Patent Publication Number: US-10314112-B2

Title: Self-regulating packed-powder resistive heater

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims the benefit of U.S. Provisional Application No. 62/252,148 filed 6 Nov. 2015, titled “Self-Regulating Packed Powder Resistive Heater” (Navy Case #103640). 
    
    
     FEDERALLY-SPONSORED RESEARCH AND DEVELOPMENT 
     The United States Government has ownership rights in this invention. Licensing and technical inquiries may be directed to the Office of Research and Technical Applications, Space and Naval Warfare Systems Center, Pacific, Code 72120, San Diego, Calif., 92152; voice (619) 553-5118; ssc_pac_t2@navy.mil. Reference Navy Case Number 103540. 
    
    
     BACKGROUND OF THE INVENTION 
     This invention relates to the field of resistive heaters. 
     SUMMARY 
     Disclosed herein is a heater comprising an outer tube, an inner tube, a conductive powder, and two electrodes. The outer tube has a first thermal expansion coefficient and the inner tube has a second thermal expansion coefficient that is less than the first thermal expansion coefficient. The inner tube is disposed concentrically with the outer tube such that there is a space between the inner and outer tubes where the conductive powder is disposed. The two electrodes are in electrical contact with the conductive powder such that when a potential is introduced between the electrodes, the conductive powder functions as a resistive heater whose resistance changes with temperature based on different degrees of thermal expansion of the inner and outer tubes. 
     The heater disclosed herein may be used in a method for heating comprising the following steps. The first step involves providing the concentric inner and outer tubes having different thermal expansion coefficients. The next step provides for packing the space between the inner and outer tubes with the conductive powder. The next step provides for providing the two electrodes in electrical contact with the conductive powder. The next step provides for introducing a potential across the electrodes such that the conductive powder functions as a resistive heater whose resistance changes with temperature based on different degrees of thermal expansion of the inner and outer tubes. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Throughout the several views, like elements are referenced using like references. The elements in the figures are not drawn to scale and some dimensions are exaggerated for clarity. 
         FIGS. 1A and 1B  are respectively perspective and cross-sectional views of a resistive heater. 
         FIG. 2  is a graphical plot showing the change in volume of conductive powder over a temperature range of approximately 1500° C. 
         FIGS. 3A and 3B  are respectively perspective and cross-sectional views of a resistive heater. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
     The disclosed methods and systems below may be described generally, as well as in terms of specific examples and/or specific embodiments. For instances where references are made to detailed examples and/or embodiments, it should be appreciated that any of the underlying principles described are not to be limited to a single embodiment, but may be expanded for use with any of the other methods and systems described herein as will be understood by one of ordinary skill in the art unless otherwise stated specifically. 
       FIGS. 1A and 1B  are illustrations of a self-regulating, packed-powder, resistive heater, hereinafter referred to as resistive heater  10  that automatically and gradually reduces the input power of the heater as the temperature increases.  FIGS. 1A and 1B  are respectively perspective and cross-sectional views of the resistive heater  10 . Resistive heater  10  comprises, consists of, or consists essentially of an outer tube  12 , and inner tube  14 , a conductive powder  16 , and first and second electrodes  18  and  20 . The resistance of the resistive heater  10  changes with temperature based on differing thermal expansion coefficients of the outer tube  12 , and inner tube  14 . The outer tube  12  has a thermal expansion coefficient that is larger than the thermal expansion coefficient of the inner tube  14 . The outer and inner tubes  12  and  14  are concentrically disposed with respect to each other. The diameters of the outer and inner tubes  12  and  14  are such that there is a space between the inner and outer tubes  14  and  12 . The conductive powder  16  is packed into the space between the inner and outer tubes  14  and  12 . The first electrode  18  in the embodiment of the resistive heater  10  shown in  FIGS. 1A and 1B  is a conductive metal coating on the inner surface of the outer tube  12 . The second electrode  20  in the embodiment of the resistive heater  10  shown in  FIGS. 1A and 1B  is a conductive metal coating on the outer surface of the inner tube  14 . Both electrodes  18  and  20  are in electrical contact with the conductive powder  16  such that when a potential is introduced between the electrodes  18  and  20 , the conductive powder  16  functions as a resistive heater whose resistance changes with temperature based on different degrees of thermal expansion of the inner and outer tubes  14  and  12 . The space between the inner and outer tubes  14  and  12  may be sealed with ceramic end caps  22 . 
     The conductive powder  16  functions as a variable resistor. Heat is generated as a function of the degree to which the conductive powder  16  resists current flow. As the heat increases, the inner tube  14  expands at a slower rate than the outer tube  12  which decreases the degree to which the conductive powder  16  is compressed between the inner and outer tubes  14  and  12 . As the conductive powder  16  becomes less compressed its resistivity increases, which in turn decreases the temperature generated by the resistive heater  10 . The heat generated by the resistive heater  10  is proportional to the power (P) dissipated through the device given by the known equation: 
     
