Radiant burner utilizing flame quenching phenomena

Oct. 11, 1966 w. h. best 3,277,948

RADIANT BURNER UTILIZING FLAME QUENCHING PHENOMENA Filed Sept. 9, 1960 3 Sheets-Sheet 1

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Fig. 2

Willie H Best

INVENTOR.

BY

Oct. 11, 1966 _{w H} best 3,277,948

RADIANT BURNER UTILIZING FLAME QUENCHING PHENOMENA

Filed Sept. 9, 1960 „ &lt;. x t- ₃ Sheets-Sheet 3

Fig. 3

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Fig. 6

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Oct. 11, 1966

W. H. BEST

3,277,948

RADIANT BURNER UTILIZING

FLAME QUENCHING PHENOMENA

Filed Sept. 9, i960

Sheets-Sheet 3

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Fig. 8

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Fig. !O

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Fig. 9

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Willie H. Best

INVENTOR.

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3,277,948

Patented Oct. 11, 1966

United States Patent Office

These together with other objects and advantages which will become subsequently apparent reside in the details of construction and operation as more fully hereinafter described and claimed, reference being had to the accom5 panying drawings forming a part hereof, wherein like numerals refer to like parts throughout, and in which:

FIGURE 1 is a plan view of a radiant burner constructed in accordance with the present invention;

FIGURE 2 is a detailed sectional view taken substanl₍₎ tially upon a plane passing along section line 2—2 of FIGURE 1 illustrating the details of construction of the burner;

FIGURE 3 is an enlarged fragmentary sectional view illustrating the orientation of the flame in the troughs or 15 valleys formed by the recessed edges of the slots or channels;

FIGURE 4 is a detailed sectional view similar to FIGURE 3 but illustrating a slightly different form of recessed edge for the slots;

2o FIGURE 5 is a detailed sectional view similar to FIGURES 3 and 4 but illustrating still another modified form of the invention;

FIGURE 6 is a detailed view illustrating the burner structure and forming a basis for certain mathematical 25 computations;

FIGURE 7 is a graph illustrating the increase in radiation efficiency dependent upon the angle of divergence of the slot wall;

FIGURE 8 is a graph illustrating the relationship of 30 the radiation area and the R distance vs. the angle of divergence;

FIGURE 9 is a graph illustrating the radiation area vs. the angle of divergence; and

FIGURE 10 is a pair of graphs illustrating compara35 tively the radiant heat distribution from a flat burning surface on a burner and a burning surface having the divergent recessed edges in the side walls of the slots.

Referring now specifically to the drawings, the numeral 10 generally relates to the radiant burner of the present 40 invention which includes an exterior frame 12 which forms means for guiding the combustible mixture to the rear surface 14 of the radiant burner. The radiant burner also is provided with a burning surface 16 and is constructed from a plate of ceramic material 18. The plate 45 of ceramic material 18 may be of one-piece construction or it may be constructed from a plurality of individual strips. When the plate 18 is of one-piece construction, there is provided a plurality of slots 20 therethrough which communicate the rear face 14 with the burning 50 surface 16. The slots 20 are arranged in any of several different patterns in the ceramic plate. They may be separated by a transverse solid member 21 or they may be staggered in relation to each other or extend completely across the burning face depending upon the size 55 of the burner and other physical factors. If the burner is constructed of a plurality of relatively thin plates, the ends of said plates or strips are provided with enlargements to provide for spacing between the strips thus defining the slots similar to slots 20. As illustrated, the θθ slots 20 are quite narrow and are provided with parallel side walls. Adjacent the burning surface 16, the side walls of the slots 20 are recessed by providing a bevel 22 thereon which defines an apex 24 generally in the center of the area of the ceramic plates between adjacent slots 20. The recess formed by the bevels 22 form troughs or valleys 26 for receiving the flame during combustion thereof whereby the flame is disposed substantially within the confines of the troughs or valleys 26 for specific purposes set forth hereinafter.

γθ FIGURE 4 illustrates a similar type of structure in which the ceramic plate is designated by numeral 28, the slots designated by numeral 30 and in this instance, the

3,277,948 RADIANT BURNER UTILIZING FLAME QUENCHING PHENOMENA

Willie H. Best, Columbia, S.C., assignor, by mesne assignments, to Thermal Engineering Corporation, Columbia, S.C., a corporation of South Carolina

Filed Sept. 9, 1960, Ser. No. 55,077

Claim. (CI. 158—116)

The present invention generally relates to radiant burners and this application is a continuation-in-part of application Ser. No. 847,480, filed October 20, 1959, for radiant burner, now abandoned.

