Shell and Tube Heat Exchanger

Industrial conjugate heat transfer case: shell-and-tube heat exchanger with inner and outer fluid regions and a solid shell.

Repository path: tutorials/conjugateHeatTransfer/ShellAndTubeHeatExchanger

Reference: Alkafri et al. (2024), multiRegionFoam: A Unified Multiphysics Framework, Sect. 7.2

Overview

Fig. 10 — Geometry of the shell-and-tube heat exchanger with inner fluid inlet (T=283 K, U=0.002 m/s) and outer fluid inlet (T=353 K, U=0.0037 m/s).

Fig. 10 — Geometry of the shell-and-tube heat exchanger with inner fluid inlet (T=283 K, U=0.002 m/s) and outer fluid inlet (T=353 K, U=0.0037 m/s).

This case demonstrates an industrial conjugate heat transfer application: a shell-and-tube heat exchanger with a shell, tubes, and baffles. Heat transfer occurs between two fluids:

  • Inner fluid — flows at lower temperature inside the tubes ($T = 283\,\text{K}$, $U = 0.002\,\text{m/s}$)
  • Outer fluid — flows within the shell but outside the tubes ($T = 353\,\text{K}$, $U = 0.0037\,\text{m/s}$)

Solid tube walls prevent mixing; baffles direct the shell-side flow. The case setup is based on a publicly available SimScale GmbH reference case.

The simulations are run for 500 s with a time step $\Delta t = 1\,\text{s}$. The coupled thermal boundary conditions are the same as in the flat-plate case (Table 3 in the paper).

Boundary conditions

Table: Boundary conditions for the heat exchanger

BoundaryThermalVelocity
Inner fluid
inlet283 K(0.002 0 0)ᵀ m/s
inner_to_solidcoupled(0 0 0)ᵀ m/s
outlet, wallszeroGradientzeroGradient
Outer fluid
inlet353 K(0 0.0037 0)ᵀ m/s
outer_to_solidcoupled(0 0 0)ᵀ m/s
outlet, wallszeroGradientzeroGradient
Solid
solid_to_innercoupled–
solid_to_outercoupled–
wallszeroGradient–

Material properties

Table: Thermophysical properties of fluid and solid

PropertySymbolUnitFluidSolid
Densityρkg/m³10278960
Thermal conductivitykW/m·K0.668401
Dynamic viscosityμkg/ms3.645 × 10⁻⁴–
Specific heat capacityc_pJ/kg·K4195385

Both inner and outer fluids share the same material properties.

Numerical schemes

Table: Numerical schemes

SchemeSetting
ddtSchemesteadyState
gradSchemeGauss linear
gradScheme grad(U)cellLimited Gauss linear 1
divScheme div(phi,U)Gauss upwind
divScheme div(phi,T)Gauss upwind
laplacianSchemeGauss linear corrected
interpolationSchemelinear
snGradSchemecorrected

Mesh

Fig. 11 — Computational mesh for the shell-and-tube heat exchanger simulation.

Fig. 11 — Computational mesh for the shell-and-tube heat exchanger simulation.

Results summary

Fig. 12 — Final temperature distribution at t = 30 s using monolithic coupling (temperature range 283–353 K).

Fig. 12 — Final temperature distribution at t = 30 s using monolithic coupling (temperature range 283–353 K).

The final temperature distribution (t = 30 s) shows no significant change thereafter, confirming a steady state is reached around t = 500 s. Both partitioned (Aitken relaxation) and monolithic coupling produce comparable field values; the partitioned approach takes longer to reach steady state.

Running the case

cd $FOAM_RUN/../multiPhysicsFoam/tutorials/conjugateHeatTransfer/ShellAndTubeHeatExchanger
./Allrun