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A coolant fluid at $30^\circ\text{C}$ flows over a heated flat plate maintained at a constant temperature of $100^\circ\text{C}$. The boundary-layer temperature distribution at a given location on the plate may be approximated as $T = 30 + 70e^{-y}$, where $y$ (in m) is the distance normal to the plate and $T$ is in $^\circ\text{C}$. If the thermal conductivity of the fluid is $1.0\ \text{W/mK}$, the local convective heat transfer coefficient $h$ (in $\text{W/m}^2\text{K}$) at that location will be

1. 0.2
2. 1
3. 5
4. 10

Correct answer: 1

Solution

At the wall, $q''=-k\,\left.\dfrac{dT}{dy}\right|_{y=0}$. From $T=30+70e^{-y}$, $\dfrac{dT}{dy}=-70e^{-y}$, so at $y=0$, $q''=70\ \text{W/m}^2$. Since $T_s-T_\infty=100-30=70^\circ\text{C}$, $h=q''/(T_s-T_\infty)=70/70=1\ \text{W/m}^2\text{K}$.

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