Convective Heat Transfer Assignment 5 — External Convection  
Question #1
Consider the wing of an aircraft as a flat plate of 2.5 m length in the flow direction. The plane is moving at $100$ m/s in air that is at a pressure of 0.7 bar and a temperature of $-10^\circ$C. If the top surface of the wing absorbs solar radiation at a rate of $800$ $\rm W/m^2$, estimate its steady-state temperature with and without the effect of viscous dissipation. Assume the wing to be of solid construction and to have a single, uniform temperature. Ignore incident radiation on the bottom surface and take $\epsilon=0.4$ on the top and bottom surfaces of the wing.
Question #2
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 #3
Consider a 1-m long copper cable with a diameter $D=1.6$ mm, an electrical resistivity of $R_{\rm c}=30 \times 10^{-9}\Omega$m and with an emissivity $\epsilon=0.5$. Air flows across the cable with a velocity $u_\infty=40$ m/s, a density $\rho_\infty=0.5$ kg/m$^3$, and a temperature $T_\infty=230$ K. If a voltage difference $\Delta V=3.4$V is applied to the cable extremities, do the following:
(a)  Find the heat generated within the cable in Watt.
(b)  Find the convective heat transfer coefficient in W/m$^2$K.
(c)  Find the surface temperature of the cable in K.
You can assume that the film temperature is 400 K and use the following thermophysical data for air:
Matter$c_p,~{\rm J/kg^\circ C}$$k,~{\rm W/m^\circ C}$$\mu$, kg/ms
1.  $-3.66^\circ$C, $-8.13^\circ$C.
2.  54.9 kW/m, 30.6$^\circ$C.
3.  775 W, 415 W/m$^2$K, 595 K.
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