Abstract:
The invention relates to a method for determining a temperature profile and the integral mean temperature and/or axis temperature in a thick wall or shaft. In order to determine a mean integral wall temperature during heating or cooling processes in a multilayer model, the mean integral wall temperature is calculated from the mean temperature of each layer. A multilayer model is used for determining the mean integral wall temperature during heating or cooling processes and draws upon the mean temperature of each layer.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is the US National Stage of International Application No. PCT/EP2006/066704, filed Sep. 25, 2006 and claims the benefit thereof. The International Application claims the benefits of European application No. 05022820.4 filed Oct. 19, 2005, both applications are incorporated by reference herein in their entirety. 
     
    
     FIELD OF INVENTION 
       [0002]    The invention relates to a method for determining the temperature profile and the average integral temperature and/or axial temperature in walls or shafts of thick-walled components, such as for example of steam collectors, steam lines, valve housings, turbine housings or shafts or the like. 
       BACKGROUND OF THE INVENTION 
       [0003]    During heating-up and cooling-down processes, as occur in component walls, for example in a steam turbine, a valve housing or a steam line, in particular when changing the operating mode, temperature gradients are produced in thick walls of these components and may lead to considerable material stresses. These material stresses may lead to premature material wear to the extent that cracks form. 
         [0004]    To monitor such temperature gradients specifically in the case of applications in steam power plants, previously at least one or more temperature measuring points were incorporated in the component wall. Measured values determined for the temperature of the wall and the temperature of the working medium can be used to estimate temperature differences within the component wall and in particular to determine the assigned average integral wall temperature. Comparison of the average integral temperature with permissible limit values makes it possible to keep the thermal material stresses within permissible limits. However, this method is comparatively cost-intensive and error-prone. 
         [0005]    Alternatively, the average integral wall temperature can also be calculated without the need for costly and error-prone measuring points incorporated in the wall or in the case of components which cannot be provided with a measuring point (for example a turbine shaft). One possible method is to calculate this temperature by means of a mathematical substitute model, in particular on the basis of the Bessel equation, for the heat conduction in a metal rod. However, systems previously realized on this basis in the instrumentation and control of industrial plants, such as for example tubes of steam power plants, have a tendency to undergo oscillations, dependent on the period of the temperature changes of the working medium, which limit reliable assessment of the temperature values obtained in such a way. 
       SUMMARY OF INVENTION 
       [0006]    The invention is therefore based on the object of providing a method for determining the average integral wall temperature/axial temperature which produces a particularly accurate picture of the temperature profile, and at the same time is particularly robust and intrinsically stable, without the use of temperature measuring points in the wall concerned. 
         [0007]    This object is achieved according to the invention by using a multilayer model based on the average temperature of each layer for determining the average integral wall temperature during heating-up or cooling-down processes. 
         [0008]    When a multilayer model is used in such a way, the component wall is additionally divided up into a number of layers lying parallel to the surface, the number of layers depending on the wall thickness. The material data used for each layer (thermal capacity, thermal conductivity) are independent of the layer geometry. A transient balancing of the heat flows entering and leaving takes place in each layer. The transient heat balance obtained is used to determine the corresponding average layer temperatures. 
         [0009]    The multilayer model advantageously uses as measured values only the process variables of the steam temperature  T   AM  and steam mass flow {dot over (m)} AM  as well as the initial temperature profile in the wall, which in the balanced initial state can be represented by an initial wall temperature  T   Anf . If there is no steam mass flow measurement, the steam throughput is calculated by means of a substitute model based on the pressure p AM  and the valve position H AV  or the free flow cross section. These process variables can be easily acquired and are generally available in any case in the instrumentation and control of a technical plant. In particular, no additional measuring points that have to be integrated in the wall concerned are required. 
         [0010]    The invention is based on the consideration that it is possible to calculate the temperature profile in the wall, and consequently the average integral wall temperature, during heating-up and cooling-down processes sufficiently accurately and stably by means of a multilayer model, thereby dispensing with cost-intensive and error-prone measuring points incorporated in the wall and also in cases where no direct temperature measurement is possible. For this purpose, determination of the momentary wall temperature profile as a function of the transient heat flow balance is envisaged. In principle, it is possible to work with the inner and outer wall surface temperatures of the thick-walled component or even with the temperature of the working medium and the ambient or insulating temperature or else just the surface temperature (for example in the case of a shaft). 
         [0011]    However, it proves to be particularly favorable to divide the thick walls up into a number of layers. A resultant advantage is better determination of the wall temperature profile, and consequently better calculation of the average integral wall temperature, since the transient temperature profile within a thick wall has strong non-linearity. The reason for this is, in particular, that the thermal conductivity of the material and the specific thermal capacity of the material are themselves temperature-dependent. A further advantage of the use of a multilayer model is that, if the wall is divided up sufficiently finely into a number of layers, a forward-directed calculation structure can be used for calculating the temperature-dependent thermal conductivity and specific thermal capacity, i.e. the average temperature of the preceding layer instead of the current layer is used, thereby avoiding feedback, which may also have a positive sign, and the calculation circuit thereby having a much more robust behavior. 
