How watt density specifications may be holding back optimal electric heat exchanger design

Typical customer specifications for a direct electric heat exchanger (DEHE) in forced convection gas applications aim for efficiency and safety given the technology principles that have been in place for the last two decades.

Scott Boehmer and Mike Bange

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Article Summary

For example, this has led to specifications calling for lower heat fluxes (watt densities) to maintain safe sheath temperatures reliably. More recently, newer technologies allow for higher watt densities while maintaining both safety and reliability. While the older specifications are conservative and safe, the design may be sub-optimal. Letting go of the assumption that watt density is roughly equivalent to a safe sheath temperature helps open up the possibilities of new design solutions, many of which can reduce overall footprint and make processes more efficient and less costly.

Typical specifications for DEHEs
Newer technologies incorporated into direct electric heat exchangers (DEHE) are allowing designs that take advantage of increased heat flux—i.e. watt density—for a given flowing gas composition and a set of application conditions. But DEHEs with higher watt densities tend to raise eyebrows due to the belief that this also coincides with higher sheath temperatures.

This is due, in part, to the industry adhering to specifications for DEHEs that were developed using outdated heater design principles and performance features. Thus, in an effort to “play it safe,” design engineers using these older specifications are ending up with sub-optimal designs, unable to take advantage of the full design space.

For example, below is a section from a typical-looking specification sheet detailing watt density for a DEHE used in the processing of hydrocarbon streams:

Or, the watt density specification may be in a section within a company’s global standard:

It has also been a long running practice in some market segments to use a simple trade- off chart for determining a temperature rise at a given mass flow rate and watt density level for air and similar gases. (Note: other standard charts are used for fluids and other liquids). While this is a step up from defaulting to a watt density value based on legacy standards, it still does not accurately take into account all the variables that influence sheath temperature in a DEHE. The data presented in these trade-off curves would only be relevant to the particular heater design that was used during the testing.

Using older existing specifications will produce a process that is safe and reliable for most applications, but it will not allow for any innovation. Nor will it allow for the most optimal designs.

So why have these specifications stayed around as long as they have? Answering that would involve mere speculation. Part of the story seems to be the assumption that watt density itself can be used as a proxy, roughly equivalent to safe sheath temperature. It is also possible that design specifications have simply been handed down through the years based on a company’s legacy standards and methods, without considering improvements in heater technology. In these scenarios, having too high of watt density can raise reasonable concerns about safety and reliability.

On the other hand, letting go of these types of assumptions or others that are utilised in industry helps open up the design space, which can reduce overall footprint and make processes more efficient and less costly (while still providing a DEHE that meets all other critical temperature requirements and is reliable and safe for operation).
The classical approach to heat transfer:
The value of the heat transfer coefficient (hc) has a significant effect on the value of thermal stress (i.e. temperature), which directly impacts safety and reliability. That said, improving the hc would allow the watt density value to be increased while maintaining a given sheath temperature value.

Most specifications are based on the classic approach to parallel flow heat transfer, which relies heavily on the A.P. Colburn approach for turbulent forced convection, which yields the equation:
Nusselt Number:  Nu = 0.023Re 0.8Pr 0.33
Substituting and rearranging provides us the heat transfer coefficient expressed as:

Heat Transfer Coefficient:
hc =  0.023G 0.8Cp 0.33
          De 0.2µ 0.47
Using  q = hc ΔΤ, we get:  Watt Density: WSI =  hc (T sheath – T outlet )

 Here we clearly see that increasing the value of hc can allow for much higher values of watt density (WSI, or watts/inch2) while maintaining a given sheath temperature value.
Parameters that affect heat transfer and subsequent sheath temperatures
Of course, the other factors embedded within the heat transfer coefficient formula, such as the thermophysical properties of the gas in question, will allow specifications to differ depending on the details of the application. Take a natural gas such as methane, for example. Methane’s high specific heat and thermal conductivity values allow for a higher heat input for a given temperature rise.

It pays, then, to look beyond mere watt density and heat transfer to determine the optimal design for a DEHE. Parameters include:
• Bundle geometry (heating element diameter, quantity, pattern, spacing)
• Mass flow rate (per unit area)
• Flange size of the heater bundle (vessel pipe I.D.)
• Thermal properties of fluid being heated (air, hydrocarbon, etc.)

These considerations and others have led Watlow’s research team to develop new heat transfer improvement technologies and a subsequent proprietary formula that better aligns with the true performance characteristics of a heater design. Though this equation is more complex, it is also more complete and accurate, allowing for better optimisation across a wide range of applications.
Watt Density:
WSI = C1kA  dT + C2hc (Ts – Tgas, local) + ...
               Conduction   +  Convection   +

C3f1 σε1V (T4s – T 4shell ) + C4f2 σε2V (T4s – T 4env, local)
Radiation to shell     +  Radiation to elements supports  

Note: C1-C4 are Watlow proprietary

Testing and case studies
Watlow has done extensive testing over the last three years on both traditional heater designs and on designs with enhanced heat transfer performance features (many of which have been incorporated into our OPTIMAX® and soon to be released HELIMAX™ designs). Our goal is to prove, through both sound engineering principles and extensive test data, that smaller heater package designs using higher watt densities will always meet all critical specifications for sheath temperature, shell temperature and other customer constraints.

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