Abstract:
A burner nozzle having a hot face, side surfaces, and a plurality of internal gas flow passages and comprising a plurality of slits oriented in at least two different directions, wherein a selected number of the slits are formed in the hot face and/or side surfaces. The optimized location and depth of the slits relieve stresses that arise from temperature differences within the burner nozzle, caused by operation in high temperature furnaces, thereby extending the life (time to failure by fracture) of the burner nozzle.

Description:
CLAIM OF PRIORTY  
       [0001]    This Application claims priority from Provisional Application No. 60/180,103, entitled DESIGN AND MANUFACTURE OF REFRACTORY BURNERS, which was filed on Feb. 3, 2000, in the U.S. Patent and Trademark Office. 
     
    
     
       BACKGROUND OF THE INVENTION  
         [0002]    1. Field of the Invention  
           [0003]    The invention relates generally to refractory burner nozzles used to fire high temperature furnaces such as those in glass melting furnaces. More specifically, the invention relates to stress-relieving mechanisms for a burner nozzle.  
           [0004]    2. Background Art  
           [0005]    Burner nozzles employed in high temperature furnaces, such as glass melting furnaces, are made of refractory materials that can withstand high operating temperatures, for example, of greater than 900° C. without softening. In operations, combustible gases flowing through internal passages of the burner nozzle typically have a much lower temperature than a “hot face” that is exposed to the combustion zone and operating temperature of the furnace. This situation results in relatively large temperature gradients across the burner nozzle. These large temperature gradients cause thermal stresses in the burner nozzle, which at high levels may be sufficient to fracture the burner nozzle. In general, compressive stress develops in the heated hot face portion and tensile stress develops in the cooler portion of the burner&#39;s refractory body. The ultimate tensile strength of refractory materials is usually much lower in magnitude than their ultimate compressive strength. Thus, thermal stresses in refractory materials result in fracture cracks propagating from the cooler region toward the hot face.  
           [0006]    [0006]FIG. 1 illustrates a burner nozzle design of the prior art, as described in detail in European Patent Application EP 0969249A2 (Snyder et al.) by Praxair Technology, Inc., filed Jun. 29, 1999. The burner is of a refractory construction with a substantially rectangular three-dimensional form, with three nozzle ports arranged in a fan-shape, terminating in the hot face of the burner, to produce a wide flame. Although this Patent Application shows slits on the side surfaces of a burner nozzle, the Patent Application does not disclose using slits in the hot face, nor does it teach the optimal placement or depth of side surface slits.  
           [0007]    FIGS.  2 A- 2 C show the types of fractures that are typically observed in burner nozzles. The fractures can be classified according to their relative orientation with respect to the longitudinal centerline of the burner nozzle. For example, the most common type of fracture, in burner nozzles of the kind described in the Praxair patent, is a so-called transverse fracture  1  as illustrated in FIG. 2A, since it transverses the longitudinal centerline of the burner. The fracture  3  shown in FIG. 2B is a longitudinal fracture. This type of fracture runs along the centerline of the burner, between from the colder region  5 , the surface of the burner that is farthest from the furnace combustion zone (not shown), and the hot face  7 . Fractures probably start in a high stress region (an area with a combined high temperature change over a small dimension and area change, such as the junction between a plenum and the discharge flow nozzles.) FIG. 2C shows a diagonal fracture  9 , which is less common.  
           [0008]    Although the scientific literature 1  has touched upon the fact that thermal stresses in a refractory article can be reduced by decreasing the linear dimension of a section of the refractory article that is perpendicular to the thermal flux, the literature does not adequately discuss, not to mention effectively teach, how to optimize thermal stress reduction in the refractory article. Nor does the literature or relevant patents suggest where to locate stress relieving slits in the refractory article and how deep a slit should be. Therefore, we believe that we have discovered the optimal placement and depth for achieving the desired result of reducing or even eliminating thermal stresses and to prolong the useful lifetime of burner nozzles.  
