A two-part COMSOL multiphysics study examining steady-state and transient heat transfer across three progressively complex systems — a single radial fin, a 15-fin heat exchanger array for steam condensation, and a concentric ring CPU heat sink. Fin geometry was systematically varied through parametric sweeps to identify optimal dimensions, with all results validated against analytical calculations.
Part A — Radial Fin
The radial fin was modelled in 2D axisymmetric mode in COMSOL — a computationally efficient approach that exploits the fin's circular symmetry to solve only a cross-sectional slice, then extrapolates the full annular result. The material chosen was aluminium alloy 6061-T6 (k = 166 W/m·K), reflecting a typical industry thermal application.
Base temperature was set to 100 °C with an ambient of 20 °C, giving an 80 K driving temperature difference. A convective heat transfer coefficient of h = 20 W/m²·K was applied to the outer surfaces — representative of high natural convection or low forced convection in air.
The steady-state solution confirmed the expected inverse-proportional temperature profile along the fin radius. The COMSOL result was benchmarked directly against an analytical straight-plate fin solution of identical thickness and length — the radial fin dissipated more heat owing to its greater surface area, as expected.
Part A — Optimisation
To determine optimal fin dimensions, a parametric sweep was conducted varying fin thickness across a defined range while holding all other parameters constant. The total heat flux out of the fin was extracted at each step and plotted against thickness.
The sweep operates under a constant-volume constraint — as thickness increases, the outer radius must decrease to preserve the same material volume. This creates the characteristic peak in the curve: below the optimum, the fin is too thin to conduct heat effectively; above it, the reduced surface area negates the conduction gain.
The optimal thickness was identified at d ≈ 0.5 mm, maximising the heat transfer rate to ~22.3 W — more than double the baseline 2 mm design. The corresponding efficiency plot confirmed that thicker fins approach 100% efficiency, driven by the shorter, wider geometry enforced by the volume constraint.
The efficiency value of 97.5% from the COMSOL simulation was independently validated against the fin efficiency chart (r*o/ri = 2.4), which returned ~98% — confirming the model accuracy.
Part A — Heat Exchanger Array
A radial fin array of 15 fins was constructed by extruding a single fin profile along a tube using COMSOL's array function, then performing a union operation to ensure continuous heat transfer through the combined geometry. The array was meshed and solved as a single body.
The heat exchanger was modelled as a steam condenser at 1 atm (100 °C) on the tube interior, with cooling air at 15 °C surrounding the array. Three tube lengths were compared — 100 mm, 150 mm, and 200 mm — to analyse the effect of fin spacing on both fin tip temperature and condensation rate.
Results confirmed the expected physics: greater fin spacing allows more airflow between fins, accelerating heat dissipation and increasing the temperature gradient along each fin. The total condensation rate at the tube interior for the 200 mm array reached 517.30 W. Temperature drops at each fin attachment point were uniform across all three configurations, reinforcing model validity.
Part B — CPU Heat Sink
Part B modelled a real-world CPU heat sink scenario: maintaining a base temperature below 75 °C under a maximum thermal design power of 60 W. The CPU die (r = 7 mm) was coupled to a copper heat spreader (r = 40 mm), which distributed the concentrated heat load before it entered the concentric ring fin array.
A required convective coefficient of h = 7,797 W/m²·K was calculated without the spreader. Adding the spreader plate reduced this requirement by a factor of ~33, bringing it to 238.7 W/m²·K — well within forced-air cooling capability. This clearly demonstrated the spreader's role in making the thermal problem tractable.
The 2D steady-state result showed the expected temperature gradient outward from the CPU contact point — maximum temperature at r = 7 mm (the die edge), decreasing progressively across each ring fin. Outer fins ran significantly cooler owing to their greater radial distance and larger surface area.
Part B — Transient Study
A transient study was run from cold start (Ti = 25 °C) to thermal steady state (Tsteady = 75 °C), capturing the temperature rise of all nine ring fin tips over 600 seconds. The simulation revealed a clear thermal wave effect — inner fins respond fastest and reach the highest steady-state temperatures, while outer fins lag and settle cooler.
The thermal time constant (τ) was extracted by identifying the time at which the base temperature reached Tτ = 56.6 °C (25 + 63.2% × 50), giving τ ≈ 50 s.
Using the exponential temperature model, the time to reach 73 °C was calculated analytically as t73 = 160 s, confirmed directly from the transient plot. Both values provide useful benchmarks for thermal management — defining how quickly the heat sink reaches critical operating conditions after power-on.
Outcomes
All three models produced results consistent with analytical theory and expected physics — validating both the COMSOL methodology and the underlying heat transfer calculations across stationary and transient domains.