Engineering task and calculation objective
This module calculates heat transfer and pressure drop in triple tubes according to the VDI Heat Atlas (VDI-Wärmeatlas). A triple tube consists of three concentric tubes forming a central tube and two annular gaps; up to three media flow in them with selectable flow arrangement (co-current or counter-current). The module determines the two heat transfers separately — central tube against annulus 1 and annulus 1 against annulus 2 — and reports heat transfer coefficients, outlet temperatures and pressure drops.
Calculating triple-tube heat exchangers is required above all where high flow velocities and defined residence times are demanded at small volume flows: in food processing (heating and cooling viscous or particulate products), in pilot plants, in refrigeration, and wherever a product stream in the middle annulus is to be heated or cooled from both sides. Compared with a simple double pipe, the second annulus doubles the heat transfer area per unit tube length, but makes the design more complex because the heat flows across the two walls are coupled.
Standard and calculation basis: VDI Wärmeatlas
Calculation workflow
- Define the geometry of the three tubes: For the central, middle and outer tube, the outside diameter, wall thickness, inside diameter and absolute roughness as well as the thermal conductivity of the tube materials are entered, along with the tube length. From these follow the flow cross-sections and hydraulic diameters of the two annular gaps.
- Specify media and operating data: For the media involved, mass or volume flows, inlet temperatures and the properties density, specific heat capacity, dynamic viscosity and thermal conductivity are entered; the flow arrangement (co-current or counter-current) is agreed. Optionally, a target heat duty can be set as the design goal.
- Calculate the heat transfer coefficients: From the Reynolds and Prandtl numbers, the heat transfer coefficients in the central tube and in both annular gaps are determined using the Nusselt correlations of the VDI Heat Atlas; for the annuli, geometry factors and the boundary condition of whether the inner, the outer or both walls participate in the heat exchange are taken into account. Correction factors for α allow adjustment to empirical values.
- Solve the coupled overall heat transfers: The overall heat transfers central tube–annulus 1 and annulus 1–annulus 2 are set up separately and solved in coupled form via the energy balance of the middle medium; from this follow the outlet temperatures of all streams and the transferred heat duties.
- Determine pressure drops and evaluate the result: Using the friction factors derived from roughness and Reynolds number, the pressure drops in the central tube and the annuli are calculated. Finally it is checked whether the target heat duty is achieved and whether velocities and pressure drops remain within permissible limits.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Inside diameter Abs. roughness Info: F3 | D1 K1 | m |
| Outside diameter Wall thickness | D2 s1 | m |
| Inside diameter Abs. roughness Info: F3 | D3 K2 | m |
| Outside diameter Wall thickness | D4 s2 | m |
| Inside diameter Abs. roughness Info: F3 | D5 K3 | m |
| Inlet temperature | ϑe | °C |
| Inlet temperature | ϑe | °C |
| Outlet temperature | ϑa | °C |
| Outlet temperature | ϑ6 | °C |
| Thermal conductivity | λ1 | W/(m·K) |
| Thermal conductivity | λ2 | W/(m·K) |
| Mass flow | M | kg/s |
| Density | ρRS1 ρR | kg/m³ |
| Thermal conductivity | λRS1 λR | W/(m·K) |
| Dynamic viscosity | ηRS1 ηR | mPa·s |
| Specific heat capacity | cpRS1 cpR | J/(kg·K) |
| Density | ρRS1 ρR | kg/m³ |
| Thermal conductivity | λRS1 λR | W/(m·K) |
| Dynamic viscosity | ηRS1 ηR | mPa·s |
| Specific heat capacity | cpRS1 cpR | J/(kg·K) |
| Reference heat duty | QSoll | W |
| Mass flow | MR+MRS2 | kg/s |
| Correction factor for α | f | - |
| Correction factor for α | f | - |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Friction factor | ζ | - |
| Friction factor | ζ | - |
| Inlet temperature | ϑe | °C |
| Inlet temperature | ϑe | °C |
| Outlet temperature | ϑa | °C |
| Outlet temperature | ϑ6 | °C |
| Mass flow | M | kg/s |
| Geometry factor | CGeo | - |
| Mass flow ratio tube/annulus 2 | MR/MRS2 | - |
| Outlet temperature | ϑa | °C |
| Outlet temperature | ϑa | °C |
| Logarithmic temperature difference | Δϑlog | K (diff) |
| Logarithmic temperature difference | Δϑlog | K (diff) |
| Heat exchanger area | A | m² |
| Heat exchanger area | A | m² |
| Heat transfer coefficient | α | W/(m²·K) |
| Heat transfer coefficient | α | W/(m²·K) |
| Heat transfer coefficient | α | W/(m²·K) |
| Overall heat transfer coefficient | k | W/(m²·K) |
| Overall heat transfer coefficient | k | W/(m²·K) |
| Actual heat duty | Qist | W |
| Actual heat duty | Qist | W |
| Mass flow | MR+MRS2 | kg/s |
| Mass flow | M | kg/s |
Frequently asked questions
When is a triple tube worthwhile compared with a simple double pipe?
Whenever the product stream in the middle annulus is to be heated or cooled from both sides: the transfer area per meter of tube nearly doubles, and the annulus enforces a thin product layer with short conduction paths and a narrow residence time distribution. This is particularly advantageous for viscous, temperature-sensitive or fouling media. The price is a higher pressure drop in the narrow gap and a more elaborate construction with two annular spaces to be sealed.
Why are the two heat transfers reported separately?
Because the middle medium exchanges heat simultaneously with the central tube and with the outer annulus. The two overall heat transfers have different areas, wall resistances and driving temperature differences and cannot be combined into a single U-value. Only the separate reporting shows which of the two walls limits the transfer performance and where a geometry change should start.
Which Nusselt correlation applies in the annular gap?
The VDI Heat Atlas provides dedicated correlations for concentric annuli, based on the hydraulic diameter (difference between the outer and inner diameters of the gap) and accounting, via the diameter ratio, for whether heat is transferred at the inner wall, the outer wall or both walls. The simple pipe-flow correlation with the hydraulic diameter alone underestimates or overestimates the heat transfer depending on the boundary condition.
What are typical sources of error in triple-tube design?
Frequently the flow cross-sections of the annuli are formed from the wrong diameters (inside diameter of the outer tube against outside diameter of the inner tube), the eccentricity of the tubes — which leads to non-uniform gap flow — is underestimated, or the properties are not evaluated at the mean fluid temperature. The assumption that the middle medium heats up uniformly across both walls can also fail when the temperature levels of the neighboring streams differ strongly — hence the coupled balance calculation.