         [0012]    The calculation of the heat transfer coefficient α preferably takes place with allowance for the steam condensation, the wet steam and the superheated steam. For this, detection of the state of the working medium takes place in a module. Both possible condensation, with the corresponding steam element and water element, and the superheated steam state are detected. If superheated steam is exclusively provided as the working medium, the heat transfer coefficient α AM  for the transfer of the heat flow from the working medium into the first layer of wall is advantageously formed as a function of the steam throughput {dot over (m)} AM . 
         [0013]    If, on the other hand, steam condensation occurs, the transfer coefficient α is advantageously calculated by a constant heat transfer coefficient α W  being used for the condensed element of the working medium, the so-called condensation component. In order to determine this condensation component, the saturation temperature T S  is used as a function of the pressure p AM , the temperature T AM  of the working medium and the temperature of the heated/cooled surface T 1  (the average temperature of the first layer). 
         [0014]    The temperature of the first layer of the thick-walled component T 1  is subtracted from the greater of the two values and the result is compared with a constant K, which can be set. The greater of these two values forms the divisor of two quotients, which have in the dividend the difference between the temperature of the working medium and the saturation temperature T AM −T S  and the difference between the saturation temperature and the temperature of the first layer of the thick-walled component T S −T 1 . The first quotient, if it is positive, is multiplied by the heat transfer coefficient α AM  of the superheated steam, the second quotient, if it is positive, is multiplied by the heat transfer coefficient α W  for water, in order to allow for the condensation. The sum of the two products is compared with the heat transfer coefficient α AM  of the superheated steam. The greater of the two values is the resultant heat transfer coefficient α. 
         [0015]    The calculation of the average integral wall temperature  T   Int  is obtained in a particularly advantageous way from a transient balancing of the entering and leaving heat flows in n individual layers. This takes place in n so-called layer modules. 
         [0016]    In the first layer module, the heat flow of the working medium into the first layer {dot over (q)} AM-1  and the heat flow from the first layer into the second layer {dot over (q)} 1-2  are calculated with the aid of the heat transfer coefficient α; the temperature T AM  of the working medium and the average temperature. With the initial temperature T Anf  in the layer concerned, the average temperature T 1  of the first layer is obtained by integration over time from the transient difference between the heat flows of the working medium into the first layer and from the first layer into the second layer {dot over (q)} AM-1 −{dot over (q)} 1-2 . 
         [0017]    In a kth layer module, the average temperature of the kth layer T k  is calculated with the aid of the transient heat flow balance of the (k−1)th layer {dot over (q)} (k−1)−k  and from the kth layer into the (k+1)th layer q k-(k+1). With the initial temperature T Anf     —     k  of the kth layer, the average temperature T k  of the kth layer is obtained by integration of the transient difference between the heat flows {dot over (q)} (k−1)−k −{dot over (q)} k−(k+1)  into and from the kth layer over time. 
         [0018]    In the last layer module, finally, the average temperature T 1  of the last (nth) layer is calculated from the transient heat flow balance from the last-but-one (n−1)th layer into the last (nth) layer and from the last layer into the thermal insulation {dot over (q)} (n-1)-n −{dot over (q)} n-ISOL . 
         [0019]    The temperature dependence of the thermal conductivity λ k  and the specific thermal capacity c k  of the kth layer is expediently approximated by polynomials, preferably of the second degree, or specified by corresponding functions. 
         [0020]    Finally, the average integral wall temperature  T   Int  is determined in a module in a particularly advantageous way by weighting of the average temperatures T k  of the individual layers with allowance for the weight of the material of the layer and the weight of the material of the equivalent portion of the wall. 
         [0021]    The entire method is preferably carried out in a specific enhanced data processing system, preferably in an instrumentation and control system of a steam power plant. 
         [0022]    The advantages achieved with the invention are, in particular, that the wall temperature profiles and the average integral wall temperature of thick-walled components can be reliably and stably specified alone from the process parameters of the mass flow and temperature of the working medium as well as the initial temperature distribution in the wall and, if no direct measurement of the temperature throughput is available or possible, additionally with pressure and a valve position or a free flow cross section, thereby dispensing with measuring points incorporated in the component walls. The greater the number of layers that is chosen here, the more accurate the determination of the average integral wall temperature/axial temperature becomes. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0023]    An exemplary embodiment of the invention with the use of a three-layer model and allowance for insulation (fourth layer) is explained in more detail on the basis of a drawing, in which: 
           [0024]      FIG. 1  shows a section through a steam tube as an example of a thick wall divided up into three layers, 
           [0025]      FIG. 2  shows a block diagram of the module for the calculation of the heat transfer coefficient, 
           [0026]      FIG. 3  shows a block diagram of the module for the calculation of the average temperature of the first layer, 
           [0027]      FIG. 4  shows a block diagram of the module for the calculation of the average temperature, of the second layer, 
           [0028]      FIG. 5  shows a block diagram of the module for the calculation of the average temperature of the third layer, and 
           [0029]      FIG. 6  shows a block diagram of the module for the calculation of the average integral wall temperature. 
       