         SUMMARY OF THE INVENTION  
         [0009]    The invention relates in one aspect to the optimized placement and depth of stress relieving slits in a burner nozzle having a hot face, side surfaces, and a plurality of internal gas flow passages. The burner nozzle comprises a plurality of stress relieving slits oriented in at least two different directions, and a selected number of the slits formed in the hot face. In some embodiments, a selected number of the slits are formed in the side surfaces. In some embodiments, the burner nozzle further includes an internal plenum smoothly or fluidly connected to the internal flow passages. In some embodiments, the slits formed in the hot face have a depth of approximately 50% to 70% of the perpendicular distance from the hot face to a leading edge of the plenum. Stated in another fashion, in some embodiments, the slits formed in the hot face have a depth of approximately 10% to 75% of a length of a radius that bisects an angle formed by the longitudinal axes of two adjacent internal flow passages as they terminate in the hot face. In some embodiments, the slits formed in the side surfaces, relative to the hot face, are positioned approximately 30% to 50% of a length of the burner nozzle. The slits formed in the side surfaces have a depth of 20% to 50% of the thickness of the side surfaces.  
           [0010]    Thermal stresses experienced by the burner nozzle are substantially reduced by at least 10%, relative to a burner that does not have a combination of: a plurality of stress-relieving slits, each having a predetermined depth, formed in the hot face, where the slits are positioned between adjacent internal flow passages, and at least one stress slit is formed in each side surface. In comparison to a burner having only stress slits formed in the side surfaces, the thermal stresses experienced by the burner nozzle are reduced by at least 15%, and to a burner having no stress slits, the thermal stresses experienced by the burner nozzle are reduced by at least 20%. In particular, the thermal stresses experienced by the burner in the roof and floor of a center internal flow passage, an outboard internal flow passage, or a plenum, and are all reduced by at least 10%, relative to a burner having only stress slits formed in the side surfaces. Moreover, by employing optimized placement of the stress-relieving slits, the useful lifetime of a burner nozzle is prolonged as a function of stress reduction by at least one order of magnitude.  
           [0011]    Other aspects and advantages of the invention will be apparent from the following description and the appended claims. 
       
    
    
     BRIEF DESCRIPTION OF THE FIGURES  
       [0012]    [0012]FIG. 1 shows a prior-art burner nozzle design, which produces a wide flame.  
         [0013]    FIGS.  2 A- 2 C show different types of fractures that can occur in burner nozzles.  
         [0014]    [0014]FIG. 3A shows a perspective view of a burner nozzle according to one embodiment of the invention having a full plenum, and with one quarter of the burner cut away.  
         [0015]    [0015]FIG. 3B shows the hot face of the burner nozzle of FIG. 3A.  
         [0016]    [0016]FIG. 4 shows a planar view of the internal structure of the burner nozzle of FIG. 3A.  
         [0017]    [0017]FIG. 5 shows a perspective view of a burner nozzle according to one embodiment of the invention having a short plenum, and with one quarter of the burner cut away.  
         [0018]    [0018]FIG. 6 shows a perspective view of a burner nozzle according to one embodiment of the invention having no plenum, and with one quarter of the burner cut away.  
         [0019]    [0019]FIG. 7 is a graph illustrating the effect of stress slits on stress at the roof of the center flow passage of the burner nozzle shown in FIG. 3A.  
         [0020]    [0020]FIG. 8 is a graph illustrating the effect of stress slits on stress at the roof of the plenum of the burner nozzle shown in FIG. 3A.  
         [0021]    [0021]FIG. 9 is a graph illustrating the effect of stress slits on stress at the roof of the outboard flow passages of the burner nozzle shown in FIG. 3A.  
         [0022]    [0022]FIG. 10A is a perspective view of a quarter of the burner nozzle shown in FIG. 3A, showing a contour illustration of the stress concentrations in the roof or floor of the center flow passage and an outboard flow passage.  
         [0023]    [0023]FIG. 10B is a close-up view of the stress contours, shown in FIG. 10A, at the hot face and the end of the plenum of the burner nozzle shown in FIG. 3A. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0024]    Embodiments of the invention provide a stress-relieving mechanism for a burner nozzle. In general, the stress-relieving mechanism comprises forming in the burner nozzle a plurality of slits oriented in at least two different directions. The slits are located on the hot face and side-surfaces of the burner nozzle. A thermal stress analysis of burner nozzles having a combination of slits formed in both the hot face and side surfaces show that we can achieve significant reduction of thermal stresses in the burner. Stress reduction also imparts a salutary effect on the lifetime of a burner nozzle, which will be discussed in greater detail below. Analytical results further show that the deeper the stress slits penetrate into the burner nozzle block, the greater the reduction in the overall stress in the burner. Yet, to ensure the structural integrity of the burner nozzle, there are practical limits to how deep the stress slits can penetrate into the burner nozzle.  
