Engineering task and calculation objective
This module calculates the film temperature in thermal oil heaters based on the VDI Heat Atlas and on Walter Wagner's heat engineering of organic heat transfer fluids. The maximum film temperature — the temperature of the oil film directly at the heated inner tube wall — is the central design limit of a heater: if it exceeds the allowable film temperature of the thermal oil, the oil cracks, forms deposits and ages at an accelerated rate. To determine it, the calculation combines a furnace balance (fuel, burner duty, excess air, combustion air state) with the heat transfer at the tube coils.
On the firing side, the flue gas quantity, the theoretical and actual combustion temperatures and the flue gas temperatures at the turning points and at the outlet are determined from the fuel (natural gas, fuel oil), the net calorific value, the excess air and the air humidity; the radiation of the flame onto the combustion chamber coil enters via the flame-to-wall emissivity. From these follow the mean and maximum heat flux density at the inner coil and the mean tube wall temperature. On the oil side, the volume flow and the in-tube heat transfer yield the temperature rise between bulk and wall temperature and hence the maximum film temperature.
The module models different coil configurations: combustion chamber and convection coils in series or parallel flow arrangement, counter-current or co-current operation, different tube dimensions and intertwined multiple coils. This makes it possible to check, already at the proposal stage, whether a heater concept stays within the film temperature limit of the selected thermal oil.
Standard and calculation basis: VDI Wärmeatlas, Walter Wagner: "Wärmetechnik mit organischen Medien" Reschverlag München
Calculation workflow
- Define the firing data: The fuel, net calorific value, burner duty or fuel mass or standard volume flow, excess air, and the temperature, pressure and humidity of the combustion air are specified. From these, the module calculates the flue gas mass flow and the flue gas composition.
- Determine combustion and furnace temperatures: The theoretical combustion temperature follows from the energy balance; empirical factors lead to the actual flame temperature. With the furnace geometry (diameter, length, nozzle factors) and the flame-to-wall emissivity, the radiant heat flow onto the combustion chamber coil and the flue gas temperature at the furnace exit are calculated.
- Determine the heat flux densities at the coil: For the inner combustion chamber coil, the mean and maximum heat flux densities are determined; the non-uniformity caused by flame radiation is captured by the ratio of maximum to mean heat flux density. The flue gas temperatures at the turning points and at the outlet result from the zone-by-zone balance with the flue gas properties (density, viscosity).
- Calculate the oil-side heat transfer: From the oil volume flow, the tube dimensions and the interconnection of the coils (series/parallel, counter-current or co-current), the flow velocity in each coil circuit follows, and from it the internal heat transfer coefficient, including the coil enhancement factor relative to a straight tube.
- Determine and assess the film temperature: At the location of maximum heat flux density, the temperature rise across the oil film is added to the local bulk oil temperature; the result is the maximum film temperature. It is compared with the allowable film temperature of the thermal oil — if it is exceeded, a higher oil flow rate, a different coil interconnection or reduced burner duty is required.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Tube inside diameter | di di | m |
| Tube outside diameter | da da | m |
| Coil diameter | Dwi Dwa | m |
| Coil pitch | hi ha | m |
| Outlet temperature Inlet temperature | ϑ ϑ | °C |
| Furnace diameter | D | m |
| Density | ρ | kg/m³ |
| Kinematic viscosity | ν | m²/s |
| Specific heat capacity | cp | J/(kg·K) |
| Thermal conductivity | λ | W/(m·K) |
| Fuel | Brennstoffs | – |
| Volume flow Mass flow | Vtotal mtotal | kg/s |
| Velocity | wi wa | m/s |
| Reynolds number | Rei Rea | - |
| Prandtl number | Pr | - |
| Heat transfer coefficient Factor | αi f1 | - |
| Heat transfer coefficient Factor | αi f1 | W/(m²·K) |
| Theoretical temperature Actual temperature | t_Th | °C |
| Empirical factors | f0 fA | - |
| Theoretical temperature Actual temperature | T_F | °C |
| Therm. performance | QN | kW |
| Lower heat value | Hu | kJ/kg |
| Efficiency | η = QN/QB · 100 | % |
| Mass flow | Brennstoff | kg/h |
Calculation options
Fuel
Natural gas · Heating Oil Extra Light · Heating Oil Heavy · Liquefied petroleum gas
Orifice plate
No orifice · At collector nozzle · In each tube of the inner coil
Flow conduction
Countercurrent flow · Cocurrent flow
Combination to inner coil
parallel · serial
Combination to outer coil
parallel · serial
Frequently asked questions
Why is the film temperature more important than the oil outlet temperature?
Organic heat transfer fluids decompose thermally above a fluid-specific limit temperature. What matters is not the bulk temperature of the oil but the temperature of the laminar boundary film at the tube wall, which at high heat flux density and low flow velocity can lie several tens of kelvins above it. Cracking in the film produces coke deposits, which impair the heat transfer, raise the wall temperature further and thus reinforce the damage.
How does the flow arrangement (counter-current/co-current) affect the film temperature?
In co-current operation, the coldest oil meets the zone of highest heat flux density near the burner — the film temperature stays low, but the outlet temperature is reached in the convection zone. In counter-current operation, the hottest oil flows through the combustion chamber region, which is thermodynamically more favourable but produces the highest film temperature. The module calculates both arrangements as well as series and parallel coil circuits.
Why distinguish between mean and maximum heat flux density?
The flame radiation is not distributed uniformly over the combustion chamber coil: near the flame, local peak values occur well above the mean. Since the film temperature depends on the local heat flux density, the maximum value must be used — a design based only on the mean heat flux density systematically underestimates the film temperature.
What role do excess air and air humidity play?
Higher excess air lowers the flame temperature and thus the radiant load on the combustion chamber coil, but increases the flue gas mass flow and the stack loss. The moisture content of the combustion air changes the flue gas quantity and its properties (density, viscosity, radiation contributions of H₂O). Both quantities therefore enter the furnace balance and the zone temperatures directly.