    
    
       [0030]    The same parts are provided with the same designations in all the figures. 
       DETAILED DESCRIPTION OF INVENTION 
       [0031]      FIG. 1  shows a tube portion  1  in section as an example of a thick wall. The interior space  2  of the steam tube is flowed through by the working medium (steam), and from here the heat flow is transferred into the first layer  4 . This is followed by the second layer  6  and the third layer  8 . The tube portion  1  is enclosed by the insulation  10 . 
         [0032]    According to  FIG. 2 , the measured value of the steam throughput {dot over (m)} AM  is fed as the input signal to the function generator  32 , which calculates from this the heat transfer coefficient α AM  as a function of the working medium {dot over (m)} AM  for the case of steam, α AM =f({dot over (m)} AM ). This function is given by a number of interpolation points, intermediate values being formed by suitable interpolation methods. 
         [0033]    In order also to allow for the case of partial condensation, the pressure of the working medium p AM  is also passed to the input of a function generator  34 , which replicates the saturation function T s =f(p AM ), and consequently supplies at its output the saturation temperature T S  for the respective pressure. This function is given by interpolation points (pressures and temperatures from steam tables), intermediate values being determined by means of suitable interpolation methods. 
         [0034]    The temperature of the working medium T AM  is compared with the saturation temperature T S  by the maximum generator  36 . The average temperature of the first layer T 1  is subtracted from the greater value by a subtractor  38 . The difference is compared by means of a maximum generator  40  with a constant K, which can be set. Consequently, the signal 
         [0000]        N =max(max( T   AM   ;T   S )− T   1   ;K ) 
         [0035]    is present at the output of the maximum generator  40 . It is passed to the divisor inputs of two dividers  42  and  44 . 
         [0036]    The divider  42  receives at its dividend input the difference T AM −T S  formed by means of the subtractor  46 . The function generator  48  only passes on the signal 
         [0000]    
       
         
           
             
               
                 T 
                 AM 
               
               - 
               
                 T 
                 XS 
               
             
             N 
           
         
       
     
         [0037]    to the one input of the multiplier  50  if it is positive. The signal indicates the percentage of the working medium that is evaporated, the so-called steam component. If the difference T AM −T S  is negative, that is to say the temperature of the working medium is lower than the saturation temperature, the signal “zero” is present at the corresponding input of the multiplier  50 . 
         [0038]    At the other input of the multiplier  50 , the heat transfer coefficient α AM  for steam is present. Therefore, the heat transfer coefficient α pD  weighted with the steam component is passed to the one input of the adder  58 . 
         [0039]    The divider  44  receives at its dividend input the difference T S −T 1  formed by the subtractor  52 . The function generator  54  only passes the signal 
         [0000]    
       