         [0025]    The optimal depth of a slit formed in the hot face is determined according to certain standard parameters and principles employed in thermal stress and structural analysis. These parameters used in predictive analysis need to balance the competing goals of forming slits that are sufficiently deep to reduce stress effectively and significantly, while simultaneously preserving the structural integrity of the burner nozzle block. Generally, to determine thermal stress analysis of brittle materials, such as ceramics or other refractory, a comparison is made of the principal stress factors with the tolerances of the material. In the present invention, we compared the first principal stress, tension, to the ultimate tensile strength of the refractory material. We found that by incorporating stress relieving slits at optimized locations and at predetermined depths, we were able reduce the first principal stress to be within the tensile strength tolerances of the material.  
         [0026]    We will describe various embodiments of the invention with reference to the accompanying figures. FIG. 3A shows a cut-away perspective view of a burner nozzle  2  that can be used in a burner unit such as disclosed in European Patent Application EP 0969249A2, herein incorporated by reference. The burner nozzle  2  is made of a refractory material such as a ceramic. The burner nozzle  2  has a top surface  4 , side surfaces  6  and  8 , a hot face  10 , and a cold face  12 . A center flow passage  14  and outboard flow passages  16  and  18  (see, FIG. 4) are located within the burner nozzle  2 . The flow passages  14 ,  16 , and  18  terminate at orifices  20 ,  22 , and  24 , respectively, in the hot face  10 . In one embodiment, the burner nozzle  2  has an internal plenum  26 . (It should be clear, however, that the present invention is not limited to burner nozzles with internal plenums.) The plenum  26  is smoothly or fluidly connected to the internal flow passages  14 ,  16 , and  18 . In operation, a gaseous fuel or oxidant enters the plenum  26  from the rear direction, near the cold face  12 , and is transferred to the flow passages  14 ,  16 , and  18 , where it exits through the orifices  20 ,  22 ,  24 .  
         [0027]    As discussed before, stresses tend to arise because of the temperature difference between the cooler internal flow passages and plenum, in those embodiments that have a plenum, and the outer hot face that is exposed to the interior of a high-temperature furnace. These large differences in temperature induce thermal stresses in the burner nozzle  2 . While this situation makes the hot face  10  of the burner nozzle  2  particularly vulnerable to fracture, maximum tensile stresses occur in the interior of the flow passages, not just at the hot face. Discontinuities in the hot face  10  created by the orifices  20 ,  22 ,  24  and the internal flow passages  14 ,  16 ,  18  tend to concentrate stresses in the roofs ( 38 ,  54 ,  56  in FIG. 3B) and floors ( 39 ,  55 ,  57  in FIG. 3B) of each of the internal flow passages  14 ,  16 ,  18 , and in those embodiments having a plenum, at the junction  36  between the internal flow passages  14 ,  16 ,  18  and the plenum  26 , as well as the roof and floor of the plenum itself. Depending on whether a plenum is present, stresses tend to concentrate, relative to the hot face, in regions located at a distance of approximately 25% of the length of the burner nozzle.  
         [0028]    Hence, to prevent the burner nozzle  2  from fracturing, as part of our invention, slits  32 ,  34  are provided in the hot face  10  to relieve stress in the burner nozzle  2 . Preferably, a stress-relieving slit  32  is positioned midway between the orifices  20  and  22  and midway between the flow passages  14 ,  16 , and another slit  34  is positioned midway between the orifices  20  and  24  and midway between the flow passages  14 ,  18 . Stress-relieving slits  28  and  30  are also provided on the side surfaces  6 ,  8  of the burner nozzle  2 , respectively, closer toward the hot face  10  of the burner nozzle  2 . The internal flow passages  14 ,  16 ,  18 , each have a longitudinal axis. The axes of two adjacent internal flow passages form an angle relative to each other, as the flow passages terminate at the hot face. The slit  32  formed in the hot face bisects the angle formed by the axes of flow passages  14  and  16 , and slit  34  bisects the angle formed by the axes of flow passages  16 , and  18 . As shown in FIGS. 3A and 3B, the external height of the slits  32 ,  34  formed in the hot face are oriented to be parallel, or vertically situated with respect to the shortest dimension, or the height (H) of the burner nozzle.  
