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RPSC ME Lecturer 2011: Official Paper

Option 3 : = 1

ST 1: Engineering Materials (Crystal Geometry)

457

16 Questions
8 Marks
20 Mins

__Explanation:__

The relationship between the thermal boundary layer and the hydrodynamic boundary layer is given by Prandtl number

Prandtl Number: It is defined as the ratio of momentum diffusivity to thermal diffusivity.

\(Pr = \frac{\nu }{\alpha } = \frac{{momentum\;diffusivity}}{{Thermal\;diffusivty}} = \frac{{\frac{\mu }{\rho }}}{{\frac{k}{{{c_p}\rho }}}} = \frac{{\mu {c_p}}}{k}\)

The relationship between the two is given by the equation

\(\frac{{{\delta }}}{\delta_t } = P_r^{ \frac{1}{3}}\)

δ = the thickness of the hydrodynamic boundary layer; the region of flow where the velocity is less than 99% of the far-field velocity.

δT = the thickness of the thermal boundary layer; the region of flow where the local temperature nearly reaches the value (99%) of the bulk flow temperature

- If Pr > 1 the momentum or hydrodynamic boundary layer will increase more compared to the thermal boundary layer.
- If Pr < 1 the thermal boundary layer will increase more compared to the momentum or hydrodynamic boundary layer.
- I
**f Pr = 1 The the thermal boundary layer and momentum or hydrodynamic boundary layer will increase at the same rate.**

If the velocity and thermal boundary layers coincide then Pr = 1.