Engineering task and calculation objective
The module calculates the overall heat transfer through vessel walls onto which pipe coils or half-pipe coils are welded, according to chapter M2 of the VDI Wärmeatlas (VDI Heat Atlas, 12th edition 2019). Unlike with a jacket, the wall here is heated or cooled directly only along the weld lines; from there the heat must spread through the wall by transverse conduction. The module captures this two-dimensional conduction process and delivers the effective overall heat transfer for various designs of welded-on channels.
Welded half-pipe coils are the standard solution in apparatus engineering for temperature-controlled vessels with higher heating medium pressures, for example steam or thermal oil heating of stirred vessels and storage tanks: they stiffen the wall, allow high pressures in the heating channel and can be divided into zones. To calculate the overall heat transfer of a half-pipe coil, the transverse conduction in the wall between the weld seams must be assessed correctly, in addition to the heat transfer coefficients in the channel and in the vessel — exactly this distinguishes the calculation from the simple flat-plate model.
The results are the overall heat transfer coefficient referred to the vessel surface and the transferable heat flow, as the basis for heat-up times and the division of the coil zones.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Select the design type: First, the design of the welded-on channels is defined: half-pipe coil, welded-on full pipe or comparable channel shapes, each with the channel dimensions, pitch of the coil and the wall thickness of the vessel wall.
- Determine heat transfer in the heating channel: For the heating or cooling medium in the half-pipe channel, the inner heat transfer coefficient is calculated from the correlations for flow through channels; for the half-pipe via the hydraulic diameter of the semicircular cross-section, for steam heating via the condensation relationships.
- Determine heat transfer on the product side: On the vessel inside, the heat transfer coefficient between wall and product is applied — for stirred vessels according to the stirred tank correlations, for stagnant media via natural convection.
- Capture transverse conduction in the wall: Between the weld lines, the vessel wall acts like a fin releasing heat on both sides. From the wall thickness, the thermal conductivity of the wall material, the coil pitch and the product-side heat transfer, the surface efficiency of the only indirectly heated wall strips is calculated.
- Assemble the effective overall heat transfer: From the partial resistances (channel inside, weld connection, transverse wall conduction, product side, fouling if applicable), the overall heat transfer coefficient referred to the vessel surface is obtained, and from it the transferable heat flow for the covered area.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Outside diameter | da | m |
| Inside diameter | di | m |
| Outside radius | ra | m |
| Inside radius | ri | m |
| Wall thickness | sr | m |
| Section | X=ra | m |
| Wall thickness of basic material | sw | m |
| Thermal coductivity, basic material | λw | W/(m·K) |
| Thickness of fouling | ssm | m |
| Thermal conductivity of fouling | λsm | W/(m·K) |
| Length of symmetric section | l | m |
| Heat transfer coefficient, wall side | αw | W/(m²·K) |
| Heat transfer coefficient, tube side | αr | W/(m²·K) |
| X/l | Quotient X/l X/l | - |
| s_w/l | Quotient sw/l sw/l | - |
| Quotient | Quotient λw/(αw∙sw) λw/(αw∙sw) | - |
| Correction factor | ε | - |
| Correction factor | χ | - |
| Heat transfer coefficient | k | W/(m²·K) |
| Width of weld | Xw | m |
| Length of symmetrical section | lw | m |
| Weld thickness | ssn | m |
| Height of weld | hsn | m |
| Length of weld | lsn | m |
Calculation options
Type
Welded on half pipe · Welded on full pipe with intermediate layer · Welded on full pipe
Frequently asked questions
Why does a half-pipe coil transfer less than a jacket of the same area?
With a jacket, the entire wall surface is directly wetted by the heating medium. With the half-pipe coil, only the strip beneath the channel is heated directly; the wall areas between the turns receive their heat by transverse conduction in the wall and operate with a reduced excess temperature, similar to a fin. The larger the pitch and the thinner or more poorly conducting the wall, the lower the surface efficiency of these intermediate strips.
When are half-pipe coils used instead of a jacket?
Half-pipe coils are advantageous at high heating medium pressures (e.g. steam above about 6 bar or thermal oil), because the small channel cross-section is pressure-resistant and additionally stiffens the vessel wall — a jacket would require thick walls or stayed constructions there. In addition, coils can be divided into several heating/cooling zones and generate defined flow velocities in the channel, which improves the inner heat transfer.
What role does the material of the vessel wall play?
A considerable one: the transverse conduction between the turns depends directly on the thermal conductivity of the wall. With austenitic steels (λ ≈ 15 W/(m·K)), the surface efficiency of the unheated strips is significantly worse than with carbon steels (λ ≈ 50 W/(m·K)). For stainless steel vessels, the coil pitch should therefore be chosen tighter, or the calculation should use a correspondingly reduced effective area.
What are typical sources of error in the design?
Often the entire covered vessel area is assumed to be fully effective, i.e. transverse conduction is ignored — this significantly overestimates the duty. Further errors: too low a flow velocity in the channel (laminar regime, poor inner transfer), unconsidered condensate removal with steam heating, and fouling deposits on the product side, which for stirred vessels often represent the largest single resistance.