       
         
           
             
               
                 
                   P 
                   = 
                   
                     IV 
                     = 
                     
                       
                         
                           I 
                           2 
                         
                         ⁢ 
                         R 
                       
                       = 
                       
                         
                           V 
                           2 
                         
                         R 
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     Where R is the resistance of the conductive powder  16  packed between the inner and outer tubes  14  and  12 , I is the current going through the conductive powder  16 , and V is the voltage across the resistive heater  10  (i.e., the voltage difference between the 1 st  and 2 nd  electrodes  18  and  20 ). If the inner tube  14  has a lower thermal expansion coefficient than the outer tube  12 , the resistance of the powder  16  will increase as the tubes get hotter. If the inner tube  14  has a higher thermal expansion coefficient then the outer tube  12 , than the resistance will decrease as the tubes get hotter. 
     The resistive heater  10  will typically be powered by an approximately-constant-voltage power source (not shown) such that, based on equation (1) above, the resistive heater  10  will generate less heat when the resistance increases. If the power source provides approximately-constant current, the resistive heater  10  will generate more heat when the resistance increases. Most power sources known in the art provide constant peak voltage, either alternating current (AC) or direct current (DC). Suitable examples of an approximately-constant-voltage power source include, but are not limited to, AC mains electricity, such as is commonly used in households and businesses to power electric devices; and DC battery power. 
     The inner and outer tubes  14  and  12  may be any ceramic tube having any desired size and/or shape. For example, in the embodiment of the resistive heater  10  shown in  FIGS. 1A and 1B , the inner and outer tubes  14  and  12  are cylinders. However, it is to be understood that the inner and outer tubes  14  and  12  are not limited to cylinders, but may have any desired cross-sectional shape and size, and may have any desired length. The conductive powder  16  may be any conductive powder capable of being packed between the inner and outer tubes  14  and  12 . A suitable example of the conductive powder  16  includes, but is not limited to, carbon black. The variation of conductivity with compression of carbon black has been well studied and documented. (See, for example J. Sánchez-González et al., “Electrical conductivity of carbon blacks under compression”/Carbon 43 (2005) 741-747, referred to hereafter as Sánchez-González, which is incorporated by reference herein.) 
     In operation, the conductive powder  16  between the inner and outer tubes  14  and  12  forms an analog, negative feedback mechanism that automatically alters the input power of the resistive heater  10  as the temperature of the resistive heater  10  changes. Analog fail safe control systems using negative feedback mechanisms are adherently safer than digital control systems since they do not rely on any other system to function. Thermal fuses and circuit breakers are good examples of such fail safe control systems; however their feedback response is an abrupt shut down when a designated peak condition is reached. In contrast, the resistive heater  10  is a self-regulating heating element whose resistance changes gradually with temperature based on differing thermal expansion coefficients of the inner and outer tubes  14  and  12 . 
     The conductive powder  16  is electrically contacted by the 1 st  and 2 nd  electrodes  18  and  20 . The volume V between the inner and outer tubes  14  and  12  at a temperature T o +ΔT is given by:
 
