Consider laminar flow of water over a wide flat plate maintained at a uniform temperature of $50^{\circ} \: \mathrm{C}$ as shown in the figure. The freestream velocity and temperature of water are $1.0 \: \mathrm{~m} / \mathrm{s}$ (parallel to the plate) and $20^{\circ} \: \mathrm{C}$, respectively. The distance $x$ from the leading edge, at which the thermal boundary layer thickness $\delta_{T}=0.01 \mathrm{~m}$, is $\_\_\_\_ \: \mathrm{m}$ (rounded off to $1$ decimal place).
GIVEN: kinematic viscosity: $v=1.0 \times 10^{-6} \mathrm{~m}^{2} / \mathrm{s}$
Prandtl number: $\operatorname{Pr}=7.01$
velocity boundary layer thickness: $\delta_{H}=\frac{4.91 x}{\sqrt{\frac{V x}{v}}}$
