Design of Heating Elements are described as two particulars:

The heating element is heated by Joules of heat produced by flowingcurrent. Heat is transferred to a variety of different places in a furnaceby radiation and/or convection. In general, the magnitude of the powerload to the heating element is expressed in electric energy per unit areaof the heating element, i.e., surface load concentration. The surface loadconcentration Wd is expressed as shown below.  

Wd = P/A ( W/cm² )

Where,

P: Power (W)

A: Surface area of Heating Element (cm²)

As shown above, the surface load concentration corresponds to the heatquantity per unit area of the heating element. It is an important factorthat determines the surface temperature and lifetime of the heatingelement. Thus, it is necessary to reduce the surface load concentrationto lower the surface temperature of the heating element and reducethe difference between the heating element temperature and furnacetemperature as far as possible to prolong the service life of the heatingelement. However, increasing the volume of the heating element toreduce the surface load concentration is not economical, and the heatingelement volume cannot be reduced as desired.

When designing the heating element, the surface load concentrationdepends on many factors, including furnace temperature, heatingelement material, use atmosphere, furnace use cycles, and heatingelement design. There is no general rule.   

If the heating element has a regular cross-sectional shape, such as around wire, it is convenient to express the load to the heating element insurface load concentration. However, as for a band wire, it is possible toreduce the surface load concentration to zero if the thickness is reducedfor a specific cross-sectional area. In such a case, the lifetime of theheating element is not always prolonged, even though the surface loadconcentration is reduced. For example, if the heating element becomesthinner than the thickness limit, the area exposed to the atmosphereincreases, and Al replenishment from the inside is restricted, resultingin difficulty in maintaining the characteristics of the protective film andaccordingly reduces lifetime. In particular, it is not desirable to makethe heating element thinner than a certain limit, if the heating elementis used in high-temperature furnaces or a carburizing atmosphere suchas RX and DX. When band wires are used in high-temperature furnacesor a carburizing atmosphere, the heating element lifetime may increasein many cases if the band wire thickness is increased at the expenseof the surface load concentration. In such a case, we need to take thecurrent density into consideration, not the surface load concentration,to determine the loads on the heating element. In general, the quantityof heat produced by a heating material is in proportion to the square ofthe current flowing through the heating element. Thus, it is possible toexpress the loads to the heating element in the current flowing througha unit area of the heating element, i.e., current density.Current density Id is expressed as shown below:  

Id = I/S ( A/mm²)  

Where, I: Current flowing through Heating Element (A)

S: Cross-sectional area of Heating Element (mm²)  

Current density is another important factor for finding the loads on theheating element. When designing a heating element, especially bandwires, it is practical to place the highest importance on current densityrather than surface load concentration and place second importance onsurface load concentration. Table 1 shows furnace temperature and themaximum values of current density of Pyromax.