When sourcing a heating element, engineers have to maneuver several design constraints to obtain the correct element to meet their needs. These constraints are different depending upon the type of element desired. For instance, band heaters often have a minimal inside diameter and width. Tubular heaters have minimum bend radii that are dependent on the cross-sectional size of the tubing. While the specifics vary, one limitation is common to electric heating elements: the design constraint of a maximum permissible power density (watt density).

This value often is measured as the power of the element divided by its total outside heat-emitting surface area. However, in this article, we will be considering the power density on the surface of the resistance wire itself. This value varies based upon many factors, including the type of heater, the heater’s housing materials, the operating environment in which the heater will be used, the certifications the heater must attain and the manufacturer’s capabilities. As you may have guessed, two inter-related goals drive this power limit value: safety and heater life.

Engineers spend a lot of time analyzing the heat transfer from an element to their process. Often, they may wish they could just get a little more power out of the same geometric envelope. This article aims to shine some light on the internal heat transfer — from the resistance wire out — to better understand from where these power limits arise.

Heating elements fail when the resistance wire breaks and the circuit goes open. In the standard lifecycle of a heating element, this happens due to oxidation of the wires, which occurs much faster at elevated temperatures. So logically, heater life is dependent upon keeping the operational temperature of the resistance wire as low as possible. This is heavily dependent upon the thermal circuit that the wire is beginning. The less thermal resistance in the system, the less thermal potential is required to fulfill the desired rate of heat transfer for the process. Thermal potential is simply the temperature difference across a boundary or system that drives the flow of heat.

This point can be understood by imagining a simple thermal circuit, where a heating element is heating a block of steel. For the sake of this example, the block has an average temperature of 200°F (93°C) and is losing 1 kW of heat to its surroundings. So, in order to keep the block at 200°F (93°C), the element must be supplying 1 kW of heat to the block. In order to do this, the element must be at a given temperature above the block’s, say 500°F (260°C) — making a 300°F (149°C) thermal potential.

Now, imagine that thermal resistance is increased in the system in the form of a layer of insulation between the heating element and block. The block is still losing 1 kW of heat to its surroundings, so the heater still needs to be delivering 1 kW of heat to the block to keep it at 200°F (93°C). In order to overcome the new thermal resistance and deliver the same amount of energy, however, the thermal potential between the element and block would have to grow. This increases the operating temperature of the element and resistance wire.

Something that is not always clear about this point is that the power output of the heating element would not need to change to accomplish this. Instead, the time required to ramp up the element temperature to the proper level to maintain the block’s temperature would increase. This is simply because the element would need to be hotter in order to have the adequate thermal potential to force the same 1 kW of thermal energy through the new insulation and into the steel.

There are three main ways that resistance wire can be held within a heating element. Keep in mind that the element needs to be electrically insulated from the heater enclosure while ideally minimizing thermal insulation. The first method involves embedding the element within an insulating material —fully supported and in contact with the insulator — or suspended between insulation points. Tubular and cartridge elements have their resistance wire fully embedded within insulation. Mica and ceramic band heaters have their resistance wire fully supported within them. Open-coil heaters, as their name implies, have sections of resistance wire supported between insulation points.

Each of these scenarios set up a different thermal circuit that affects the rate at which the resistance wire is able to dissipate the heat that it is generating. This support system, along with the environment the heater is operated in, are the two largest contributors to the maximum safe and efficient power density of a finished heating element.

Consider a tubular element insulated with magnesium oxide (MgO) and a mica-insulated element. Both are located in the same environment — in this case, stagnant room temperature air. The tubular element’s thermal circuit would pass heat via conduction from the wire, through the compacted insulation into which it is embedded, to the metal sheath and then, via free convection, from the sheath out of the element. The resulting total thermal resistance would be the inverse of the sum of:

• The thickness of magnesium oxide insulation divided by its thermal conductivity (k).

• The thickness of the sheath divided by its thermal conductivity (k).

• The inverse of the free convection coefficient (h).

Similarly, the mica heater’s total thermal resistance would be the inverse of the sum of:

• The thickness of the mica divided by its thermal conductivity (k).

• The thickness of the metal shell divided by its thermal conductivity (k).

• The inverse of the free convection coefficient.

For simplicity, assume similar thicknesses of insulation and metal for both heaters. Also assume equal convection coefficients due to the analogous environments. This way, the only difference in the total resistances would be the thermal conductivity values of the different insulations. This would result in the tubular element having a much lower total resistance due to the fact that MgO has a much higher thermal conductivity (approximately 42 W/m-K) than mica (0.7 W/m-K). The conclusion that can be drawn from this is that the MgO-insulated tubular element needs less thermal potential to transmit the same amount of heat as a mica element. This results in higher possible power densities in tubular elements because the generated heat can be wicked away from the resistance wire faster than in the mica element.

Consider the same extremely simplified scenario, but in this case, we will swap the mica-insulated heater for a steatite ceramic-insulated element. The only significant change to the ceramic heater’s thermal circuit would be the thermal conductivity of steatite versus mica. Steatite has a thermal conductivity of about 2.5 W/m-K. This would result in it having less thermal resistance than the mica heater. It also would result in higher possible power densities in the ceramic band heater than in the mica heater. However, the steatite ceramic-insulated element still would have a significantly lower possible power density than a MgO-insulated tubular element.

Operating environment also significantly contributes to the maximum power density. For instance, consider three identical tubular heaters in different environments: stagnant air, stagnant water and flowing water. The only difference in their respective thermal circuits would be their convection coefficients and resulting rates of heat transfer to the fluid.

Depending upon the shape and surface area of the element, the convective coefficient in air would be somewhere between 5 and 12 W/m²K. In stagnant water, the coefficient would be closer to 100 W/m²K. If an element was submerged in fast-flowing water, the convection coefficient could be greater than 1,000 W/m²K. This large difference theoretically implies that the power density for an element in extremely fast flowing water could be as much as one hundred times greater than that of one in stagnant air.

 Attempting to skirt around or exceed the power density limits on heating elements often times seems like a quick and easy way to solve process issues. However, at the end of the day, it may drastically shorten the expected life of the heating element and could be unsafe. Ensuring that the heating element being sourced matches the application it is intended for is crucial and will assist in maximizing heater life.