The primary object of the present invention is to provide a radiant burner constructed of ceramic material or other suitable refractory material capable of becoming incandescent when heated to a predetermined high temperature whereby radiant heat rays will emit from the incandescent surface of the burner. The primary feature of the present invention is its construction with openings in the form of relatively narrow and elongated slots in which the width of the slot is such that a flame will be quenched before it will pass through the slots. This results in a burner which is incapable of backflashing, that is, incapable of permitting passage of flame from the burning surface of the burner to the rear surface thereof from which the combustible mixture originates. Another advantage of this arrangement is the fact that the velocity of the combustible mixture may be materially lowered since it is not necessary that the velocity of the combustible mixture be greater than the flame propagation rate of the combustible mixture as is necessary in conventional burners in order to prevent backflashing.

Another primary object of the present invention is to provide a radiant burner having relatively narrow slotlike openings as defined in the preceding paragraph together with a structure in which the outer edge portions of the side walls of the slot are recessed by either bevelling or providing a stepped wall structure for increasing the cross sectional area of the slot at the burning surface thereof, thereby further reducing the velocity of the combustible mixture and, in fact, substantially decreasing the velocity to zero movement or only very small movement whereby the combustion of the combustible mixture will take place within the confines generally of the trough formed by the recesses for producing more effective flame impingement upon the burning surface of the ceramic plate from which the burner is constructed. A very important feature of the recessed construction or the troughlike construction results from the orientation of the flame within the trough so that flame agitation is reduced to an absolute minimum by any air flow over the burning surface of the burner, thereby further increasing the efficiency of flame impingement upon the burning surface and further increasing the temperature of the burning surface of the burner. Another very important result from the construction of the recessed side walls of the slot-like openings is an increase in the effective area of the burning surface of the radiant burner. Inasmuch as the efficiency of the burner is dependent in part upon the burning surface area or incandescent area of the radiant burner, the increase in the surface area will, of course, increase the efficiency of the radiant burner.

The most important feature of the increase in the width of the slot or channel at the discharge end thereof is the provision of a width such that will not quench the flame whereas the parallel side walls of the slot or channel inwardly of the recess edges will quench the flame since the width of the slot or channel is less than the critical quenching distance for the material from which the radiant burner is constructed.

3,277,948 separation and variable plate width, because this appeared to be the most convenient method for obtaining accurate measurements. The investigations have been conducted with the use of plane parallel plates made from a ceramic material; however, investigations could easily be made involving other material.

The fact that the quenching effect of one type surface of a material is not different from any other type of surface does not permit any conclusion as to the importance of diffusion in quenching, since it is conceivable that one type of surface can be equally useful in promoting free radical recombinations, under the conditions in the vicinity of a flame. One proposed mechanism of flame propagation is based on the diffusion of atoms and free radicals ahead of the flame front. The approximate equation for flame velocity derived on this basis has been found to be consistent with measured flame velocities for a number of systems including hydrocarbons in air. Because of the success of this equation and the prediction of burning velocities, an extension of the mechanism to the quenching process appeared to have some merit.

The spreading of a flame may be considered to be the result of the perpetuation of a chain reaction by the diffusion of chain initiators. This means that initiation of the oxidation reaction in successive elements of combustible gas is accomplished by the diffusion of chain initiators into each element.. The number of chain initiators, their chemical and physical nature, and the velocity and direction of diffusion are determined by internal structure of the flame front. The flame structure consists of the gradients of temperature, pressure, and chemical species which exist in the flame as a result of the effect of the chemical oxidation reaction on the environment. If the structure of the flame is changed, either by the use of a different combustible mixture or by changes in the conditions of the environment, the rate of flame propagation ought to reflect these changes.

In order to apply the diffusion principle of flame propagation to the process of flame quenching, it is assured that

-. ------ ------ -- a surface near a propagating flame is the destruction of the chain carriers on the surface. Then, when a propagating flame approaches the entrance of a narrow duct, the first effect of the surface occurs in some thin cross-section ahead of the _ flame front. If the number of molecules that react in this ^io thin cross-section is sufficient to support the flame, it will pass into the ducts; otherwise, it will be extinguished.

The flame front is considered as a region of high temperature thermal equilibrium including a number of chain carriers. The chain carriers diffuse ahead of the burn, . _mivacuuti. Chain branching is negligible, and chain carriers are destroyed by collision with the surface. The extent of the oxidation reaction_ is limited by the destruction of chain carriers. This principle was used to formulate the approximate equation for the pressure limit of flammability in tubes of different diameters.