         
           
             
               
                 T 
                 S 
               
               - 
               
                 T 
                 1 
               
             
             N 
           
         
       
     
         [0040]    on to the one input of the multiplier  56  if it is positive. The signal specifies the percentage made up by the condensation component. If the difference T S −T 1  is negative, that is to say the average temperature of the first layer is higher than the saturation temperature, the signal “zero” is present at the corresponding input of the multiplier  56 . 
         [0041]    The heat transfer coefficient α W  for water is present at the other input of the multiplier  56 . Therefore, the heat transfer coefficient α pW  weighted with the condensation component is passed to the second input of the adder  59 . 
         [0042]    At the maximum generator  60 , the heat transfer coefficient α AM  for the case of steam is present at one input. The heat transfer coefficient 
         [0000]      α p =α pW +α pD    
         [0043]    for the case of partial condensation, formed by the adder  58 , is present at the second input. The greater of the two values is the current heat transfer coefficient α. 
         [0044]    If there is no steam mass flow measurement, the steam mass flow is calculated, for example with the aid of the following calculation circuit. In a function generator  12 , the actual value of a valve position H AV  is converted into a free flow area A AV . The free flow area is provided with suitable conversion factors K U1  and K U2  by means of multipliers  14  and  16  and passed to a further multiplier  18 . The pressure of the working medium p AM  is passed—likewise by means of a multiplier  20  with a suitable conversion constant K U4 —to the second input of the multiplier  18 , the result of which is passed to the input of a multiplier  22 . The temperature T AM  of the working medium provided with a suitable conversion factor K U5  by means of a multiplier  24  is passed to the denominator input of a divider  26 , the numerator input of which receives a one. The reciprocal value is present at the output. The root of the reciprocal value is passed to the second input of the multiplier  22  by means of a root extractor  28 . The signal at the output of the multiplier  22 , provided with a suitable conversion factor K U3  by means of a multiplier  30 , represents the steam throughput {dot over (m)} AM . Altogether, the following is consequently obtained for the calculation of the steam throughput: 
         [0000]    
       
         
           
             
               A 
               AV 
             
             = 
             
               f 
                
               
                 ( 
                 
                   H 
                   AV 
                 
                 ) 
               
             
           
         
       
       
         
           
             
               
                 m 
                 . 
               
               AM 
             
             = 
             
               
                 K 
                 
                   U 
                    
                   
                       
                   
                    
                   3 
                 
               
               * 
               
                 
                   1 
                   
                     
                       K 
                       US 
                     
                      
                     
                       T 
                       AM 
                     
                   
                 
               
                
               
                 K 
                 
                   U 
                    
                   
                       
                   
                    
                   4 
                 
               
                
               
                 T 
                 AM 
               
                
               
                 K 
                 
                   U 
                    
                   
                       
                   
                    
                   1 
                 
               
                
               
                 K 
                 
                   U 
                    
                   
                       
                   
                    
                   2 
                 
               
                
               
                 
                   A 
                   AV 
                 
                 . 
               
             
           
         
       
     
         [0045]    The module for the first layer according to  FIG. 3  determines the average temperature of the first layer T 1  from the transient heat flow balance. For this purpose, the temperature difference T AM −T 1  is first formed by means of a subtractor  62  from the temperature of the working medium T AM  and the average temperature of the first layer T 1  and is multiplied by the heat transfer coefficient α by means of a multiplier  64 . A multiplier  66  provides the signal with a suitable coefficient K AL , which can be set and represents an equivalent first surface—for the heat transfer from the working medium into the component wall. Present at the output of the multiplier  66  is the signal for the heat flow from the working medium into the first layer 
         [0000]        {dot over (q)}   AM-1   =αK   AL ( T   AM   −T   1 ) 
         [0046]    which is passed to the minuend input of a subtractor  68 . 
         [0047]    In the exemplary embodiment, the temperature dependence of the thermal conductivity λ 1  and the specific thermal capacity c 1  of the first layer is approximated by polynomials of the second degree, which are represented by coefficients W 01 , W 11  and W 21  as well as C 01 , C 11  and C 21 . The polynomials used in the example have the following form: 
         [0000]      λ 1   =W   01   +W   11   T   AM   +W   21   T   AM   2    
         [0000]    
       
      
       c 
       1 
       =C 
       01 
       +C 
       11 
       T 
       AM 
       +C 
       21 
       T 
       AM 
       2  
      
