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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 104Red5×10410^{4} \leq R e_{d} \leq 5 \times 10^{4}, the face-averaged Nusselt numbers are well correlated by an expression of the form Nud=hˉd/k=CRedmPr1/3\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:

Facec/dCmFront0.33c/d1.330.6741/2Side0.330.1532/3Side1.330.1072/3Back0.330.1742/3Back1.330.1532/3\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=300KT_{\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.

Question

Air at a free stream temperature of Tx=20CTx=20CT_{\mathrm{x}}=20^{\circ} \mathrm{C}T_{\mathrm{x}}=20^{\circ} \mathrm{C} is in parallel flow over a flat plate of length L=5 m and temperature Ts=90CT_{s}=90^{\circ} \mathrm{C}. However, obstacles placed in the flow intensify mixing with increasing distance x from the leading edge, and the spatial variation of temperatures measured in the boundary layer is correlated by an expression of the form T(C)=20+70T\left(^{\circ} \mathrm{C}\right)=20+70exp (-600xy), where x and y are in meters. Determine and plot the manner in which the local convection coefficient h varies with x. Evaluate the average convection coefficient hˉ\bar{h} for the plate.

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