In prior investigations it was found that the quenching distance is proportional to the pressure to the minus 0 91 power for stoichiometric propane-air flame, and that the exponent numerically decreases with decreasing propane concentration in air. It has been further shown that the average ratio of quenching distances measured by flashback through plane parallel plates to quenching diameters tor cylindrical ducts is approximately 0.70 for lean propane-air mixtures, while for all propane mixtures, the averages was 0.62. This work indicates that the experimental critical diameters for propagation in the tube multiplied by 0.70 would be equivalent to the quenching distance measured by flash-back through parallel plates if both are governed by the same process.

In order to compare the values for quenching distances found m prior investigations, the effect of the geometry of the quenching surface must be considered. In recent investigations a series of thin parallel plates formed the geometry of the surface. The quenching distances deter10 recess at the outer edge or burning surface of the side walls of the slot 30 are provided by a square cut recess 32 formed in the side walls of the slot 30 which effectively increases the width of the slot and forms troughs or valleys 34 for receiving the flame whereby the flame will impinge against the side walls of the recess 32.

FIGURE 5 illustrates an arrangement in which the ceramic plate is designated by numeral 36 and the slots designated by numeral 38. In this form of the invention, the recess is formed in the side walls of the slots 38 by providing two square cut recesses 40 and 42 therein as illustrated in FIGURE 5 thus defining an increase in the width of the slot 38 and further defining a valley 44 in which the flame is disposed for more effective impingement upon the burning surface of the radiant burner.

In each of the forms of the invention, the slot or channey for passage of the combustible mixture is relatively narrow and has a width less than that critical width which will enable passage of flame. Thus, the width of the slots is such that flame will be quenched thus preventing backflash of the flame from the burning surface to the rear surface of the burner. While the flame quenching phenomena of a slot is not clearly understood, recent investigations of the engineering principles involved in connection with a radiant burner has resulted in some fundamental principles that were not heretofore fully accounted for. Investigation has shown the quenching distance of a flame, that is the gap between the flame and relatively cold surfaces is a very important aspect of the operation of a radiant burner such as that previously described.

The quenching distance of a flame can be measured quite accurately and reproducibly. The object of recent experimental investigations has been to make such measurements on hydrocarbon flames, the chemical kinetics of which are relatively well understood, in the hope that the resultant correlated data would be useful in the development of a theory that could be applied to the design of radiant burners. No completely adequate theory of flame behavior in terms of chemical kinetics and transport prop- _ _ ____„________ erties of gas molecules has yet been developed; however, 40 the most important effect of measurements of quenching distance provides an experimental approach to the study of flame structure. Furthermore, from the practical point of view, quenching is a very important aspect in the mechanism of flame anchoring which is of utmost importance in the operation of a radiant burner.

The mechanism by which quenching occurs is not well understood even qualitatively. Before the importance of free radicals and atoms in flames was fully appreciated, it was accepted that quenching was entirely governed by ____________ «uwu ui i heat conduction from the flame to the cold surface, chem- ^{50 ln} zone and initiate the oxidation reaction ical reactions being able to proceed only in those regions ........

of the gas where the temperature was greater than a vaguely defined ignition temperature. Now, in the light of present knowledge of chain reactions, it appears possible that the diffusion of chain carriers to the wall may play a significant role in quenching.

Four methods of measuring quenching distance have been proposed: (a) Observation of a gap between a stable flame and the cold burner rim, (b) the determination of the minimum tube diameter or distance between plane parallel plates through which flask-back can occur, (c) the determination of the minimum distance between plane parallel plates by which a flame will propagate from a spark of minimum ignition energy, and (d) the determination of the ratio of the burning velocity to the critical velocity gradient for flash-back.

The plan of this experimentation has been to make an accurate study of the effect of all convenient variables upon which hydrocarbon flame quenching depends. ₇₀Among these variables are the gas-air pressure, gas concentration, fraction of stoichiometric, the slot width, and the separating plate width.

Method (b) above, has been used to measure quenching distances, using plane parallel plates with variable 75

3,277,948 case, the process of flame propagation would also be effected by the surface. Further experimental work appears to be needed to establish the effect of the nature of the surface of quenching, limits of flammability, and flame 5 propagation.

