element geometric configuration factors of coaxial cylinder
gas space, by a number of which torch is simulated on dF
spaces, layers which electric arc and torch consisted of are
surface element of 0.5×0,5 m. (Fig. 4).
equal» .The notation of the first law is given by:
lк 1
j =j =j
2 F dF F dF F dF (14)
3
1 2 3
li
dF The first law of radiation emitted by coaxial cylinder gas
lср spaces was first considered in [28] and confirmed in [29].
Simulating radiation of hundreds and thousands coaxing
cylinder gas layers, forming the volume of the first cylinder
lj space, we will obtain the analog result :element angular
dF1i
coefficients of radiation of coaxing cylinder gas layers are
equal. Equality of element angular coefficients of radiation
of coaxing cylinder gas layers implies the equality of
angular mean radiation coefficients since they are the sum
Fig 4. To the calculation of radiant fluxes from coaxial cylinder 1 – 3, li, lj, of element angular coefficients of radiation of coaxing
lam – the distance from surface elements and arithmetic mean distance to cylinder gas spaces, layers. Angular mean radiation
dF calculated area.
coefficient demonstrates the irradiation dose of coaxial
Assume, that during fuel combustion isothermal cylinder cylinder space, layer on the surface consisted of a set of
gas body of 10 m height, 4.9 m diameter, 180.9 m3 volume surface elements. From the first law follows, that during
is formed. The power of 700 MWt ⋅h, which uniformly design of angular coefficients of radiation of coaxing
distributed on all the space of cylinder, is generated. Divide cylinder gas layers, spaces of coaxing cylinder gas spaces,
isothermal cylinder emitting and absorbing gas space by layers, it is enough to determine angular coefficients of
three cylinder bodies of equal volume. (Fig. 4). Radius of radiation of coaxing cylinder space of small diameter,
the third cylinder is 1.39 m, the second is 1.96 m, the first aligned with cylinder gas space. of coaxing cylinder space
is 2.4 m, volume of each cylinder is 60.3 m3. Perpendicular of small diameter or linear configuration source , aligned
to the center of surface element transits of 900 to axis of with cylinder gas space.
symmetry cylinder gas space through its upper foundation. Angular coefficients of radiation are the main design
The shortest distance. lsh from axis of coaxing cylinder gas quantities of radiative heat exchange. Angular coefficient of
radiation represent complicated geometric character of
 Science Discovery 2014; 2(2): 34-42 39

shape, size and mutual attitude of two bodies in mutual isothermal coaxial cylinder layer equals arithmetic mean
radiative heat exchange. In heat engineering calculations distance from summitry axis of coaxial cylinder layer to dF
the great difficulties are usually connected with optical and calculated platform.
geometric characters of radiative heat exchange between Assume, that 10×1030 atoms, electrons are in radiative
bodies. Using analytic methods of calculation, element and layer and they are uniformly distributed along space layer.
mean angular coefficients of body radiation are determined When atom or electron moves to a new or previous energy
by direct integrating of corresponding dependences for level, it accompanied by radiation of 10×1030 energy
coefficients. Determinating integration of angular photons. Assume, that 10×1030 beams are incident on
coefficients of radiation of bodies, surfaces, spaces is calculated area from a large radiative gas volume, layer.
connected with double and four-times integrals calculation, Calculations show, that average path length, radiated by gas
that complicated the task. layer to dF calculated platform equals arithmetic mean
Calculating angular radiation coefficient of great volume, distance from symmetry axis of coaxial cylinder layer to dF
1 layer on dF platform, it is necessary to perform the calculated platform.
integration as by the height, perimeter, so by the depth of Calculated data by formula (15) give evidence of another
cylinder volume, layer i.e.to solve threefold iterated two laws of radiation emitted by coaxial radiating and
integral, quadrivariate integral. absorbing cylinder gas spaces constituting the electric arc
The first law relieves us of threefold iterated, and flame.
quadrivariate integrating and solves the problems through The second law: «Average beam path length from
single integration by the height of cylinder gas volume of coaxial cylinder gas spaces, that torch and arc consist of, to
small diameter. calculated platform equals arithmetic mean distance from
The first law of radiation emitted by isothermal coaxial summatry axis of cylinder layers to calculated platform».
