Engineering task and calculation objective
The ELLU module performs the thermal and fluid dynamic design of electric air and gas heaters with heating rods. From the medium, the inlet pressure, the inlet and outlet temperatures and the mass flow or standard volume flow, the required heat duty is balanced; the module then calculates the heat transfer from the heating rod bundle to the gas flowing across or along the rods – including the radiation contribution via the emissivities of the heating rods and the shell.
As results, the calculation delivers the heat transfer coefficient and the overall heat transfer coefficient at the outlet, the pressure drop across the heater bank, and the two safety-relevant temperatures: the maximum surface temperature of the heating rods and the maximum duct wall temperature. Geometrically, the heater is described by the nominal size, the outside and inside diameters and the wall thickness of the duct or housing and the resulting flow velocities; a fouling resistance can be taken into account.
In practice, this design calculation is needed for process air heaters, nitrogen and natural gas preheaters or start-up heaters in plant engineering. The critical quantity is almost always the rod surface temperature: it limits the allowable surface power density of the heating rods, determines the service life of the heating elements, and is the governing safety parameter for flammable media or in potentially explosive atmospheres.
Calculation workflow
- Define the medium and the operating point: The gas to be heated is selected; inlet pressure, inlet and outlet temperature as well as mass flow or standard volume flow define the task. The required electrical power of the heater follows from the enthalpy difference.
- Describe the heater bank geometry: The nominal size or duct dimensions, the diameter and arrangement of the heating rods and the free flow cross-sections are recorded. From these follow the velocity in the free cross-section at the inlet and the velocities within the bank.
- Calculate the heat transfer: For the flow around the heating rods, the convective heat transfer coefficient is determined from the fluid properties at mean temperature; the radiation exchange between the heating rods and the shell enters via the emissivities. Together with an optional fouling resistance, this yields the overall heat transfer coefficient at the outlet.
- Check surface temperatures: From the surface power density and the heat transfer, the maximum surface temperature of the heating rods and the maximum duct wall temperature are calculated. These values must be assessed against the allowable limits of the heating element material, the medium (decomposition, ignition temperature) and, where applicable, the explosion protection temperature class.
- Determine the pressure drop: The pressure drop across the heating rod bundle and the duct section is calculated from the velocities and resistance coefficients and provides the specification for the fan or supply pressure design.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Mass flow | m | kg/s |
| Mean volume flow | Vm | m³/s |
| Standard volume flow Standard density | VN ρN | m³/s |
| Inlet volume flow Outlet volume flow | Ve Va | m³/s |
| Inlet volume flow Outlet volume flow | Ve Va | m³/s |
| Inlet pressure Geodetic height | p hgeo | Pa |
| Inlet temperature Outlet temperature | Te Ta | °C |
| Inlet temperature Outlet temperature | Te Ta | °C |
| Mean temperature | Tm | °C |
| Heat duty | Q | W |
| Fouling resistance | fa | m²·K/W |
| Inlet pressure Geodetic height | p hgeo | m |
| Heat flux density | q | W/m² |
| Standard volume flow Standard density | VN ρN | kg/m³ |
| Density | ρm ρa | kg/m³ |
| Specific heat capacity | cp,m cp,a | J/(kg·K) |
| Thermal conductivity | λm λa | W/(m·K) |
| Dynamic viscosity | ηm ηa | mPa·s |
| Density | ρm ρa | kg/m³ |
| Specific heat capacity | cp,m cp,a | J/(kg·K) |
| Thermal conductivity | λm λa | W/(m·K) |
| Dynamic viscosity | ηm ηa | mPa·s |
| Density at inlet temperature | ρe | kg/m³ |
| Emissivity of heating rods Emissivity of shell | εHS εM | – |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Max. surface temperature of heating rods | TW | °C |
| Maximum duct wall temperature | TM | °C |
| Heat transfer coefficient at outlet | α | W/(m²·K) |
| Overall heat transfer coefficient at outlet | k | W/(m²·K) |
| Pressure drop | ∆p | Pa |
| Velocity in the free cross-section (inlet) | wfrei | m/s |
Calculation options
Medium
Free input · Steam · Natural gas L · Natural gas H · Air · Fuel gas · Nitrogen · Carbon dioxid · Gas mixtures · Natural gas (Free input of the concentrations)
Arrangement of heating rods
aligned · staggered
Staggered row with 1 tube less than base row?
Yes · No
RHK-Form
1 · 2 · 4
Frequently asked questions
Why is the surface temperature of the heating rods the critical design quantity?
The rod temperature results from the imposed surface power density and the heat transfer to the gas – it is always well above the gas temperature. Excessive values drastically shorten the service life of the heating elements, can damage temperature-sensitive media, and are safety-relevant for flammable gases or in hazardous areas (margin to the ignition temperature, temperature class). At part-load flow or with non-uniform approach flow, the rod temperature rises further; therefore the design must always consider the most unfavorable operating point, not just the rated point.
What role does thermal radiation play in the heater?
At the surface temperatures of several hundred degrees typical for heating rods, radiation to the colder duct wall contributes noticeably to the heat dissipation – which is why the emissivities of the heating rods and the shell are requested. Radiation relieves the rods but heats the duct wall, which is why the module also reports the maximum duct wall temperature. At low rod temperatures and high gas velocities, on the other hand, convection dominates.
How does a fouling resistance affect the design?
Dust or oil films on the heating rods act as an additional thermal resistance between the rod surface and the gas. Since the electrical power is imposed, the transferred power does not decrease; instead, the rod surface temperature rises – in contrast to a conventional heat exchanger, where fouling primarily reduces the duty. A realistic fouling resistance is therefore important above all for the temperature margin of the heating rods.