 V=L   o ×(1+Δ T×A )×(π( R   o ×(1+Δ T×A )) 2 −π( r   o ×(1+Δ T×a )) 2 )  (2)
 
where L o , R o , and r o , respectively are the length of the outer tube  12 , the inner radius of the outer tube  12 , and the outer radius of the inner tube  14  at temperature T o +ΔT, while A and a are the thermal expansion coefficients of the outer tube  12  and inner tube  14 , respectively. As documented in Sánchez-González, the conductance a of powdered carbon black changes significantly with the change of volume of the powdered carbon. With a constant voltage source V the, heat output power P may be given by P=σV 2 . The change in volume of the resistive heater  10  over a given temperature range can be engineered by choosing the proper materials and dimensions of the conductive powder  16  and the inner and outer tubes  14  and  12 . Table 1 below gives the coefficients of linear expansion and maximum operating temperature of various ceramic materials that may be used to construct the inner and outer tubes  14  and  12 .
 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Coefficients of linear expansion and maximum operating 
               
               
                 temperature of various ceramics 
               
            
           
           
               
               
               
               
            
               
                   
                   
                   
                 Maximum 
               
               
                   
                   
                 Coefficient of Linear Thermal 
                 Temperature 
               
               
                   
                 Ceramic 
                 Expansion (μm/m-° C.) 
                 (° C.) 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                   
                 Al 2 O 3   
                 8.4 
                 1750 
               
               
                   
                 AlN 
                 4.6-5.7 
                 1600 
               
               
                   
                 B 4 C 
                 5.54 
                 2450 
               
               
                   
                 BN 
                 1.0-2.0 
                 985 
               
               
                   
                 Cordierite 
                 1.7 
                 1371 
               
               
                   
                 Graphite 
                 8.39 
                 3650 
               
               
                   
                 Mullite 
                 5.3 
                 1700 
               
               
                   
                 Sapphire 
                 7.9-8.8 
                 2000 
               
               
                   
                 SiC 
                 5.12 
                 1400 
               
               
                   
                 Si 3 N 4   
                 3.4 
                 1500 
               
               
                   
                 Steatite L-5 
                 7 
                 1425 
               
               
                   
                 TiB 2   
                 7.4-9.8 
                 2000 
               
               
                   
                 WC 
                 5.9 
                 ng 
               
               
                   
                 ZrO2 
                 11 
                 500 
               
               
                   
                   
               
            
           
         
       
     
       FIG. 2  is a graphical plot showing the change in volume of the conductive powder  16  over a temperature range of approximately 1500° C. for an example embodiment of the resistive heater  10 . In this example embodiment, the inner tube  14  is a Cordierite cylinder that has a length of 20.0 cm and an outer diameter of 5.0 cm; and the outer tube  12  is an Alumina (Al 2 O 3 ) cylinder that has a length of 20.0 cm and an inner diameter of 5.1 cm. The resistive heater  10  can operate at very high temperatures (e.g., ˜2000° C.). 
       FIGS. 3A and 3B  are respectively perspective and cross-sectional views of another embodiment of the resistive heater  10 . In this embodiment (i.e., the one shown in  FIGS. 3A and 3B ), the first and second electrodes  18  and  20  are annular rings made of conductive material disposed at opposing ends of the inner and outer tubes  14  and  12 . The means of connecting the conductive powder  16  to a power source is not limited to the opposing annular ring electrodes shown in  FIGS. 3A and 3B  or the radially-separated metal coatings shown in  FIGS. 1A and 1B , but the conductive powder  16  may be connected to the power source by any means known in the art. In another example, the electrodes  18  and  20  may be electrodes submersed in the conductive powder  16  in the space between, and on opposing ends of, the inner and outer tubes  14  and  12 . 
     From the above description of the resistive heater  10 , it is manifest that various techniques may be used for implementing the concepts of resistive heater  10  without departing from the scope of the claims. The described embodiments are to be considered in all respects as illustrative and not restrictive. The method/apparatus disclosed herein may be practiced in the absence of any element that is not specifically claimed and/or disclosed herein. It should also be understood that resistive heater  10  is not limited to the particular embodiments described herein, but is capable of many embodiments without departing from the scope of the claims.