cylinder gas radiative layers of which electric arc and torch
 10×10 
30
consisted allow to determine slope radiation factors of any
 ∑ lj 
cylinder gas space, layer by one time integrating geometric
lср=l1=l2=l3=  
j =1
(16)
and trigonometric dependences of coaxial cylinder gas (10 × 1030 ) 
space of small diameter or, that it often determined, linear  
configuration source. The author by integration of  
geometric dependences between linear configuration
sources and heating surfaces at any attitude, solve The third law « Radiation flux density, incident on
practically the tasks of determination of angular radiation calculated platform from isochoric coaxial cylinder gas
coefficients of stated bodies and surfaces [30]-[32]. In this spaces, layers, which arc and torch consisted of are equal»:
way, proceeded from the first property of isothermal gas q =q =q
layers, the author obtain analytical dependences for F dF F dF F dF (17)
1 2 3
determinating angular radiation coefficients of coaxing
cylinder gas spaces of any size, at different attitude of gas Total radiation flux density incident from three coaxial
spaces and heating surfaces. cylinder gas spaces on dF platform is determined according
Calculate radiation flux on dF platform of coaxial to the superposition principle:
cylinder gas spaces, in which radiation power Р1 = Р2 = Р3 3
= 700/3 = 233.3 MW is generated. Take medium q FdF = ∑ q F dF = 330 kW/m 2 (18)
i =1 i
parameters character to steam boiler furnace: particle
concentration is 0.06 g/m3,diameter dr = 0.3 mcm, flux 2 × Assume, that radiating power of 700 MW is generated in
103 kg/m3, medium rejection ratio k = 1,5µ/ (drρ) = one of cylinder gas spaces, in the third, for instant. Let find
0.15.Calculation results of radiation fluxes of coaxial radiation flux density of the third cylinder gas space on dF
cylinder gas spaces on dF platform. platform:
φ ×P φ
F dF 1 − kl dFF ×Р 0.0003815×700×103
=q =q = 1 e 1= 3 3=
q
F dF F dF F dF F q = е-
1 2 3 dF F dF F 0.25
3 dF (19)
φ ×P φ P
F dF 2 − kl F dF 3 − kl (15) −0.15 ×7.8 = 330 kW / m2 .
= 2 e 2 = 3 e 3=
F F
dF dF
0.0003815 × 233.3 × 10 3 − 0.15×7.8 The fourth law of radiation of electric arc and torch is
= e = 110 kW / m 2
0.25 cleared from calculated data by the formulas (18) and (19):
where l1 = l2 = l3 – average paths length of 1 – 3 cylinders. «Total radiation flux incident on calculated platform from
Average path length lср (fig. 4) was determined as several radiative and absorbing cylinder gas spaces, layers,
arithmetic mean distance from surface elements, which which electric arc and flame consist of, equals radiation
surface of cylinder radiating layer consisted of to dF flux density of coaxial cylinder gas space of small diameter
calculating platform [1]. Average paths length of any on calculated platform at radiating power, released in
40 Anatoly Nikolaevich Makarov: Theory of Radiative Heat Exchange in Furnaces, Fire Boxes, Combustion Chambers is
Replenished by Four New Laws

cylinder gas space of small diameter that equals total methodology combines two different physical
radiated power, released in all coaxial cylinder gas spaces phenomenons: heating energy release at fuel combustion
radiating at calculated area»: and current flow in gas on the basis of general result of
conversion of fuel and electric arc energy to radiation
3 energy.
q F dF = ∑ q F dF (20) Volume torch pattern, consisted of a set of coaxial
3 i=1 i
radiating and absorbing cylinder gas volumes, layers is
This is very important law of radiation emitted by used in radiative heat exchange calculation in torch
coaxing radiative and absorbing cylinder gas spaces, which furnaces, steam boiler boxes, combustion chambers.
electric arc and torch consist of , since it confirms the Calculated data agree closely with measured data of
sufficiency of the passage from threefold iterated, heating flux and temperatures in furnaces, fire boxes,
quadrivariate integrating to single integration when combustion chambers. The discovery enabled us to design
calculating the local angular coefficients of radiation of new torch furnaces, fire boxes, combustion chambers.On
cylinder gas spaces on surface elements and make it the basis of disclosed laws of radiation of large gas
possible to determine local angular coefficients of radiation volumes 18 innovative steam boiler boxes, torch heating
of cylinder gas spaces of small diameter (line radiation and electric arc melting furnaces, combustion chambers,
source) on surface elements at their any mutual attitude ways of heating and melting the metal, providing the
[30]–[32]. improvement in the quality of production, reduction in time
From laws of radiation of large gas volumes follows: of heating and melting the metal, improving the efficiency
«When torch and electric arc are simulated by coaxial of plants, decrease in fuel and electric energy consumption,
cylinder gas spaces, layers, the calculated results of heat pollutant emissions_ [ 33-37].
