Question

Please describe the value associated with momentum and heat transfer analogies and the role of the Prandtl number

Answer 1

Analogy between heat momentum transfer-It is used to find the heat transfer coefficient. Useful for analysis turbulent transfer processes. We cannot write temperature distribution directly but the transfer can be explained in simplified model. We can explain mixing in a direction perpendicular to mean flow for transfer of momentum and energy similar to motion of gas molecules as in kinetic theory.

Role of prandtl no - The Nusselt number is defined as a function of the Reynolds number (specifying the boundary layer thickness for momentum) modified by the ratio of boundary layer thicknesses for heat (tH) and for momentum (tM). The ratio tM/tH is a function of the Prandtl numberdefined by (ν/κ).

The relative Thickness of the thermal boundary layer and velocity boundary layer depend on Prandtl no. For Fluids prandl no >>1,thickness of thermal boundary layer =momentum boundary layer. Nu∝RenPrm,

where m and n are constants and Prm=tM/tH.

Prandtl no (Pr) is defined as ratio of kinematic viscosity and thermal diffusivity (a) . If v=a, Pr=1 the momentum and energy equations are identical Thus Prandtl no controls the relation between velocity and temperature distribution.