The Peclet number may be interpreted as the ratio of

Explanation:

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

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

Prandtl Number: 

• It is defined as the ratio of momentum diffusivity to thermal diffusivity.

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

Rayleigh number: 

• The product of Grashof number and Prandtl No is called Rayleigh number

Ra = Gr pr

\(= \frac{{g\beta {\rm{\Delta }}T{L^3}}}{{{\nu ^2}}} \times \frac{\nu }{\alpha }\)

\(= \frac{{g\beta {\rm{\Delta }}T{L^3}}}{{\nu \alpha }}\)

Grashof number: 

• It is the ratio between the buoyancy force and the viscous force:

\(Gr = \frac{{g\beta \left( {{T_s} - {T_\infty }} \right)L_c^3}}{{{\nu ^2}}}\)

• It represents the natural convection effects and is called the Grashof number.
• Peclet number: The product of the Reynolds number and Prandtl number is called Pecklet number.
• The Peclet number is a measure of the relative importance of advection versus diffusion
• Or, the Peclet number may be interpreted as the ratio of the heat capacity rate of fluid in the boundary layer to axial heat conductance of the boundary layer
• Where a large number indicates an advectively dominated distribution, and a small number indicates a diffuse flow.