exchange include volume radiation and absorption of all the The author is to continue this article, in which heat
layers of torch and electric arc ( all atoms and electrons) exchange design procedure, developed on the basis of
and their heat exchange with all heating surfaces». scientific discovery and its praxis in electric arc steel
Advantages of flame simulation by cylinder gas spaces: melting and flame furnaces, fire boxes, combustion
1 Cylinder gas spaces are geometric figures, inscribing chambers will be stated.
in the torch, made by single burner and representing
spheroid, filled up the space more than rectangular 5. Conclusion
parallelepipeds, which flame traditionally is simulated
by. Modern science isn’t a dogma and some of its base may
2 Calculating radiative heat exchange by cylinder be revised. It is known that no one scientific theory
radiating and absorbing gas spaces, volume radiation pretends to be an absolute truth, it only describes definite
of torch is simulated, in case of simulation by physic phenomenon with more or less degree of accuracy.
rectangular parallelepipeds, torch surface radiation by Subsequently, when images of physic phenomenon extend
sides of parallelepiped is simulated a concrete theory may be refined or converted into one of
3 In cylinder, used for torch simulation, hundred and the particular cases of new theory. Thus, for instance,
thousand coaxial cylinder gas spaces, which simulate Newtonian mechanics became a component of modern
radiation and absorption of inner gas torch layers can mechanics, consisted of classical and quantum mechanics.
be inscribed, with equal result of radiative heat And analogous processes occur in radiative heat exchange
exchange calculation is obtained, replaced a number theory: new data arise from exploitation practice of electric
of radiating and absorbing cylinder gas layers with arc and torch furnaces, fire boxes, combustion chambers
one cylinder gas space. In the following way, from and new refined design procedures, making scientists,
declaration of volume radiation of torch by researchers reconsider their attitude to existing heat
rectangular simulation, we pass into real volume exchange design procedure in furnaces, fire boxes,
radiation of flame. combustion chambers. In the 19th -20th centuries the laws
All the four laws are registered as scientific discovery of black body radiation were disclosed for calculating heat
and united by common concept of radiation invariance of exchange between hard surfaces. In the 21st century the
isothermal coaxial cylinder gas ionized and non-ionized author of this paper disclosed the laws of radiation of large
spaces, layers formed in gas, liquid, pulverized fuel firing gas volumes for calculating heat exchange between gas
and arc glowing in metallic vapors at atmospheric pressure. volumes of torch and hard surfaces in torch furnaces, fire
The way of transfer heat from power sources to heating boxes, combustion chambers.
surfaces combines torch and electric arc furnaces, steam
boiler boxes, combustion chambers: radiative heat
exchange and its dependence on power and size of References
radiation sources. A unified methodology of radiative heat
[1] A.G. Blokh, Thermal Radiation in Boilers , Energiya,
exchange calculation in torch and arc furnaces, fire boxes, Moscow, 326 p. 1967.
combustion chambers is constructed on this fact. A
 Science Discovery 2014; 2(2): 34-42 41

[2] A.N. Makarov, A.D. Svenchanskii, Optimum Thermal [21] On the cjlculation of spatical temperature and radiative
Conditions of Electric Arc Furnaces, Energoatomisdat, transfer in industrial watertube boiler / S. Zanelly, R. Corsi,
Moscow, 96 p., 1992. Y. Rieri // Heat Transfer in Flames. Washington, Scripta
Book Company. pp. 18-24, 1973.
[3] A. N. Makarov, Heat Exchange in Arc Steel-melting
Furnaces, TSTU, Tver, 184p., 1998. [22] A.N.Makarov, A Regular correlation between the
parameters characterizing radiation from isothermal coaxial
[4] Heat engineering calculations in metallurgical furnaces: cylindrical gas layers generated during flame combustion of
textbook / under the editorship of A.S. Telegin. Metallurgiya, fuel and during the burning of electric arc in metal vapors at
Moscow,368 p., 1993. atmospheric pressure (Makarov’s regularities, diploma №
417) // Scientific discoveries: collected short descriptions of
[5] V.A. Krivandin, А.V. Egorov, Thermal performance and scientific discoveries, scientific hypotheses, scientific ideas
constructions of iron and steel furnaces: textbook. – 211 / Compiler V.V. Potocky. Publsh. RANS, Moscow, pp.
Metallurgiya, Moscow, 462 p., 1989. 33-37, 2012.
[6] Stationary gas turbine plants // under the editorship of L.V. [23] A.N. Makarov, A.D. Svenchanskii, Estimates of reflected
Arsenyev and V.G. Tyryshkin. Mashinostroeniye, Leningrad, irradiance component of lining from arcs in arc steel melting
462 p.,1989. furnaces // Electrotech. industry. Ser. Electrothermics. No 5.
pp. 1-2, 1983.
[7] R.Zigel, J. Howell, Radiative heat exchange. Mir,Moscow,
934 p., 1975. [24] A.N.Makarov, Pecularities of heating flux test on metal bath
in arc and plasma-arc furnaces // Electro and thermophysical
[8] E.М. Sparrow, R.D. Cess, Radiative heat exchange. Energia, processes in electroheat installations and control matters :
Leningrad, 294 p., 1971. MIH. pp. 108-111, 1985.
