Fundamentals of Convective Heat Transfer

NPTEL Live Session - 2

Durga Prasad Pydi

02-08-2025

Contents

• Reynolds Transport Theorem
• Derivation of Energy equation

Reynolds Transport Theorem

$$ \left. \frac{DN}{Dt} \right|_{sys} = \underbrace{\frac{\partial }{\partial t} \int_{CV} \rho \eta dV}_{\text{rate of change in CV}} + \underbrace{\int_{CV} \rho \eta (\vec{v_r}.\hat{n})dA}_{\text{net flux out of CV}} $$ where $N$,$\eta$ are extensive and intensive properties respectively
$\rho$: density of fluid,
$\vec{v_r}$: velocity of fluid relative to the CV
$\hat{n}$: outward normal vector to control surface