The brake disc and the exhaust line are the hottest components on a vehicle. The question for thermal analysis usually has two layers: does the component itself survive, and do the parts around it survive?
Brakes: short duration, very high power
A brake converts the vehicle's kinetic energy to heat in seconds. The power density is very high but the duration is short, so what governs is not the steady state but the thermal mass and transient behaviour.
In repeated braking the heat accumulates and the disc temperature climbs in steps. The critical scenario is not a single stop but repeated braking down a gradient, or a race cycle.
The vents of a ventilated disc are a rotating machinery problem: the disc is its own pump, the vane geometry sets the flow rate, and that flow rate varies with rotational speed.
Exhaust: continuously hot, radiation dominant
The exhaust line runs continuously at high temperature. Here the main mechanism is radiation, and heat reaches the neighbouring parts — fuel lines, wiring harnesses, body panels, rubber components — largely by radiation. See the radiation note.
Heat shields exist precisely for this, and their effectiveness depends on surface emissivity and the air gap between. Shield design is a view factor problem.
The critical scenario: heat soak after shutdown
When the vehicle stops, the air flow ceases but the hot mass is still there. The temperature briefly rises (heat soak), and for many components that is the critical moment — not during driving but a few minutes after parking.
This is by definition a transient, conjugate problem, and a steady-state analysis misses it entirely. The flow side is now natural convection.
References
- Modest, M. F. & Mazumder, S. (2021). Radiative Heat Transfer, 4th ed. Academic Press. ISBN 978-0-323-98406-5.
- Churchill, S. W. & Chu, H. H. S. (1975). Correlating equations for laminar and turbulent free convection from a vertical plate. International Journal of Heat and Mass Transfer, 18(11), 1323–1329. DOI: 10.1016/0017-9310(75)90243-4