[9] S. Chandrasekar, Radiation transfer. IL, Moscow, 431 p., [25] A.N.Makarov, Math model of plasma-arc furnace with
1993. dominant radiation as electrothermal intensifier //
Proceedings of high schools. Ferrous metallurgy. No 7, pp.
[10] М.L. Herman, Engineering design method of fire-tube 139-142, 1989.
boilers with terminal furnace М.L. Herman, V.А. Borodylia ,
E.F. Nogotov, G.I. Palchenok // The fourth Minsk [26] A.N.Makarov, Effect of electrode radiation on roof wear of
International Forum on heat-mass exchange MIF-2000 : arc steel melting furnaces // Proceedings of high schools.
Proceedings of Forum. P. 2. Radiative and combined heat Ferrous metallurgy. No 2, pp. 80-82, 1991.
exchange. Minsk: ANK Publishing Institute for Heat and
Mass Transfer named after A. V. Lykov, pp. 21-31, 2000. [27] A.N. Makarov, Radiation flux design on metal bath under
inclined position of plasmatrons in plasma arc furnaces.
[11] Radiative Transfer-1. Proceeding of the First International Proceedings of high schools. Ferrous metallurgy. No. 8, pp.
symposium on Radiation Transfer (edited by prof M.Pinar 55-57, 1991.
Mengus). Kusadasi, Turkey. ICHMT, p. 800,1995.
[28] A.N. Makarov, Heat-flux distribution in steam boiler box
[12] A.G. Blokh, Yu. A. Juravlev, L.N. Ryzkov, Radiative heat ТGМP – 204 // Electric Power Plants. No. 1, pp. 20-25,
exchange: Reference. Energoatomizdat, Moscow, 432 p., 2003.
1991.
[29] A.N. Makarov, Flame simulating by radiative cylinders in
[13] Process fuel combustion and use / А.А. Vintovkin, М.G. heat exchange calculation in furnaces and steam boiler
Ladygichev, Yu.М. Goldobin, G.P. Yasnikov. Metallurgiya, boxes // Power engineering. No. 4, pp. 33-39, 2003.
Moscow, 286 p, 1998.
[30] A.N. Makarov, Estimates of angular radiation coefficients of
[14] Roslyakov P.V., Zakorov I.А. Nonstoichiometric natural gas linear source on parallel and normal planes //Heat power
and oil fuel combustion at steam power plant. MIH,Moscow, engineering. pp. 65-68, 1997.
144 p, 2001.
[31] A.N. Makarov, Estimates of angular radiation coefficients of
[15] A.G. Blokh Heat transfer in steam boiler boxes. linear source on arbitrarily-spaced planes. // Heat power
Energoatomizdat, Leningrad, 240 p, 1984. engineering. No 12, pp. 58-62, 1998.
[16] N.V. Lavrov, Physicochemical foundation of fuel [32] A.N. Makarov, Estimates of angular radiation coefficients of
combustion. Science, Moscow, 275 p., 1971. linear source and furnace flame of steam boilers // Heat
power engineering. No 8, pp. 63-66, 2000.
[17] B.S. Mastrukov, Thermotechnical calculations of industrial
furnaces: textbook. Metallurgy , Moscow, 368 p., 1972. [33] A.N. Makarov, Heat exchange in electric arc and flame
metallurgical furnaces and energy plants :Tutorial, St-
[18] Monte Carlo Solution of Thermal Transfer through Radiant Petersburg: Lan,p.384, 2014.
Media Betweer Gray Walls / Y.R. Howell, M. Permutter //
Yourn. Heat Transfer. pp. 116-122,1964. [34] A.N. Makarov, M.N. Shevchenko, Gas –fuel combustion
chamber. RF Patent 2400668, 2010.
[19] On radiative properties of polydispersions / M.P. Mengus, R.
Viskanta // Combust Scine and Technicke Vol. 44, pp. 143- [35] А.N. Makarov, A.G. Sheglov, Regenerative heating pit. RF
159, 1985. Patent 2457262, 2012.
[20] Predictions of radiative properties of pulverized coal and [36] A.N. Makarov, E.V. Kruglov, V.V. Rybakova, DC Arc Steel
fly-ash polydispersions / R. Viskanta, A. Ungan, M.P. melting furnace.RF Patent 2516896,2014.
Mengus // ASME Publication 81HT24. pp. 1-11, 1981.
42 Anatoly Nikolaevich Makarov: Theory of Radiative Heat Exchange in Furnaces, Fire Boxes, Combustion Chambers is
Replenished by Four New Laws

[37] A.N. Makarov, E.V. Kruglov, V.V. Rybakova, Ring-

bottomed heating furnace RF Patent 2517079,2014.