Question

(25 points) The inside surface of a spherical copper shell of radii r, = 10 mm and r2 = 15 mm is maintained at T1 = 220 °C. It is

covered in a 5 mm blanket of insulation. The insulated sphere is subjected to air with h = 40 W/m^2-K and To = 20 °C. The thermal conductivities of the copper and the insulation are 1. (а)Draw the analogous electric circuit, labeling all of the appropriate resistances. kcu = 400 W/m·K and kins = 30 W/m·K respectively. \text { For a sphere: } \quad \mathbf{A}=4 \pi^{2} \quad \mathbf{V}=\frac{4}{\mathbf{3}} \pi^{3} (b)Calculate the steady-state heat transfer rate, Q , and outside surface temperature, T3. (c)Calculate the external heat flux, q". (d) A colleague suggests increasing the thickness of the insulation blanket to 15 mm in order decrease the heat loss from the sphere. Do you agree? Why?

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