Topic: Heat Transfer
A coolant fluid at $30^{\circ}C$ flows over a heated flat plate maintained at $100^{\circ}C$. The boundary layer temperature distribution at a given location on the plate may be approximated as $T = 30 + 70 \exp(-y)$, where y is the distance normal to the plate in meters and T is in $^{\circ}C$. If thermal conductivity of the fluid is $1.0 W/mK$, then the local convective heat transfer coefficient in $W/m^2K$ at that location will be
- A. 0.2
- B. 1
- C. 5
- D. 10
Answer: B. 1
Explanation: By equating convective heat transfer with conduction at the fluid-plate boundary ($y=0$), we get $h(T_w - T_{\infty}) = -k \left. \frac{dT}{dy} \right|_{y=0}$. The temperature gradient is $\frac{dT}{dy} = \frac{d}{dy}(30 + 70e^{-y}) = -70e^{-y}$. Evaluating at $y=0$ provides $\frac{dT}{dy} = -70$. Substituting the respective values gives $h(100 - 30) = -1 \times (-70)$, which simplifies to $70h = 70$. Therefore, $h = 1 \text{ W/m}^2\text{K}$.