     
         [0048]    This is replicated in terms of circuitry by the temperature of the working medium T AM  being passed to the inputs of three multipliers  70 ,  72  and  74 . For the purpose of avoiding possible positive feedback (depending on the properties of the material) and consequently an increase in the stability of the system, the forward-directed structure is used, i.e. the temperature of the working medium T AM  is used instead of the average temperature of the first layer T 1 . 
         [0049]    To calculate the thermal conductivity, the polynomial constant W 11  is present at the second input of the multiplier  70 . The output is connected to an input of an adder  76 . 
         [0050]    Present at the output of the multiplier  72  that is connected as a squarer is the signal for the square of the temperature of the working medium T 2   AM . It is multiplied by the polynomial constant W 21  by means of the multiplier  78  and subsequently passed to a second input of the adder  76 . 
         [0051]    The polynomial constant W 01  is switched to a third input of the adder  76 . Present at its output is the temperature-dependent thermal conductivity λ 1 , given by the above expression. 
         [0052]    To calculate the specific thermal capacity, the polynomial constant C 11  is applied to the second input of the multiplier  74 . The output of the multiplier  74  lies at an input of an adder  80 . Present at a second input of the adder  80  is the polynomial constant C 01 . The square of the temperature of the working medium T 2   AM  that is present at the output of the multiplier  72  is provided with the polynomial coefficient C 21  by means of the multiplier  82  and is subsequently passed to a third input of the adder  80 . Present at its output is the temperature-dependent specific thermal capacity c 1 , given by the above expression. 
         [0053]    The subtractor  84  forms the temperature difference from the average temperatures of the first layer and the following layer T 1 −T 2 . It is multiplied by the temperature-dependent thermal conductivity λ 1 , from the output of the adder  76 , by means of the multiplier  86  and multiplied by the constant K W1 , which includes the dependence on the layer thickness and the equivalent surface, by means of the multiplier  88 . Present at the output of the multiplier  88  is the signal for the heat flow from the first layer into the second layer 
         [0000]        {dot over (q)}   1-2 =λ 1   K   W1 ( T   1   −T   2 ). 
         [0054]    This signal is passed to the subtrahend input of the subtractor  68 . Present at its output is the signal for the heat flow difference {dot over (q)} AM-1 −{dot over (q)} 1-2 , which is provided by means of the multiplier  90  with a coefficient K T1 , which allows for the rate of change of the temperature in the first layer in dependence on the weight of the material of the layer. 
         [0055]    The resultant signal is divided by the signal that is present at the output of the adder  80  for the temperature-dependent specific thermal capacity c 1  by means of a divider  92 . 
         [0056]    The average temperature of the inner layer is obtained by integration of the heat flow difference over time t 
         [0000]    
       
         
           
             
               T 
               1 
             
             = 
             
               
                 
                   
                     K 
                     
                       T 
                        
                       
                           
                       
                        
                       1 
                     
                   
                   
                     c 
                     1 
                   
                 
                  
                 
                   
                     ∫ 
                     0 
                     t 
                   
                    
                   
                     
                       ( 
                       
                         
                           
                             q 
                             . 
                           
                           
                             AM 
                             - 
                             1 
                           
                         
                         - 
                         
                           
                             q 
                             . 
                           
                           
                             1 
                             - 
                             2 
                           
                         
                       
                       ) 
                     
                      
                     
                        
                       t 
                     
                   
                 
               
               + 
               
                 
                   T 
                   
                     Anf 
                      
                     
                         
                     
                      
                     1 
                   
                 
                 . 
               
