Engineering task and calculation objective
The GGLR module calculates the heat transfer and pressure drop on the shell side of shell-and-tube heat exchangers with longitudinally finned tubes in axial flow without internals. Longitudinal fin tubes are used when the shell-side medium has a poor heat transfer coefficient – typically gases, hot oil or highly viscous liquids – and the outside surface must be enlarged considerably compared with a plain tube.
The calculation covers rectangular and trapezoidal fin cross sections and applies to both laminar and turbulent flow in the annular space between shell and fin tubes. From the bundle geometry – shell inside diameter, tube outside and inside diameter, number of fin tubes, number of fins per tube, fin height and the fin thicknesses at root and tip – the module first determines the free flow cross-section and the wetted perimeter, and from these the equivalent (hydraulic) diameter as the characteristic length.
With the calculated heat transfer coefficient, the fin efficiency (via the thermal conductivity of the fins) and the pressure drop, a double-pipe or bundle unit with longitudinal fins can be designed thermally and hydraulically, as commonly used in oil coolers, gas heaters and economizers.
Calculation workflow
- Capture bundle and fin geometry: The inputs are shell inside diameter, tube outside and inside diameter, tube length, number of fin tubes and the fin geometry: number of fins per tube, fin height, fin thickness at the root and at the tip of the fin (rectangular or trapezoidal).
- Form the flow cross-section and equivalent diameter: From the geometry, the module calculates the free flow cross-section and the wetted perimeter; the equivalent diameter d_eq = 4·A/U serves as the characteristic length for the Reynolds and Nusselt numbers.
- Determine the flow regime: With the mass flow and the fluid properties, the flow velocity and Reynolds number follow; this decides whether the laminar or turbulent correlations for heat transfer and pressure drop are to be applied.
- Calculate heat transfer with fin efficiency: The heat transfer coefficient is referred to the total surface consisting of the fin area and the free outside tube surface; the fin efficiency is taken into account via the thermal conductivity of the fins, since the fin temperature drops towards the tip.
- Pressure drop and balance: The shell-side pressure drop is determined from the friction factor, tube length, equivalent diameter and dynamic pressure – for several shell-side passes including the turnarounds. The balance ensures the consistency of the transferred heat duty.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Total mass flow | m | kg/s |
| Inlet temperature | ϑe | °C |
| Outlet temperature | ϑa | °C |
| Mean temperature | ϑm | °C |
| Mean wall temperature | ϑw | °C |
| Dynamic viscosity | η | mPa·s |
| Density | ρ | kg/m³ |
| Thermal conductivity | λ | W/(m·K) |
| Specific heat capacity | cp | J/(kg·K) |
| Prandtl number | Pr | - |
| Prandtl number at wall temperature | PrW | - |
| Thermal conductivity of the fins | λf | W/(m·K) |
| Fluid liquid /gaseous? | gasförmig | - |
| Tube length | l | m |
| Shell inside diameter | Di | m |
| Number of fin-tubes | Nt | - |
| Number of fins per tube | Nf | - |
| Outside tube diameter | da | m |
| Fin height | Hf | m |
| Fin thickness at the top of fin | Tf | m |
| Fin thickness at the root of fin | Rf | m |
| (laminar non-disturbed flow) | Num = | - |
| (laminar entrance flow) | Num = | - |
| (turbulent flow) | Num = | - |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Free flow cross-section | NFA | m² |
| Wetted perimeter | Wp | m |
| Equivalent diameter | de | m |
| Fin area | Af | m² |
| Free tube surface on the outside | Ab | m² |
| Internal tube surface | Ai | m² |
| Velocity | w | m/s |
| Reynolds number | Re | - |
| Balance | Q = mg ∙ cp ∙ (ϑa - ϑe ) Q | W |
| Heat transfer coefficient | α | W/(m²·K) |
Calculation options
Fluid liquid /gaseous?
liquid · 1
Frequently asked questions
When are longitudinal fin tubes worthwhile compared with plain tubes?
When the shell-side heat transfer coefficient is significantly smaller than the tube-side one – as a rule of thumb by a factor of about 3 to 5, as with gases or viscous oils against water or steam. The fins enlarge the outside surface severalfold and thus balance out the mismatch of the thermal resistances. If the heat transfer coefficients on both sides are similarly good, finning brings little benefit and only costs pressure drop.
What role does the fin efficiency play?
The fin is at tube temperature only at its root; towards the tip its temperature approaches that of the fluid, so the outer fin regions transfer less heat. The fin efficiency decreases with increasing fin height, increasing heat transfer coefficient and decreasing thermal conductivity of the fin material. Tall, thin steel fins with good heat transfer can reach uneconomically low efficiencies.
Why is the calculation based on the equivalent diameter?
The annular space between the finned tubes and the shell is not a circular pipe; the Reynolds number and friction factor are therefore referred to the hydraulic diameter d_eq = 4·(free cross-section)/(wetted perimeter). This allows the proven pipe-flow correlations to be transferred to the complex channel geometry – an approximation that is well established for longitudinal flow.
Does the calculation also apply to fin tubes in cross flow or with helical fins?
No. GGLR assumes pure longitudinal flow without internals. Bundles in cross flow with baffles, helically finned tubes or cross-flow coils follow different correlations and are handled in dedicated modules.