21 - Convection - Introduction

The molecular diffusivities of momentum and energy (heat) have been defined previously as \[\begin{aligned} \text{momentum diffusivity:} \qquad \nu &= \frac{\mu}{\rho} \\ \text{thermal diffusivity:} \qquad \alpha &= \frac{k}{\rho C_P} \end{aligned}\] Both have same dimensions \(L^2/t\); thus their ratio must be dimensionless. This ratio, that of molecular diffusivity of momentum to the molecular diffusivity of heat, is designed the Prandtl number. \[\boxed{ \text{Pr} = \frac{\nu}{\alpha} = \frac{C_P\mu}{k} }\] Prandtl number is observed to be a combination of fluid properties; thus Pr itself may be thought of as a property. Primarily it is a function of temperature.