             
           
         
       
     
         [0057]    The signal present at the output of the divider  92  is fed to an integrator  94 , which uses the initial temperature of the first layer T Anf1  as the initial condition. 
         [0058]    The module for the second layer according to  FIG. 4  determines the average temperature of the second layer T 2  from the transient heat flow balance. For this purpose, the difference T 2 -T 3  is initially formed by means of a subtractor  96  from the temperature of the third layer T 3  and the average temperature of the second layer T 2  and multiplied by the temperature-dependent thermal conductivity λ 2  of the second layer by means of a multiplier  98 . A multiplier  100  provides the signal with a suitable coefficient K W2 , which can be set and includes the dependence of the thermal conductivity on the layer thickness and surface. Present at the output of the multiplier  100  is the signal for the heat flow from the second layer into the third layer 
         [0000]        {dot over (q)}   2-3 =λ 2   W   W2 ( T   2   −T   3 ), 
         [0059]    which is passed to the subtrahend input of a subtractor  102 . 
         [0060]    Present at the minuend input of the subtractor  102  is the signal for the heat flow {dot over (q)} 1-2  from the first layer into the second layer. Its input supplies the heat flow difference {dot over (q)} 1-2 −{dot over (q)} 2-3 . A multiplier  104  provides this signal with a coefficient K T2 , which can be set and allows for the rate of change of the temperature in the second layer in dependence on the weight of the material of the layer. Subsequently, the signal is divided by the temperature-dependent specific thermal capacity c 2  of the second layer by means of a divider  106  and is then passed to the input of an integrator  108 . The integrator  108  uses the initial temperature T Anf2  of the second layer as the initial condition. Present at its output is the average temperature of the second layer 
         [0000]    
       
         
           
             
               T 
               2 
             
             = 
             
               
                 
                   
                     K 
                     
                       W 
                        
                       
                           
                       
                        
                       2 
                     
                   
                   
                     c 
                     2 
                   
                 
                  
                 
                   
                     ∫ 
                     0 
                     t 
                   
                    
                   
                     
                       ( 
                       
                         
                           
                             q 
                             . 
                           
                           
                             1 
                             - 
                             2 
                           
                         
                         - 
                         
                           
                             q 
                             . 
                           
                           
                             2 
                             - 
                             3 
                           
                         
                       
                       ) 
                     
                      
                     
                        
                       t 
                     
                   
                 
               
               + 
               
                 
                   T 
                   
                     Anf 
                      
                     
                         
                     
                      
                     2 
                   
                 
                 . 
               
             
           
         
       
     
         [0061]    The temperature dependence of the thermal conductivity λ 2  and the specific thermal capacity c 2  of the second layer is again approximated by polynomials with coefficients W 02 , W 12  and W 22  as well as c 02 , c 12  and c 22 . The polynomials are: 
         [0000]      λ 2   =W   02   +W   12   T   1   +W   22   T   1   2    
         [0000]    
       
      
       c 
       2 
       =C 
       02 
       +C 
       12 
       T 
       1 
       +C 
       22 
       T 
       1 
       2  
      
