Encyclopedia Magnetica™

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===== Calculator of induction heating power =====

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|  {{/calculator/icon_calc.png?60&nolink}}  | //[[user/Stan Zurek]], Calculator of induction heating power, Encyclopedia Magnetica//, \\ @PAGEL@, {accessed: @YEAR@-@MONTH@-@DAY@} |
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[[/file/induction_heating_calculator_e-m.png|{{/induction_heating_calculator_e-m.png}}]]
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The order of magnitude for the required [[/induction heating]] power can be estimated as a rough approximation, through a number of simplifying assumptions:
  * only the heated layer is taken into account (the rest of the material is ignored)
  * adiabatic heating conditions (no cooling due to [[/cooling by convection|convection]], [[/cooling by radiation|radiation]], or [[/cooling by conduction|conduction]])
  * the same heating power is delivered to the material during the whole heating time (it is controlled regardless of temperature of the material)
  * [[/magnetic permeability]] is assumed constant
  * transition to [[/paramagnetism]] is not taken into account
  * [[/skin depth]] is calculated for resistivity at the hottest temperature
  * the suggested frequency is estimated by assuming the skin depth being 4 times thinner than the heated layer
  * apart from resistivity all other values are assumed constant, and melting or any phase transition is ignored.

----
<HTML>
<!-- ==================== calculator starts here ============== -->
<HEAD>
<SCRIPT Language="JavaScript">

<!--
/**
 * Function that introduces calculator of a given function.
 **/
 
function getSelectedValue(selectList){
   return selectList[selectList.selectedIndex].value
}

function calculate_function(frm){
// set up variables
var shape     = getSelectedValue(frm.shape)
var metal     = getSelectedValue(frm.metal)
var eff       = frm.eff.value
var time      = frm.time.value
var t_start   = frm.t_start.value  // start temperature
var t_end     = frm.t_end.value    // end temperature
var length    = frm.length.value/1000  // div 1000 to make it in m
var width     = frm.width.value/1000
var thick     = frm.thick.value/1000

var volume      = 0
var mass        = 0
var density     = 0
var t_coef      = 0
var rho_corr    = 0
var heat_cap    = 0
var ur          = 0

var dT = 0
var dT_corr = 0

var skin_depth  = 0
var freq_optim  = 0
var p_req       = 0
var p_gen       = 0
var pi = 3.14159265
var u0 = pi*4e-7

// read values and convert to numbers
shape = parseInt(shape)
metal = parseInt(metal)

eff = parseFloat(eff)
time = parseFloat(time)
t_start = parseFloat(t_start)
t_end = parseFloat(t_end)
length = parseFloat(length)
width = parseFloat(width)
thick = parseFloat(thick)

// select shape, 1 = flat, 2 = round
if (shape == 1) {
volume = length*width*thick
//volume = volume.toPrecision(4)
}
if (shape == 2) {
  volume = (pi/4)*(width*width - (width-2*thick)*(width-2*thick))*length 
//  volume = volume.toPrecision(4)
  if (thick > 0.5*width) {  
    volume = "dimension error"  // layer too thick
  }
}


// select materials
// aluminium, Al
if (metal == 1) { 
density = 2712 //kgm3
rho = 26.5e-9 //at 20 oC
t_coef = 0.0043
heat_cap = 897 //JkgK
ur = 1.000022
} 

// brass
if (metal == 2) { 
density = 8550 //kgm3
rho = 65e-9 //at 20 oC
t_coef = 0.003
heat_cap = 377 //JkgK
ur = 1.06
} 

// cobalt
if (metal == 3) { 
density = 85746 //kgm3
rho = 90e-9 //at 20 oC
t_coef = 0.006
heat_cap = 420 //JkgK
ur = 1000
} 

// Copper Cu
if (metal == 4) { 
density = 8940 //kgm3
rho = 17.2e-9 //at 20 oC
t_coef = 0.00393
heat_cap = 390 //JkgK
ur = 0.999994
} 

// iron Fe
if (metal == 5) { 
density = 7850 //kgm3
rho = 97.1e-9 //at 20 oC
t_coef = 0.00641
heat_cap = 450 //JkgK
ur = 5000
} 

// gold Au
if (metal == 6) { 
density = 19320 //kgm3
rho = 22.4e-9 //at 20 oC
t_coef = 0.0035
heat_cap = 130 //JkgK
ur = 1
} 

