For flow of fluid over a heated plate, the following fluid properties are known viscosity = 0.001 Pa.s ; specific heat at constant pressure = 1 kJ/kg.K ; thermal conductivity = 1 W/m.k. The hydrodynamic boundary layer thickness at a specified location on the plate is 1 mm. The thermal boundary layer thickness at the same location is

Concept:

Prandtl number Pr is defined as the ratio of momentum diffusivity to thermal diffusivity.

In another way, we can define Prandtl number as, the ratio of the rate that viscous forces penetrate the material to the rate that thermal energy penetrates the material.

where δ is hydrodynamic boundary layer thickness and δT is thermal boundary layer thickness.

Calculation:

Given:

μ = 0.001 Pa.s, C_p = 1 kJ/kg.k, K = 1 W/m.k

Since, Prandtl number,  

So, 

Since 

∴ Thermal boundary layer thickness at the same location = 1mm