Related questions with answers

In a particular application involving airflow over a heated surface, the boundary layer temperature distribution may be approximated as $\frac{T-T_{s}}{T_{\infty}-T_{s}}=1-\exp \left(-\operatorname{Pr} \frac{u_{\infty} y}{\nu}\right)$ where y is the distance normal to the surface and the Prandtl number, $P r=c_{p} \mu / k=0.7$ , is a dimensionless fluid property. If $T_{\infty}=400 \mathrm{K}, \quad T_{s}=300 \mathrm{K}$ , and $u_{\mathrm{co}} / \nu=5000 \mathrm{m}^{-1}$ , what is the surface heat flux?

Parallel flow of atmospheric air over a flat plate of length L=3 m is disrupted by an array of stationary rods placed in the flow path over the plate. Laboratory measurements of the local convection coefficient at the surface of the plate are made for a prescribed value of V and $T_{s}>T_{\infty}$ . The results are correlated by an expression of the form $h_{x}=0.7+13.6 x-3.4 x^{2}$ , where $h_{x}$ has units of $\mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}$ and x is in meters. Evaluate the average convection coefficient $\bar{h}_{L}$ for the entire plate and the ratio $\bar{h}_{L} / h_{L}$ at the trailing edge.

Experiments have been conducted to determine local heat transfer coefficients for flow perpendicular to a long, isothermal bar of rectangular cross section. The bar is of width c parallel to the flow, and height d normal to the flow. For Reynolds numbers in the range $10^{4} \leq R e_{d} \leq 5 \times 10^{4}$ , the face-averaged Nusselt numbers are well correlated by an expression of the form $\overline{N u}_{d}=\bar{h} d / k=C R e_{d}^{m} P r^{1 / 3}$ The values of C and m for the front face, side faces, and back face of the rectangular rod are found to be the following:

\begin{matrix} \text{Face} & \text{c/d} & \text{C} & \text{m}\\ \text{Front} & \text{}{0.33 \leq c / d \leq 1.33} & \text{0.674} & \text{1/2}\\ \text{Side} & \text{0.33} & \text{0.153} & \text{2/3}\\ \text{Side} & \text{1.33} & \text{0.107} & \text{2/3}\\ \text{Back} & \text{0.33} & \text{0.174} & \text{2/3}\\ \text{Back} & \text{1.33} & \text{0.153} & \text{2/3}\\ \end{matrix}

Determine the value of the average heat transfer coefficient for the entire exposed surface (that is, averaged over all four faces) of a c=40-mm-wide, d=30-mm-tall rectangular rod. The rod is exposed to air in cross flow at V=10 m/s, $T_{\infty}=300 \mathrm{K}$ . Provide a plausible explanation of the relative values of the face-averaged heat transfer coefficients on the front, side, and back faces.