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Subroutine MAP_UTIL_FDHEAT

  • Provenance of code.
  • Purpose of code.
  • Specification.
  • Description of subroutine's operation.
  • References.
  • Parameter descriptions.
  • Error indicators.
  • Accuracy estimate.
  • Any additional information.
  • Example of code
  • Auxiliary subroutines required.
  • Keywords.
  • Download source code.
  • Links.

    • Provenance of Source Code

    D. Gaude-Fugarolas,
    Phase Transformations Group,
    Department of Materials Science and Metallurgy,
    University of Cambridge,
    Cambridge CB2 3QZ, U.K.

    E-mail: dg241@cam.ac.uk
     
     

    Added to MAP:  2006

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    Purpose

    This program contains a model of the  induction heating and water spray quenching of a plate or cylinder of steel. The heat flow equation is integrated numerically using the Crank-Nicholson method.

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    Specification

     
    Language:  FORTRAN 
    Product form:  Source code.
     
    Complete program.
     

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    Description

    This program is a simplified model of the induction heating and water spray quenching of a plate or a cylinder of steel. The heat flow equation is integrated numerically following the Crank-Nicholson method.  Physical and thermal properties of the steel are taken to be independent of temperature. Geometry, thickness of the plate or radius of the cylinder, properties of steel and thermal parameters of the process (density, specific heat, thermal conductivity, severity  of the quench, initial and target temperatures, cooling water temperature, dead time) are introduced as input parameters from an input file. The inputs of the program are the names of the input and output files and the heat flux at the surface. The heat flux during induction heating is also considered constant.

    It is  also assumed that the heating stage of the process is temperature controlled, and  that the heat generation is maintained until some desired temperature is reached at the surface. At that point the coil stops heating the material and the cooling stage begins.  As in the industrial process, the existence of a dead time between the end of the heating stage and the beginning of the water spray cooling one is possible. During this dead time only air convection is considered.

    The output of the program is a file with the evolution of temperature, at different depths into the component, as a function of  time.

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    References

    1. Crank, J. and Nicholson, P. A practical method for numerical evaluation of solutions of partial differential equations of the heat conduction type. Proceedings of the Cambridge Philosophical Society, 43: 50-67, 1947.
    2. Carslaw, J.W. and Jaeger, J.C. Conduction of Heat in Solids. Oxford University Press, Oxford, 1959.
    3. Press, W.H.; Flannery, S.A.; Teukolsky, S.A. and Vetterling, W.T. Numerical Recipes. Cambridge University Press, Cambridge, 1986.
    4. Poirier, D.R. and Geiger, G.H. Transport Phenomena in Materials Processing. The Minerals, Metals & Materials Society, Warrendale, 1994.
    5. Zill, D.G.; Cullen, M.R. Differential Equations with Boundary-Value Problems. Brooks/Cole Publishing Company, Pacific Grove, 1997.
    6. Gaude-Fugarolas, D. Modelling of transformations during induction hardening and tempering (CPGS thesis). Cambridge University, Cambridge, 2000.
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    Parameters

    Input parameters

    FILE1- character*55
                FILE1 is the name of the input file.
    FILE2- character*55
                FILE2 is the name of the output file.
    Q- double precision
                Q is the heat flux introduced during induction heating (in W m ^-2).

    Content of the input file-

    N (MAX 20)
Tmin Tmax To
kth, hair, hwater, rho, Cp
L, Symmetry (0=cyl, 1=plate)
incTIME
Top_temperature_in_heating
Dead_time

    Output parameters

    The program prints on the standard output device the state of the calculations (induction heating, dead time cooling, water sprays active). A numerical parameter P is also shown. Finally, the results of the calculation is saved to a file in the format shown below.

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    Error Indicators

    ERR = 1 Number of nodes is too large (N > JMAX).

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    Accuracy

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    Further Comments

    None.

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    Example

    1. Program text

    Complete program.

    2. Program data

    Example of input file-

    5

    25 1400 25

    41 6 35e3 7800 600

    0.01 0

    0.01

    1000

    0.5
    Example of input heat flow- 
    5e6

    3. Program results

     Time /s     ... Temperatures /C ...     from centre to surface
   0.0000     25.0    25.0    25.0    25.0    25.0    25.0
   0.0100     25.0    25.0    25.0    25.0    27.5   128.1
   0.0200     25.0    25.0    25.0    25.2    32.4   229.5
   0.0300     25.0    25.0    25.0    25.4    39.5   329.3
   0.0400     25.0    25.0    25.0    25.9    48.6   427.4
   0.0500     25.0    25.0    25.1    26.6    59.8   524.1
   0.0600     25.0    25.0    25.1    27.5    72.8   619.2
   0.0700     25.0    25.0    25.2    28.8    87.5   713.0
   0.0800     25.0    25.0    25.3    30.4   103.9   805.3
   0.0900     25.0    25.0    25.5    32.4   121.8   896.4
   0.1000     25.0    25.0    25.7    34.7   141.2   986.2
   0.1100     25.0    25.1    25.9    37.5   161.9  1074.8
   0.1200     25.0    25.1    26.3    40.7   181.4  1059.2
   0.1300     25.0    25.1    26.7    44.2   199.8  1044.1
   0.1400     25.0    25.2    27.2    48.0   217.1  1029.5
   0.1500     25.0    25.3    27.8    52.0   233.4  1015.6
   0.1600     25.0    25.4    28.4    56.3   248.7  1002.1
   0.1700     25.1    25.5    29.2    60.8   263.2   989.1
   0.1800     25.1    25.6    30.0    65.5   276.8   976.7
   0.1900     25.1    25.8    31.0    70.3   289.6   964.6
   0.2000     25.1    25.9    32.0    75.3   301.7   953.0
   0.2100     25.2    26.1    33.2    80.3   313.0   941.8
   0.2200     25.2    26.4    34.4    85.4   323.7   930.9
   0.2300     25.3    26.6    35.7    90.6   333.8   920.5
   0.2400     25.3    26.9    37.1    95.8   343.3   910.4
   0.2500     25.4    27.3    38.6   101.1   352.3   900.6
   0.2600     25.5    27.6    40.1   106.4   360.7   891.1

    ...

       4.9400    116.4   108.8    97.0    80.2    60.1    39.1
   4.9500    116.1   108.5    96.7    80.0    60.0    39.0
   4.9600    115.7   108.2    96.4    79.8    59.8    39.0
   4.9700    115.4   107.9    96.2    79.5    59.7    38.9
   4.9800    115.1   107.6    95.9    79.3    59.6    38.9
   4.9900    114.7   107.3    95.7    79.1    59.4    38.8
   5.0000    114.4   107.0    95.4    78.9    59.3    38.8
   5.0100    114.1   106.7    95.1    78.7    59.2    38.7
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    Auxiliary Routines

    MAP_UTIL_3DSOLV

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    Keywords

    induction hardening numerical heat quench

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    Download

    Download source code

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    MAP originated from a joint project of the National Physical Laboratory and the University of Cambridge.

    MAP originated from a joint project of the National Physical Laboratory and the University of Cambridge.

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