Mini Project
In Construction

Nusselt Correlation Derivation

First-Principles Problem Solving

How this project demonstrates each skill

First-Principles Problem Solving
Skill

First-principles derivation of $Nu = C \cdot Re^m \cdot Pr^n$ rearranged to isolate $h$. Shows the velocity exponent $m$ dominates the scaling, so doubling cooling capacity roughly needs 16× fan power (fan affinity laws, $m \approx 0.7$). Grounds the empirical h-correlation I derived on the FSAE accumulator.

Derivation

Short first-principles derivation. The Nusselt correlation gives a non-dimensional form for convection; rearranging it shows how the heat transfer coefficient actually scales with fluid velocity.

Nusselt Correlation

Reynolds and Prandtl

Substituting

Rearranging

Simplified

What this tells you

scales with velocity to the power. For most forced-convection correlations I've seen, is around 0.6 to 0.7.

Combine that with fan affinity laws, which say flow scales with fan power as . So .

With , doubling cooling capacity takes roughly 16× the fan power. That's the practical takeaway: pushing harder on fans gets expensive fast.

I later validated this experimentally on the FSAE accumulator and got , which sits inside the range this derivation predicts.