Although, equations have been developed describing the phenomena of flame quenching the complete process by which a flame is quenched is not fully understood. It is certainly apparent that more mathematical methods will have to be developed which are capable of simultaneously handling the chemical kinetics, diffusion and heat transfer in a rigorous fashion, considering at least two dimensions, if the quenching of a flame is to be completely understood. However, without completely understanding 15 the phenomena of flame quenching, the end results of this phenomena can be applied quite accurately in the construction of radiant burners because it is certainly apparent that a close relationship between the flame properties of burning velocity, concentration limits of flam20 mability, and quenching distance does exist.

A burner has been constructed by your applicant utilizing the phenomena of quenching as the only method of preventing rearwardly extending combustion, into the plenum. It has been determined that gas air velocities in 25 a burner utilizing quenching can be as low as approximately 2 to 3 feet per second whereas the flame propogation can be as high as 9 to 12 feet per second and yet rearwardly extending combustion or backflashing will not occur because of the phenomena of flame quenching.

Referring specifically now to FIGURE 6 it is apparent that a channel is established that has an increasing cross sectional width near the surface of the burner. The purpose of increasing the width gap is to provide a gap width such that the flame will not quench, that is the width ex35 ceeds the critical quenching distance for the material and other factors mentioned in the preceding discussion. At some position between point (a) and point (5) the critical quenching distance will not be exceeded because of the converging nature of the channel, resulting in anchoring 40 of the flame to the surrounding walls. The flame cannot recede in a rearwardly direction beyond point (a) because the slot width at point (a) is less than the critical quenching distance therefore, trapping the flame in the given channel. It is of importance to note that the di45 vergent channels serve the two-fold purpose of controlling the quenching criticalities as well as controlling velocities of the gas air mixture which are certainly critical in this region of the burner. In other words if the gas air mixture velocity at point (a) exceeds the rate of propagation 50 of the flame then it is evident that this velocity can be reduced to a point less than the rate of propagation of the flame at point (5). Therefore, with the same type of construction or the same geometry involved critical factors relative to radiant burners are controlled, resulting 55 in the flame being firmly anchored to the channel, increasing the surface temperature to a great degree.

It has been shown in investigations with reference to the theories involved on a radiant burner that it is more likely that the phenomena of quenching is more critical 60 that the gas air velocity in comparison to the rate of flame propagation. It has been shown that a burner utilizing the phenomena of flame quenching should have a gap width not to exceed an order of magnitude of approximately .040 inch. The critical gap width of which 65 varies somewhat with the thickness of the plate, but a plate thickness not exceeding .075 inch can tolerate a gap width of approximately .040 inch and still quench the flame. It has further been shown that as the plate width is increased the critical gap distance can also be 70 increased. It is felt that the length of the thin slot also to some extent determines the critical width, however, the dimension of length is very nearly negligible as compared to the width of the slot.

If a channel is formed by a ceramic plate such as shown in FIGURE 6 it is evident the critical gap width mined by this method will not necessarily correlate data obtained by other methods. In the series plate method the flame is quenched on either surface of the plate whereas in other investigations only one surface of the plate was exposed to the flame. It seems the heat sinking properties of the plate will certainly be effected by exposing each surface of the plate to the flame as compared to the one surface being exposed in prior investigations.

The quenching distances determined, during recent investigations utilizing a series of plates, were less than those determined in prior investigations where only one surface of the plate was exposed to the flame. A typical quenching distance determined utilizing sixteen parallel plates, thickness of which was .060 inch, gas pressure 14 inches of water, fraction of stoichiometric equal to one utilizing C₃H₈ for the fuel, was .035 inch.

Reference has been made from time to time to the fact that the base of the inner cone of an aerated flame does not have immediate contact with the burner head, but it is separated from the rim by a small but finite distance known as the dead space, although this phenomena appears to have received little attention previously, it is felt that it is of some importance in the design of a radiant burner. More recently during the course of a comprehensive study of a burner flame, the dead space has been investigated systematically and measurements have been made covering a wide margin of experimental conditions. As a result, the true significance of the phenomena has been clearly revealed, thus not only is dead space an important factor in any measure of burning velocity by the dynamic method, but also it is one of the principal factors governing flame stability, the realization of which has enabled the mechanism of flash-back to be understood more clearly. A detailed description of the method employed for the measurement of dead space has been published elsewhere and the values of dead space as just defined have been obtained from many mixtures with air of ethylene, carbon monoxide and propane burning at various pressures between 20 cm. of mercury and atmospheric pressure upon burners of several diameters.