         [0029]    In the discussions that follow, it would be helpful to refer to FIG. 4. The hot face  10  is used as a reference point for precisely describing the stress slits  28 ,  30 ,  32 , and  34  on the burner nozzle  2 . Referring to FIG. 4, the length “L” of the burner nozzle  2  is defined as the perpendicular distance from the hot face  10  to the back surface  12 . The position of the stress slits  28  and  30  on the side surfaces  6 ,  8  is a fraction of the length “L” as measured from the hot face  10 . Typically, the position of the stress slits  28  and  30  will be between approximately 0.3 L and 0.5 L. In our experiments, we set the location of stress slits  28  and  30  at approximately 0.35 L. The width “w” of the plenum  26  relative to the width “W” of the burner nozzle  2  limits the depth of the stress slits  28  and  30 . The side surfaces  6 ,  8  have a predetermined thickness  
         (       W   -   w     2     )     ,                         
 
         [0030]    and the stress slits  28  and  30 , have a depth of 20% to 50% of the thickness. As studied, the depth was approximately 33⅓% of the thickness.  
         [0031]    In FIG. 4, the stress slits  32  and  34  have a depth “d” that is the perpendicular distance from the hot face  10  to the center of cylindrical portions  100 ,  102 , respectively, of the stress slits  32  and  34 . Depth “d” is approximately 50% to 75% of a face depth “D.” The face depth “D” is the perpendicular distance from the hot face  10  to the leading edge  37  of the plenum  26 . Stated in other words, the stress slits formed in the hot face have a depth of approximately 10% to 75% of a length of a radius that bisects the angle formed by the longitudinal axes of two adjacent internal flow passages, relative to each other, as the flow passages terminate at the hot face. This second characterization would apply equally as well to embodiments of the burner nozzle  2  that did not include an internal plenum, such as shown in FIG. 6, where the flow passages  14 ,  16 ,  18  would extend to the back surface  12  of the burner nozzle  2 , such that the face depth “D” would be the same as the length “L” of the burner nozzle  2 , or even to an embodiment that had a short plenum, such as shown in FIG. 5.  
         [0032]    [0032]FIG. 7 is a graph that illustrates the effect of stress slits  28 ,  30 ,  32 , and  34  on reducing stress in the roof  38  or floor of the center flow passage  14 . In this illustration, “d” is the depth of the hot face stress slits  32 ,  34  and “D” is the depth of the hot face  10 . The x-axis of the graph expresses the depth of the hot face stress slits  32  and  34  in a ratio of “d/D,” and the y-axis expresses the percentage of stress reduced relative to a maximum stress level in a center flow passage roof or floor that does not have slits of any kind —as a function of the depth of the hot face stress slits. The position of the side stress slits  28  and  30  with respect to the hot face  10  is maintained constant at roughly 0.35 L, where “L” is the length of the burner nozzle  2 . Three sets of data points are given in the graph. First, a line  40  connects the data points corresponding to a scenario where the burner nozzle  2  has only side stress slits  28 ,  30 , i.e., the hot face stress slits  32 ,  34  are absent from the burner nozzle  2 . Second, a line  42  connects the data points corresponding to a scenario where the burner nozzle  2  has only hot face stress slits  32 ,  34 , i. e., the side stress slits  28 ,  30  are absent from the burner nozzle  2 . Third, a line  44  connects the data points corresponding to a scenario where the burner nozzle  2  has both hot face stress slits  32 ,  34  and side stress slits  28 ,  30 .  
         [0033]    In burner-nozzle designs having only side stress slits  28 ,  30 , line  40  indicates that stress is reduced in the roof  38  of the center flow passage  14  by approximately 5%. By way of comparison, burner nozzle designs having only front stress slits  32 ,  34  experience a reduction of stress in the roof  38  or floor of the center flow passage  14  that ranges from approximately 5% to 23% for d/D ranging from 0.17 to 0.6. In one example, at d/D=0.6, we were able to reduce stress in roof  38  or floor of the center flow passage by as much as 18% over a burner having only side stress slits  28 ,  30  (shown in FIG. 3A) with the same d/D ratio. In our experiments, burner nozzle designs that have a combination of both hot face stress slits  32 ,  34  and side stress slits  28 ,  30  experience a reduction of stress in the roof  38  or floor of the center flow passage  14  that ranges from approximately 12% to 28% for a d/D ranging from approximately 0.17 to 0.6. Again, at d/D=0.6, we gained an additional 5% in stress reduction over the stress reduction that was achieved when deploying only front stress slits  32 ,  34 .  
