Question

In a certain process, oil at 35°C flows over a flat plate at 6 cm/s. The plate is 6 m long is heated uniformly and maintained at the surface
the temperature of 95°C. What will be the thermal boundary layer thickness at the trailing edge of the plate?
At the mean film temperature, t${}_m$ = 65°C, the relevant fluid properties are
Thermal diffusivity, $\alpha$ = 7.2 x 10${}^{-8}$ m${}^2$/s
Thermal conductivity, k = 0.213 W/mK
Kinematic viscosity, v = 0.65 x 10${}^{-4}$ m${}^2$/s
Density, ρ = 956.8 kg/m${}^3$

• A. 3.897 m
• B. 0.0417 m
• C. 0.4849 m
• D. 0.4032 m

Answer 1

The correct option is B 0.0417 m

Reynolds Number,
$Re=\frac{l{U}_{\infty }}{v}=\frac{6\times 0.06}{0.05\times {10}^{-4}}=5538.5$

$\therefore$ flow will be laminar.

Hydrodynamic boundary layer thickness, at $x=6$

$\delta =\frac{5x}{\sqrt{R{e}_x}}=\frac{5\times 6}{\sqrt{5538.5}}=0.4031m$

Prandtl Number,
$Pr=\frac{v}{\alpha }=\frac{0.65\times {10}^{-4}}{7.2\times {10}^{-8}}=902.78$

Now, theraml boundary layers,
${\delta }_1=\frac{\delta }{(Pr{)}^{1/3}}=\frac{0.4031}{(902.78{)}^{1/3}}=0.0417m$