Question

Water at ${20}^{o}C$ flows with a velocity of 10m/s over a flat plate which is maintained at ${80}^{o}C$. Find the thermal boundary layer thickness at 1.5m from the leading edge. Viscosity and thermal conductivity of water are $4.5\times {10}^{-4}$ Pa-s and 0.65 W/m-K respectively.

• A. 17.4 mm
• B. 1.85 mm
• C. 12.5 mm
• D. 0.91 mm

Answer 1

The correct option is A 17.4 mm

$R{e}_x=\frac{\rho .V.x}{\mu }=\frac{1000\times 10\times 1.5}{4.5\times {10}^{-4}}=3.33\times {10}^7$

$Pr=\frac{\mu .c_p}{k}=\frac{4.5\times {10}^{-4}\times 4180}{0.65}=2.893$

HBL thickness for turbulent boundary layer is

$\delta =\frac{0.37x}{(R{e}_x{)}^{\frac{1}{5}}}=\frac{0.37\times 1.5}{(3.33\times {10}^7{)}^{\frac{1}{5}}}=17.4mm$

We know for turbulent boundary layer the correlation

$\delta \approx {\delta }_t\approx 17.4mm$