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Element Calculations for Electric Resistance Heating Element Materials

 

Do it the easy way

The formula listed below is captured in an Excel Spreadsheet. It is a small demo program for performing element calculations for Metallic Heating Elements for Furnaces. 

This Spreadsheet allows calculations based on 8 different heating element alloys. 

We make no warranty or claims with regard to this program and is provided on an "as is basis". Feedback is desired. e-mail us at sales@911bob.com.

Download the Excel Spreadsheet

 

 

The basic method for calculating heating elements reverts to Ohm's law. The basic rules are as follows:

Formula F1:

                  

Where:
            V is Voltage applied to the heating element (Volts)
            I is the current flowing through the heating element (Amperes / Amps) and 
            R is the resistance of the heating element (Resistance)

A second law is also required to determine the power, it is:

Formula F2:

Where:
            P is the Power Generated by the heating element in watts
   
         V and I are the same as in formula F1 above.

 

 

These two simple equations can allow you to calculate any heating element. Knowing this will not guarantee that the element will perform, as you desire, only that electrically it will produce the power you desire.

Replacing the Voltage in F2 with I X R from F1 results in the following that can also be useful

 Formula F3:

 

 

Where to get the rest of the information:

When designing the heating element, you probably know the power and the voltage you want to operate the heater at.

Knowing the Power desired (watts) and the Voltage that is available the current can be calculated from Formula F2. By plugging this current into Formula F1, you can determine the resistance required. As long as the heating element matches that resistance, electrically you are OK. The life of the element, will be determined by other characteristics such as environment, (meaning temperature and chemical make up), and surface loading. Occasionally you cannot get the all of the characteristics into an acceptable range and you will have to re-visit the electrical design, possibly using a lower voltage or other means to get a reasonable life expectancy.

The above formula provides a method of determining the resistance of the heating element. Once this is known, the size and length of the heating element must be determined. Generally this is an iterative process where one wire or strip size is chosen, then the length is calculated, and finally the physical size is checked to see if it will fit in the space available. Then, if needed, the size is increased or decreased to lengthen or shorten the element and the design is again rechecked.

The resistance per unit length of a given cross section can be calculated or looked it up in a table provided by manufacturers of resistance materials. If you choose to calculate it, it can be calculated by knowing the resistivity of the material.

With the resistivity of a material, one can calculate the resistance per unit length for any cross section. Resistivity technically is in units of "Ohm-length", results in "Ohm-foot" for English units and or "Ohm-meter" for Metric. This is actually a reduction units from the formula that is somewhat easier to understand:

                        Where R is the Resisitivity and

                        L is the unit of length.

As you can see this expression can be reduced to Ohm-Length, but is not as user friendly.

In the English System, (inches and feet)

For round wire: 
            Resistivity has the units of Ohms/circular-mil-foot.
            To calculate the resistance per foot, the resistivity is divided by the diameter (expressed in mills) squared.

         For a rectangular section, 
                        Resistivity has the units of Ohms/square-mil-foot.
                        To calculate the resistance per foot, the resistivity is divided by the width (expressed in mills) times the thickness (expressed in mills).

                        

The difference between the rectangular and circular Resistivity is the factor of pi divided by 4 .

For dimensions in metric units:
                        For round and rectangular cross sections:
                        Resistivity has the units of ohms-mm^2/m.
   
                     To calculate the resistance per m, the resistivity is divided by the cross sectional area in mm.

                                                

The key design criteria for determining the life of an element is the temperature that the element operates at. Unfortunately there is no easy way to determine what that temperature will be. A set of guidelines for element configurations combined with a set of allowable watt loading are best used to review the design and if the life will be acceptable.

The watt loading of an element is the amount of energy being transmitted through a unit of surface area. The greater the amount of energy to be transferred per unit surface area, the hotter the element must run in order to transmit the energy to the objects receiving the energy.

The easiest way to understand this is to consider an element in open air. In order to get it to glow red it has to be loaded very heavy, transmitting a large amount of energy. If you now place the same element in a furnace at 1800F / 1000C, the element will glow (with the same intensity as the rest of the furnace) without and power being applied to the element. As you now increase the power the element is generating, the element will be at a temperature above 1800F / 1000C. If you would place the same load on the element that was required to heat it to a glowing red in at room temperature, it would overheat and fail very quickly.

If the surface loading on the element is too high, you should increase the length. Increasing the size of the cross section can do this.

The surface of the heating element is calculated by calculating the perimeter of the heater, multiplied by its length

For more information on the surface loading for elements click on this link:

Surface Loading for Heating Elementst

 

 

Another issue has to do with the Environment the heater is operating in. For more on environmental considerations click on the following link:

Environmental Considerations

 

 

 

 

 

 

 


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