         [0034]    [0034]FIG. 8 is another graph which illustrates the effect of stress slits  28 ,  30 ,  32 , and  34  on reducing stress in the roof  46  or floor of a burner designed with a plenum  26 . For this example, like in the FIG. 7, the depth “d” of the hot face stress slits  32  and  34  is expressed as a ratio of the depth “D” of the hot face, while the position of the side stress slits  28  and  30  is maintained constant at roughly 0.35 L with respect to the hot face  10 . Again, three sets of data points are shown in the graph. First, the data points that are connected by line  48 , correspond to a scenario where the burner nozzle  2  has only side stress slits  28 ,  30 . Second, the data points that are connected by line  50 , correspond to a scenario where the burner nozzle  2  has only hot face stress slits  32 ,  34  (shown in FIG. 3A). Third, the data points that are connected by line  52 , correspond to a scenario where the burner nozzle  2  has both hot face stress slits  32 ,  34  and side stress slits  28 ,  30 .  
         [0035]    As shown in the graph of FIG. 8, the percentage of stress reduced is relative to the amount of stress in the roof  38  or floor of the center flow passage  14  at junction with the plenum  26 . In burner nozzle designs that have only side stress slits  28 ,  30 , line  48  appears to suggest that stress reduction in the roof  46  of the plenum  26  dips below 10%. That is, the amount of stress in the roof  46  or floor of the plenum  26  actually increases. This phenomenon could possibly be explained as a function of computer modeling. If corrected for variations in mesh-density of the burner block, line  40  would be level at approximately 10% stress reduction.  
         [0036]    In contrast, burner-nozzle designs having only hot face stress slits  32 ,  34 , stress reduction ranges from approximately 10% to 42% for a d/D ranging from 0.17 to 0.6. Again, “d” is the depth of the hot-face stress slits  32 ,  34  and “D” is the depth of the hot face  10 . In general, for a given depth “D” of the hot face  10 , the stress reduction in the roof  46  of the plenum  26  increases as the depth “d” of the stress slits  32 ,  34  increases. For burner-nozzle designs having a combination of hot-face stress slits  32 ,  34  and the side stress slits  28 ,  30 , stress is reduced by a range of approximately 10% to 39% for a d/D ranging from 0.17 to 0.6.  
         [0037]    [0037]FIG. 9 is another graph that illustrates the effect of stress slits  28 ,  30 ,  32 , and  34  on reducing stress in the roofs  54 ,  56  or floors of the outboard flow passages  16 ,  18 . Like in the two prior illustrations, “d” is the depth of the hot-face stress slits  32  and  34 , as expressed as a ratio “d/D” of the depth “D” of the hot face  10 . The position of the side stress slits  28  and  30  is again maintained constant at roughly 0.35 L with respect to the hot face  10 . Three sets of data points are shown in the graph. The first set of data points, connected by the line  58 , corresponds to a scenario where the burner nozzle  2  has only side stress slits  28 ,  30 . The second set of data points, connected by the line  60 , corresponds to a scenario where the burner nozzle  2  has only hot-face stress slits  32 ,  34 . The third set of data points, connected by the line  62 , corresponds to a scenario where the burner nozzle  2  has both hot-face stress slits  32 ,  34  and side stress slits  28 ,  30 .  
         [0038]    [0038]FIG. 9 indicates that burners nozzles with only side stress slits  28  manage to reduce the amount of stress in the roofs  54 ,  56  or floors of the outboard flow passages  16 ,  18  by a range of from 10% to 27%. On average, the stress reduction is approximately 22%. Burner nozzles that possessed only hot-face stress slits  32 ,  34  experienced a stress reduction of approximately 10% to 37% for a d/D ranging from 0.17 to 0.6. We observed that the deeper we made the hot-face stress slits, the greater the percentage of stress reduction, as is reflected in the graph. With a combination of both hot-face stress slits  32 ,  34  and side stress slits  28 ,  30 , stress levels in the roofs or floors of the outboard flow passages reduced by as much as 32%, from approximately 10% to 42%, for a d/D ranging from 0.17 to 0.6.  
         [0039]    As can be seen from FIG. 8, the incorporation of hot-face stress slits  32 ,  34  alone, into the design of a burner nozzle is sufficient to achieve significant stress reduction. In fact, we observed a surprising result. Just having hot face stress slits is more effective in reducing stresses in the roof  46  of the plenum  26  than either having a combination of hot face stress slits  32 ,  34  and side stress slits  28 ,  30  or side stress slits  28 ,  30  alone.  