// lead Pb
if (metal == 7) { 
density = 11340 //kgm3
rho = 206e-9 //at 20 oC
t_coef = 0.0035
heat_cap = 130 //JkgK
ur = 1
} 

// magnesium Mg
if (metal == 8) { 
density = 1738 //kgm3
rho = 44.5e-9 //at 20 oC
t_coef = 0.003
heat_cap = 1050 //JkgK
ur = 1
} 

// nickel Ni
if (metal == 9) { 
density = 8908 //kgm3
rho = 68.5e-9 //at 20 oC
t_coef = 0.0064
heat_cap = 440 //JkgK
ur = 600
} 

// carbon steel magnetic
if (metal == 10) { 
density = 7850 //kgm3
rho = 150e-9 //at 20 oC
t_coef = 0.005
heat_cap = 490 //JkgK
ur = 100
} 

// stainless steel magnetic
if (metal == 11) { 
density = 7750 //kgm3
rho = 700e-9 //at 20 oC
t_coef = 0.001
heat_cap = 466 //JkgK
ur = 500
} 

// stainless steel non-magnetic
if (metal == 12) { 
density = 7750 //kgm3
rho = 700e-9 //at 20 oC
t_coef = 0.001
heat_cap = 450 //JkgK
ur = 1.1
} 


// tungsten W
if (metal == 13) { 
density = 19255 //kgm3
rho = 55e-9 //at 20 oC
t_coef = 0.0045
heat_cap = 132 //JkgK
ur = 1
} 


// zinc Zn
if (metal == 14) { 
density = 7135 //kgm3
rho = 59e-9 //at 20 oC
t_coef = 0.0037
heat_cap = 390 //JkgK
ur = 1
} 


dT = t_end - t_start
dT_corr = t_end - 20
rho_corr = rho * (1 + t_coef * dT_corr)


// calculate the main function
mass = volume * density
p_req = heat_cap * mass * dT / time / 1000  //1000 because of kW
p_gen = p_req / (eff/100)   //100 because eff is in %
freq_optim = rho_corr / (pi*ur*u0*0.0625*thick*thick)  //0.0625 = 4x heated thickness d, squared
skin_depth = 1000*Math.sqrt(rho_corr/(pi*freq_optim*ur*u0))  //1000=mm
freq_optim = freq_optim/1000   //1000=kHz

// format number to x digits precision, result will equal 5.611e+2
// volume = volume.toPrecision(4)
density = density.toPrecision(4)
heat_cap = heat_cap.toPrecision(4)
t_coef = t_coef*100 //percent
t_coef = t_coef.toPrecision(4)
rho_corr = rho_corr.toPrecision(4)
ur = ur.toPrecision(4)
mass = mass.toPrecision(4)
p_req = p_req.toPrecision(4)
p_gen = p_gen.toPrecision(4)
freq_optim = freq_optim.toPrecision(4)
skin_depth = skin_depth.toPrecision(4)

// display result
volume = volume * 1e6     // in cm3 = 100*100*100 = 1e6
volume = volume.toPrecision(4)
frm.volume.value = volume
frm.density.value = density
frm.heat_cap.value = heat_cap
frm.t_coef.value = t_coef
frm.rho_corr.value = rho_corr
frm.ur.value = ur
frm.mass.value = mass
frm.p_req.value = p_req
frm.p_gen.value = p_gen
frm.freq_optim.value = freq_optim
frm.skin_depth.value = skin_depth

}

//-->
</SCRIPT>
</HEAD>
<body>

<form method="post" action="">

<table style="width:100%">
<th> Input values </th>
<tr><td>

<b><i>shape</i></b>:  

       <SELECT name="shape" onChange="calculate_function(this.form)">
           <OPTION value="1" selected>flat plate</OPTION>
           <OPTION value="2">round rod</OPTION>
        </SELECT>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
 
<b><i>metal</i></b>:  
 
