Coupled airflow and bioheat transfer modeling of knee cooling during cold air therapy

Local cryotherapy is used to reduce pain and inflammation in knee joint disorders and during rehabilitation after injuries and surgery. Among its modalities, CAT allows adjustment of cooling intensity and exposure duration, which determine the temperature response of the skin and deeper tissues. Because direct measurement of internal tissue temperatures is invasive and impractical, numerical modeling is needed to support assessment of cooling regimes. This study develops a coupled CFD–bioheat model for CAT of the knee joint, evaluates its predictions against experimental measurements, and compares reduced-complexity turbulence configurations. A three-dimensional anatomical knee model was coupled with the Pennes bioheat equation. Turbulent airflow from two opposed cold-air jets was computed using Reynolds-averaged Navier–Stokes equations and used as input for a transient 20 min heat-transfer simulation. Numerical predictions were compared with experimental surface-temperature measurements. The reference SST k-ω model reproduced the cooling dynamics with a mean absolute error of 0.98 °C, root mean square error of 1.15 °C, bias of −0.96 °C, and R² = 0.96. Cooling was concentrated near the jet-impingement regions, where the local effective heat transfer coefficient reached approximately 100 W m⁻² K⁻¹, while the surface-averaged value was approximately 44.8 W m⁻² K⁻¹. Relative to the SST k-ω reference, the computational cost was reduced by approximately 19% for the k-ε model and by 49% for the Zero Equation model. The k-ε model provided closer agreement for local skin temperature and convective heat flux, whereas the Zero Equation model provided the larger reduction in computational cost. The developed framework enables numerical assessment of knee cooling and comparison of turbulence-model simplifications under the investigated CAT conditions.