Question

A fluid (Prandtl number, Pr = 1) at 500 K flows over a flat plate of 1.5 m length, maintained at 300 K. The velocity of the fluid is 10 m/s. Assuming kinematic viscosity, v = 30 × 10^-6 m²/s, the thermal boundary layer thickness (in mm) at 0.5 m from the leading edge is _________

Answer 1

Concept:

Since in question not any velocity profile is given so we will use Blasius equation.

Calculation:

 Pr = 1, T = 500 K, L = 1.5 m, T_∞ = 300 K

\({\left( {{P_r}} \right)^{\frac{1}{3}}} = \frac{{{\delta _{hy}}}}{{{\delta _{th}}}} \Rightarrow \frac{{{\delta _{hy}}}}{{{\delta _{th}}}} = 1\)

∴ δ_hy = δ_th

\(Re = \frac{{\rho VD}}{\mu } = \frac{{VD}}{v} = \frac{{10 \times 0.5}}{{30 \times {{10}^{ - 6}}}} = 1.66 \times {10^5}\) 

∵ Re ≤ 5 × 10⁵

∴ Flow is laminar flow

∴ Blasius equation for laminar flow

\({\delta _{hy}} = \frac{{5x}}{{\sqrt {{R_{ex}}} }} = \frac{{5 \times 0.5}}{{\sqrt {1.66 \times {{10}^5}} }} \times 1000\;mm\) 

δ_hy = 6.12 mm

δ_hy = δ_th = 6.12 mm

Mistake Point: While calculating Reynold number. Calculate the Reynold no. at a point at which hydrodynamic boundary length is required.