Convective Heat Transfer Assignment 5 — External Convection  
Question #1
A tube bank uses an in-line arrangement with $S_p=S_n=1.9$ cm and 6.33-mm-diameter tubes. The tube bank is 6 rows deep and $50$ tubes high. The surface temperature of the tubes is constant at $90^\circ$C, and air at a pressure of 1 atmosphere, a temperature of $20^\circ$C, and a speed of $4.5$ m/s is forced across them. Calculate the total heat transfer per unit length for the tube bank as well as the outlet temperature of the air.
Question #2
A flat plate 10 cm long and 1 m wide is placed in a wind tunnel where the air properties in the test section are $u=2500$ m/s, $P=1/40$ atm, and $T=-40^\circ$C. Assuming the flow is laminar throughout, how much cooling must be used to maintain the plate temperature at $700^\circ$C?
Question #3
A solid sphere made of a radioactive material is cooled by natural convection in an inert gas: $T_\infty=20^\circ$C. The diameter of the sphere is 0.02 m, and there is a constant rate of heat generation per unit volume, $S$, inside it. Under steady-state conditions, measurements indicate that the surface temperature of the sphere is $T_{\rm w}=100^\circ$C. Radiation heat transfer may be considered negligible. The thermal conductivity $k_{\rm s}$ of the radio-active material is of 0.49 W/m$^\circ$C. The thermophysical properties of the inert gas can be taken as $k=0.025$ W/m$^\circ$C, $c_p=1000$ J/kg$^\circ$C, $\mu=2 \times 10^{-5}$ kg/ms, $\rho=1.0$ kg/m$^3$, and $\beta=0.003$ K$^{-1}$. Perform the following tasks:
(a)  Calculate the volumetric rate of heat generation, $S$, inside the sphere.
(b)  Calculate the maximum temperature inside the sphere.
1.  54.9 kW/m, 30.6$^\circ$C.
2.  34.8 kW.
3.  0.24 MW/m$^3$, 108.2$^\circ$C.
Due on Wednesday May 9th at 17:00. Do Questions #1, #2, and #3a.
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