Unlike the burning velocity itself, dead space cannot be regarded as a physical constant of any one explosive mixture, and besides being dependent upon temperature and pressure, it is conditioned also by such factors as burner size and shape, the material of construction of the burner and to a lesser extent, flame area. It has not been shown thus far the degree, if any, that dead space effects the operation of a radiant burner. However, if this phenomena does occur it is evident that anything that could decrease this space would result in a higher surface temperature of the radiant burner. With proper quenching techniques the distance known as dead space between the burner surface and the flame front can be reduced to zero or to a negligible distance.

In recent investigations many experiments have been conducted utilizing a varying cross sectional area at the face of the burner surface. The purpose of this investigation was to determine what effect would occur in the process of the surface combustion. The experiments were carried out on a burner surface, the geometry of which allowed the critical quenching distance to be exceeded at the surface of the burner. The flame was immediately quenched a short distance from the surface of the burner by a geometry resulting from divergence of each ceramic plate. By utilizing this method of flame quenching, superiod anchoring to the surface of the burner was the net result.

Quenching is probably governed to a great extent by heat conduction from the flame to the cold surface; however, the destruction of chain carriers on the surface appears to be an important part of the quenching process. The present interpretation shows that the destruction of chain carriers on a surface could provide a termination step in the oxidation chain reaction which could be sufficiently important to suppress flame propagation. In that

3,277,948 at point (έ) can exceed the critical quenching distance which in this case may be of the order of magnitude of .040 inch, however, the gap width at point (a) is less than the critical quenching distance thereby anchoring the flame in the channel between point (a) and (έ). By 5 quenching the flame in this manner a distance that exists between the flame front and the burner surface known as dead space can be virtually eliminated. Also it is evident the flame can be entirely stable and generally embedded in the channels when the burner is located in ₁₀an area where air current exists.

Flame quenching can also be accomplished utilizing a surface geometry shown in FIGURE 4 and FIGURE 5. Utilizing configuration of FIGURES 4 and 5 the flame is quenched in the open channel above the cross 15 section labeled C. It is evident from the foregoing discussion that the flame can be quenched utilizing a configuration shown as in FIGURES 4 and 5, but with reference to the engineering principles involved certain other critera must exist in order that maximum efficiency 20 be attained with respect to the operation of a radiant burner. It is a well known fact that radiation is a function of the emitting surface temperature to the 4th power but is also a function of the surface area. For maximum efficiency, the ideal situation would be to 25 quench the flame and also expose maximum surface area for radiation emitting purposes. With reference to FIGURE 6 of a mathematical solution has been derived to determine the critical dimensions that will expose the greatest surface area to emit unobstructed radiation. 39 FIGURE 6 and the accompanying derivation and curve is self-explanatory and points out the fact that for maximum unobstructed radiation area, a certan angle of divergence of the plates must exist.

FIGURE 7 is a curve A of Predicted Radiation Effi- ³⁵ciency vs. Angle of Divergence and imposed upon this curve is curve B of Radiation Efficiency Actual vs. Angle of Divergence. It is readily seen that the maximum efficiency is attained at a given angle, however, the efficiency does not vary to a great extent in a given region ⁴θ of the curve. FIGURE 9 is a curve of Radiation Area vs. Angle of Divergence and illustrates how the effective radiating area drops off after a certain critical angle is exceeded.

Because of the phenomena of quenching, the flame _4rfront is securely anchored to the surface of the radiant burner and the surface temperature has been increased considerably. Increasing the surface temperature plays a significant role in the radiation efficiency but it appears that it has also increased the catalytic effect on the com- ₅₀bustion process. The increase in catalytic effect on the combustion process can probably be attributed to the increase in the surface temperature. The increase in surface, temperature has resulted in the emissivity of the radiating surface being also increased. By increasing 55 the emissivity of the surface, the total radiation emitted can be further increased.

By utilizing a geometry which has been described and shown in FIGURE 6 certain critical factors are controlled in a manner which results in the efficient opera- ₆₀tion of a radiant burner.

(A) Because of the natural divergence angle of gas exiting small apertures it is a fundamentally sound principle to allow the ceramic surface to follow closely the pattern of gas flow for maximum flame impingement. 55 It has been found that this gas pattern is different in thin slots than it is in round apertures. Regardless of benefits obtained from flame quenching or if the gas velocities were greater than or less than the flame propagation it would be fundamentally sound to closely follow the pat- 70 tern formed by the exiting gases to expose greater flame area to the surface. (See curve.) (B) By following a geometry as shown in FIGURE 6, the maximum unobstructed radiation area is exposed if the proper divergence angle is selected. FIGURE 9 75 ε

illustrates the increase in unobstructed radiation area by the mehod of divergence. In a typical example the radiation area in inches square of a flat burner was approximately 2.82 and by diverging the openings at an angle beta of approximately 54° the radiation area was increased to approximately 4.82 square inches.