     
         [0062]    This is replicated in terms of circuitry by the average temperature of the first layer T 1  being passed to the inputs of three multipliers  110 ,  112  and  114 . For the purpose of avoiding possible positive feedback (depending on the properties of the material) and consequently an increase in the stability of the system, a forward-directed structure is used, i.e. the average temperature of the first layer T 1  is, used instead of the average temperature of the second layer T 2 . 
         [0063]    To calculate the thermal conductivity, the polynomial constant W 12  is present at the second input of the multiplier  110 . The output is connected to an input of an adder  116 . 
         [0064]    Present at the output of the multiplier  112  that is connected as a squarer is the signal for the square of the average temperature of the first layer T 1   2 . It is multiplied by the polynomial constant W 22  by means of the multiplier  118  and subsequently passed to a second input of the adder  116 . The polynomial constant W 02  is switched to a third input of the adder  116 . Present at its output is the temperature-dependent thermal conductivity λ 2 , given by the above expression. 
         [0065]    To calculate the temperature-dependent specific thermal capacity, the polynomial constant C 12  is applied to the second input of the multiplier  114 . The output of the multiplier  114  lies at an input of an adder  120 . Present at a second input of the adder  120  is the polynomial constant C 02 . The square of the average temperature of the first layer T 1   2  that is present at the output of the multiplier  112  is provided with the polynomial coefficient C 22  by means of the multiplier  122  and is subsequently passed to a third input of the adder  120 . Present at its output is the temperature-dependent specific thermal capacity c 2 , given by the above expression. 
         [0066]    The module for the third layer according to  FIG. 5  determines the average temperature of the third layer T 3  from the heat flow balance. For this purpose, the temperature difference (T 3 −T ISOL ) is first formed by means of a subtractor  124  from the temperature of the insulation T ISOL  and the average temperature of the third layer T 3  and is multiplied by a suitable constant K ISOL , which can be set and represents the magnitude of the heat losses of the insulation, by means of a multiplier  126 . Present at the output of the multiplier  126  is the signal for the heat flow from the third layer into the insulation (here there is also the possibility of the heat losses of the insulation being directly specified) 
         [0000]        {dot over (q)}   3     —     ISOL   =K   ISOL ( T   3   −T   ISOL ) 
         [0067]    which is passed to the subtrahend input of a subtractor  128 . 
         [0068]    Present at the minuend input of the subtractor  128  is the signal for the heat flow {dot over (q)} 2-3  from the second layer into the third layer. Its input supplies the heat flow difference {dot over (q)} 2-3 −{dot over (q)} 3     —     ISOL . A multiplier  130  provides this signal with a coefficient K T3 , which can be set and allows for the rate of change of the temperature in the third layer in dependence on the weight of the material of the layer. Subsequently, the signal is divided by the temperature-dependent specific thermal capacity c 3  of the third layer by means of a divider  132  and is then passed to the input of an integrator  134 . The integrator  134  uses the initial temperature of the third layer T Anf3  as the initial condition. Present at its output is the average integral temperature of the third layer 
         [0000]    
       
         
           
             
               T 
               3 
             
             = 
             
               
                 
                   
                     K 
                     
                       W 
                        
                       
                           
                       
                        
                       3 
                     
                   
                   
                     c 
                     3 
                   
                 
                  
                 
                   
                     ∫ 
                     0 
                     t 
                   
                    
                   
                     
                       ( 
                       
                         
                           
                             q 
                             . 
                           
                           
                             2 
                             - 
                             3 
                           
                         
                         - 
                         
                           
                             q 
                             . 
                           
                           
                             3 
                             - 
                             ISOL 
                           
                         
                       
                       ) 
                     
                      
                     
                        
                       t 
                     
                   
                 
               
               + 
               
                 
                   T 
                   
                     Anf 
                      
                     
                         
                     
                      
                     3 
                   
                 
                 . 
               
             
           
         
       
     
         [0069]    The temperature dependence of the specific thermal capacity c 3  of the third layer is approximated by a polynomial with coefficients C 03 , C 13  and C 23 . 
         [0070]    The polynomial is: 
         [0000]        c   3   =C   03   +C   13   T   2   +C   23   T   2   2 . 
         [0071]    For the purpose of avoiding possible positive feedback (depending on the properties of the material) and consequently an increase in the stability of the system, a forward-directed structure is used here, i.e. the average temperature of the second layer T 2  is used here instead of the average temperature of the third layer T 3 . 
         [0072]    This is replicated in terms of circuitry by the average temperature of the second layer T 2  being passed to the inputs of two multipliers  136  and  138 . The coefficient C 13  is applied to the second input of the multiplier  136 . The output of the multiplier  136  lies at an input of an adder  140 . Present at a second input of the adder  140  is the polynomial constant C 03 . The square of the average temperature of the second layer T 2   2  that is present at the output of the multiplier  138  is provided with the polynomial coefficient C 23  by means of a multiplier  142  and is subsequently passed to a third input of the adder  140 . Present at its output is the temperature-dependent specific thermal capacity C 3 , given by the above expression. 
         [0073]    According to  FIG. 6 , the average integral wall temperature  T   Int  is determined from the average temperatures of the individual layers T 1 , T 2  and T 3 . Three multipliers  144 ,  146  and  148  provide the temperature signals with suitable weighting factors K G1 , K G2  and K G3 , which weight the average temperatures of the individual layers in a way corresponding to the weight of the material of the layer. The weighted temperature signals pass to inputs of an adder  150 . Its output signal is provided with a coefficient K G , which allows for the influence of the overall weight of the material of the equivalent portion of the wall, by means of a multiplier  152 . Present at the output of the multiplier  152  is the signal for the average integral wall temperature  T   Int .