          <SELECT name="metal" onChange="calculate_function(this.form)">
           <OPTION value="1">aluminium, Al</OPTION>
           <OPTION value="2">brass (Cu-Zn)</OPTION>
           <OPTION value="3">cobalt, Co</OPTION>
           <OPTION value="4">copper, Cu</OPTION>
           <OPTION value="5">iron, Fe</OPTION>
           <OPTION value="6">gold, Au</OPTION>
           <OPTION value="7">lead, Pb</OPTION>
           <OPTION value="8">magnesium, Mg</OPTION>
           <OPTION value="9">nickel, Ni</OPTION>
           <OPTION value="10" selected>steel, carbon, magnetic</OPTION>
           <OPTION value="11">steel, stainless, magnetic</OPTION>
           <OPTION value="12">steel, stainless, non-magnetic</OPTION>
           <OPTION value="13">tungsten (wolfram), W</OPTION>
           <OPTION value="14">zinc, Zn</OPTION>
        </SELECT> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 

<br><br>

<b><i>heating efficiency</i></b> (%) = <input type="text" value="85" name="eff" size="5" maxlength="5" onChange="calculate_function(this.form)"> <i>(typically: Al = 40%, Cu = 30%, non-magnetic steel = 60%, magnetic steel = 85%)</i>

<br><br>

<b><i>heating time t</i></b> (s) = <input type="text" value="3.6" name="time" size="5" maxlength="5" onChange="calculate_function(this.form)"> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 


<b><i>T start</i></b> (°C) = <input type="text" value="20" name="t_start" size="5" maxlength="5" onChange="calculate_function(this.form)"> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;

<b><i>T end</i></b> (°C) = <input type="text" value="100" name="t_end" size="5" maxlength="5" onChange="calculate_function(this.form)">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;

<br><br>

<b><i>length L</i></b> (mm) = <input type="text" value="10" name="length" size="5" maxlength="5" onChange="calculate_function(this.form)"> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;

<b><i>width w</i></b> (mm) = <input type="text" value="10" name="width" size="5" maxlength="5" onChange="calculate_function(this.form)"> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;

<b><i>heated thickness d</i></b> (mm) = <input type="text" value="1.5" name="thick" size="5" maxlength="5" onChange="calculate_function(this.form)">

</td>
</tr>
</table>

<table style="width:100%">
<tr>
<th> Output values  </th>
<th> Auxiliary output values </th>
</tr>

<tr>
<td>

<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<input type="button" name="Button" value="== Calculate ==" onClick="calculate_function(this.form)">
<br><br>

<b><i>Suggested frequency</i></b> (kHz) = <input type="text" name="freq_optim" size="10" maxlength="10"> 
<br><br>

<b><i>Skin depth (at suggested freq.)</i></b> (mm) = <input type="text" name="skin_depth" size="10" maxlength="10"> 
<br><br>

<b><i>Required heating power</i></b> (kW) = <input type="text" name="p_req" size="10" maxlength="10"> 
<br><br>

<b><i>Required generator power</i></b> (kW) = <input type="text" name="p_gen" size="10" maxlength="10"> 
<br><br>

</td>

<td>
<b><i>Volume of heated layer</i></b> (cm<sup>3</sup>) = <input type="text" name="volume" size="20" maxlength="10"> 
<br><br>

<b><i>Mass of heated layer</i></b> (kg) = <input type="text" name="mass" size="10" maxlength="10"> 
<br><br>

<b><i>Density</i></b> (kg/m<sup>3</sup>) = <input type="text" name="density" size="10" maxlength="10"> 
<br><br>

<b><i>Thermal coefficient of resistivity</i></b> (%/K) = <input type="text" name="t_coef" size="10" maxlength="10"> 
<br><br>

<b><i>Resistivity at T end</i></b> (Ω·m) = <input type="text" name="rho_corr" size="10" maxlength="10"> 
<br><br>

<b><i>Specific heat capacity</i></b> (J/(kg·K)) = <input type="text" name="heat_cap" size="10" maxlength="10"> 
<br><br>

<b><i>Relative magnetic permeability</i></b> (-) = <input type="text" name="ur" size="10" maxlength="10"> 

</td>
</tr>
</table>

</form>
 

</BODY>
<!-- ==================== calculator ends here ============== -->
</HTML>

<WRAP lo>
  * Material data such as resistivity, heat capacity, and permeability was taken from several sources, but mainly from [[https://www.engineeringtoolbox.com/resistivity-conductivity-d_418.html|Engineering Toolbox]] {accessed 2023-08-13}.
  * This calculator was inspired by [[https://www.plustherm.com/power-calculation.html|Plustherm, Online induction heating power calculation]] {accessed 2023-08-12}.
</WRAP>

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{{tag>Calculators Induction_heating_power Skin_depth Skin_effect}}