(C) By utilizing the geometry as previously described the phenomena of flame quenching is definitely controlled. If in a particular application the gas-air velocities were the controlling factor, then the same geometry the gas-air velocities could be reduced to a point less than flame propagation before they exited the burner, again attributing to superior flame impingement and flame stability. The most important aspect is the control of the phenomena of flame quenching; without proper control of this phenomena, rearwardly extending combustion could result. The proposed geometry also serves the purpose of increasing the coefficient of forced convection heat transfer. This can be attributed to the turbulence of the gas.

(D) Because of the increase in surface temperature the emissivity of the radiating surface has also been increased contributing to an increase in radiant efficiency.

(E) By embedding the flame in the channels as described the flame stability is far superior to the flame of a burner utilizing a flat surface.

(F) By utilizing this geometry the pattern of heat distribution is far superior to that of conventional burners. (Please refer to FIGURE 10.) It is common knowledge that a radiant ray of maximum flux concentration leaves normal to a surface. If a burner was suspended horizontally the ray of maximum concentration would leave normal to the surface and would be represented by ray A of FIGURE 10 (note FIGURE 10 is a diagrammatical representation but the rays are drawn to an approximate scale). As the angle is changed from the normal flux concentration represented by c, d, d is decreased and the resulting heat distribution of a burner utilizing a flat surface would be similar to the pattern in the drawing of FIGURE 10. With a design utilizing the divergent section, the ray of maximum concentration travels the longest distance and as the rays flux concentration diminish, the distance the ray has to travel is also decreased resulting in a more even heat pattern distribution. The heat pattern distribution can be of importance when this type burner is utilized in space heating. In operation of the conventional flat surface burner, the area immediately beneath the center of the burner is usually much hotter than the area a few feet away from the center. However, by using the geometry of divergence, this hot spot to some extent is eliminated and it is easier to accomplish a more uniform heat pattern across the area to be heated. It should be pointed out that if the rays need to be concentrated that concentration could be accomplished with the use of a reflector and that if the principle of quenching was to be utilized without the added benefit of ' divergence then a geometry similar to FIGURES 4 or 5 could be used.

From the above discussion, it is apparent that many factors attributing to the increase in radiation efficiency can be influenced by the geometry described in this patent application. There is no question to the theories involved because a burner utilizing these principles has been reduced to practice and many rigorous investigations involving the above theories have been conducted.

From an examination of FIGURE 6 it is apparent that the following relations exist:

(1) c D

Cosine B=— f (2) _{f ;}(/₂z) ^J cos B cos B

3,277,948 (4) Tangent B—-7F— (/22:) (5) h = y₂ x tan B

In order for ray R to clear point b and be normal to surface /, the following relation exists:

(6) (7) (8) (9)

Sine IL sin E

H=180° —90°—B

B=90°-B

But from Equation 5 h=Vix tan B and Equation 9 E=90°-B (10) /Xtan B sin (909—B)

But if R satisfies the conditions of the hypotenuse of triangle cbd then:

^(U) Cos (90°-B)=^±^ (¹²) r, y+fa cos (90°—B)

It is obvious that R must satisfy Equations 10 and 12 if it is to meet the stated conditions.

(13) y₂ x tan B___y+}ix sin (90°—B)~cos (90°—B)

It is further obvious that for any value of x+y that only one angle will satisfy the Equation 13.

In certain instances, the velocity of the combustible mixture is controlled and the geometry discussed previously not only serves as a control for back flashing but in certain instances, the velocity is also controlled for assuring proper flame anchorage to the burning surface. Various thicknesses of burner plate may be employed and by balancing the thickness of the plate, the width or size of the openings and the velocity of the gases, a highly efficient radiant burner is produced. A very important factor is the actual increase of exposure area for radiation and also, the flame contact area with the burning surface is increased by the divergent surfaces at the burning surface of the burner.

The foregoing is considered as illustrative only of the principles of the invention. Further, since numerous modifications and changes will readily occur to those skilled in the art, it is not desired to limit the invention to the exact construction and operation shown and described, and accordingly all suitable modifications and equivalents may be resorted to, falling within the scope of the invention as claimed.