Engineering task and calculation objective
The INLR module calculates heat transfer and pressure drop in internally finned tubes. Internal fins — usually longitudinal or helical ribs formed into the tube wall — enlarge the heat-transferring inner surface and act partly as turbulence promoters; they thus increase the inside heat transfer coefficient but at the same time raise the flow resistance. If you want to calculate internally finned tubes, you must weigh both effects against each other.
The calculation determines the inside heat transfer coefficient and the inside pressure drop as functions of the tube and fin geometry, the fluid properties and the flow conditions. The basis is the Heat Exchanger Design Handbook (HEDH) and the investigations on the "Heat transfer performance of internally finned tubes in turbulent flow" (ASME, 18th National Heat Transfer Conference 1979), from which the well-known correlations for turbulently flowed internally finned tubes emerged.
Internally finned tubes are used wherever the tube-side heat transfer limits the design and installation space is tight: in evaporators and condensers of refrigeration technology, in charge air and oil coolers, and in compact gas heat exchangers.
Standard and calculation basis: Heat-Exchanger-Design-Handbook, Hemisphere Publishing Corporation, New York 1983 'Heat transfer performance of internally finned tubes in turbulent flow'; Advances in Enhanced Heat Transfer Asme; 18. National heat transfer conference 6.-8.8.1979; New York 1979
Calculation workflow
- Define the tube and fin geometry: The description covers the core tube diameter, the number of fins, fin height, fin thickness and, if applicable, the helix angle of helical fins. From these follow the free flow cross-section, the wetted perimeter, the hydraulic diameter and the area ratio relative to the plain tube inner surface.
- Enter temperatures and operating data: Inlet and outlet temperatures fix the mean fluid temperature at which the properties are evaluated; in addition, the mean wall temperature, the pressure and the total mass flow are specified.
- Provide the fluid properties: Density, specific heat capacity, thermal conductivity, dynamic viscosity and Prandtl number are needed at the mean fluid temperature and additionally at the wall temperature — the ratio of the values corrects for the influence of temperature-dependent properties on heat transfer and pressure drop.
- Determine the flow regime: From the mass flow and the free cross-section follows the flow velocity, and with the hydraulic diameter the Reynolds number. The built-in correlations apply to turbulent flow; in the laminar range, the fin benefit is considerably smaller.
- Calculate heat transfer and pressure drop: The Nusselt number of the internally finned tube is determined using the geometry-extended correlations from HEDH and the ASME literature and converted into the inside heat transfer coefficient; in parallel, the associated friction factor yields the inside pressure drop. Both results enter the overall heat transfer coefficient and pressure drop balance of the apparatus.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Inlet temperature | ϑE | °C |
| Outlet temperature | ϑA | °C |
| Mean wall temperature | ϑW | °C |
| Pressure | p | Pa |
| Dynamic viscosity | η | mPa·s |
| Dynamic viscosity | ηW | mPa·s |
| Density | ρ | kg/m³ |
| Density | ρW | kg/m³ |
| Thermal conductivity | λ | W/(m·K) |
| Specific heat capacity | cp | J/(kg·K) |
| Prandtl number | Pr | - |
| Prandtl number | PrW | - |
| Grashof number | Gr | - |
| Total mass flow | Gesamtmassenstrom | kg/s |
| Inside diameter of the tube | d | m |
| Tube length | l | m |
| Number of tubes with parallel flow | n | - |
| Number of fins per tube | nRipp | - |
| Fin height | Hf | m |
| Fin thickness at the top of the fin | Tf | m |
| Fin thickness at the root of the fin | Rf | m |
| Free flow cross-section | NFA | m² |
| Wetted perimeter | Wp | m |
| Hydraulic diameter | dh | m |
Calculation options
Geometry
Tubes with straight fins · Tubes with spiral fins
Frequently asked questions
When do internal fins pay off compared with a plain tube?
When the tube-side heat transfer resistance dominates and the flow is turbulent — typically with gases, oils or viscous media in the tube and a well-transferring medium outside. The inner surface enlarged by 30 to over 100 % and the turbulence promotion can raise the heat transfer, referred to the plain tube, considerably. With inherently high tube-side coefficients (e.g. water at high velocity) or with heavily fouling media that clog the fin channels, extra cost and pressure drop prevail instead.
Which diameter is used to form the Reynolds number in an internally finned tube?
Common practice is the hydraulic diameter d_h = 4·A/U from the free flow cross-section A and the wetted perimeter U, which is smaller than the core tube inside diameter because of the fins. Some correlations use an equivalent diameter instead, or refer to the empty tube — the definition basis of the respective correlation must be strictly observed, otherwise systematic errors arise in the Nusselt number and friction factor. The module uses the reference quantities consistent with the built-in correlation.
Why are the fluid properties also needed at the wall temperature?
During heating or cooling, the temperature of the near-wall layer differs significantly from that of the core flow; the viscosity of liquids in particular changes strongly. The correlations correct for this via ratio factors such as (Pr/Pr_W) or (η/η_W) with exponents that can differ for heating and cooling. Without this correction, heat transfer is underestimated when heating viscous media and overestimated when cooling them.
Do internal fins increase the fouling tendency?
Yes, potentially. The narrow channels between the fins are difficult to clean mechanically, and with particle-laden or deposit-forming media the spaces between the fins can clog — the area gain is then lost while the pressure drop rises further. Internally finned tubes should therefore be reserved for clean media or be combinable with chemical cleaning; a realistic tube-side fouling resistance must be applied in the design.