         [0040]    While, stresses in the roof  38  of the center flow passage  14  tend to contribute to longitudinal fracturing, stresses in the roofs  54 ,  56  or floors  55 ,  57  of the outboard flow passages  16 ,  18  tend to contribute to the development of diagonal fractures. Data plotted in FIGS. 7 and 9, demonstrate that a combination of both hot-face stress slits  32 ,  34  and side stress slits  28 ,  30  together is more effective in reducing stress in both the roof or floor  38 ,  39  of the center flow passage  14 , and in the roofs  54 ,  56  or floors  55 ,  57  of the outboard flow passages  16 ,  18 , respectively, than using either element independent of the other.  
         [0041]    In general, hot-face stress slits  32 ,  34  are more effective in reducing stress in the roof  38  of the center flow passage  14  and the roof  46  of the plenum, while side stress slits  28 ,  30  tend to be more effective in reducing stress in the roofs  54 ,  56  of the outboard flow passages  16 ,  18 . Overall, a combination of hot-face stress slits  32 ,  34  and side stress slits  28 ,  30  can result in significant reduction in the stress on the burner nozzle  2 , especially in the areas that are most prone to fracture (see FIGS.  2 A- 2 C). Preferably, the depth of the front stress slits  32 ,  34  range from 50% to 70% of the depth of the hot face  10 .  
         [0042]    To summarize, from the data provided in FIGS. 7, 8, and  9 , we made certain observations of the present invention. With the combination of both hot face slits  32 ,  34 , and side slits  28 ,  30  and d/D ratio ranging from 0.17 to 0.6 the maximum stress: (i) in the roof  38  or floor of the center flow passage  14  can be reduced by about 12% to 28%; (ii) in the roof  46  or floor of a burner with a plenum  26  can be reduced by about 10% to 39%; (iii) in the roofs  54 ,  56  or floors of outboard flow passages  16 ,  18  can be reduced by 32%. These are significant amounts of stress reduction, which as discussed below, can prevent burner nozzle failures and extend the useful nozzle life by orders of magnitude.  
         [0043]    As previously mentioned, most failures in burner nozzles are due to transverse fractures cause by stresses in the roof or floors of the plenum  26 . FIGS. 10A and 10B illustrate as contour lines the reduction of stresses in a quarter view of a roof  46  or floor of a burner nozzle shown in FIG. 3A. Although the prior art may show what amounts to a ten percent stress reduction, this amount of reduction is not ubiquitous or universal. Our invention raises the level of stress reduction considerably higher in all  3  critical places where fractures have been observed.  
         [0044]    To quantify the practical effect of stress reduction, the life of a burner nozzle  2  as a function of stress reduction can be obtained from equation (1) below:  
             t   =         t   0          (       σ   0     σ     )       n             (   1   )                               
 
         [0045]    where σ 0  is the stress in a burner nozzle without stress slits, σ is stress in a burner nozzle with stress slits, to is the nozzle life for stress σ 0 , t is the nozzle life for stress σ, and n is the fatigue constant for the nozzle material. Equation (1) is further discussed in detail in papers 2  by A. G. Evans and S. T. Gulati, respectively, which are both herein incorporated in their entirety by reference.  
         [0046]    Table 1, below, shows the effect of stress reduction on nozzle life, for an example assuming that n=25.  
                                           TABLE 1                           Increase in Nozzle Life as a Function of Stress Reduction                σ/σ 0  =   Increase       Stress Reduction (%)   [1 − (Stress reduction)/100]   in Nozzle Lifetime                    10   0.90   13.93t 0         15   0.85   58.15t 0         20   0.80   264.70t 0         25   0.75   1328.83t 0         30   0.70   7456.74t 0         35   0.65   47551.70t 0         40   0.60   351737.56t 0         45   0.55   3096949.80t 0                    
 
         [0047]    As shown in Table 1, the present invention greatly enhances the useful life of a burner nozzle. By using a combination of both hot-face stress slits and side stress slits, the overall thermal stress levels throughout the burner nozzle are significantly reduced, especially the high stress regions. This stress reduction can prolong the lifetime of the burner nozzle by at least one order, but more probably several orders of magnitude. A longer useful life for a burner nozzle has many commercial advantages for high-temperature furnace operation. Furnace operators need not replace nozzles as often as currently required, or possibly need to rebuild a furnace as frequently. Both of these effects can contribute significantly to cost savings.  
         [0048]    Although the present invention has been described by way of a limited number of embodiments, it will be apparent to those skilled in the art that various modifications and variations can be made to the present glass compositions without departing from the spirit and scope of the invention. Therefore, unless such changes and modifications otherwise depart from the scope of the present invention, they should be construed as included herein.