Question

An aircraft instrument nacelle with characteristic length L1 = 0.15 m experiences air flow at T[infinity] = 35°C and V1 = 100 m/s. When the surface temperature is Ts, 1 = 300°C, the total heat transfer rate from the object is found to be q1 = 1500 W. Estimate the rate of heat transfer rate from a second larger object that has the same shape but a characteristic length L2 = 0.3 m if the surface temperature is now Ts, 2 = 400°C in an airflow with T[infinity] = 35°C and V2 = 50 m/s. Hint: What’s the dependence of surface area on characteristic length, e.g. for a sphere.

Answer 1

Answer:

8264.15w, therefore the heat transfer increase because the characteristic length increased.

Explanation:

Please look at the attachments

Answer 2

Answer:

The rate of heat transfer is 8264.2 W

Explanation:

The heat transfer is:

Q = hAs(Ts-T∞)

A sphere:

$L=\frac{\frac{4}{3}\pi r^{3} }{4\pi r^{2} } =r/3\\A_{s} =4\pi r^{2}$

if the area is considered, h will be constant and we have

$\frac{Q_{2} }{Q_{1} } =\frac{L_{2} }{L_{1} } (\frac{T_{2}-T_{\alpha } }{T_{s1}-T_{\alpha } } )\\\frac{Q_{2} }{1500} =\frac{0.3^{2} }{0.15^{2} } (\frac{400-35}{300-35} )\\Q_{2} =8264.2W$