A truncated solid cone is of circular cross section, and its diameter is related to the axial coordinate by an expression of the form \(D=a x^{3 / 2}\), where \(a=2.0 \mathrm{~m}^{-1 / 2}\).

The sides are well insulated, while the top surface of the cone at \(x_{1}\) is maintained at \(T_{1}\) and the bottom surface at \(x_{2}\) is maintained at \(T_{2}\).

(a) Obtain an expression for the temperature distribution \(T(x)\).

(b) What is the rate of heat transfer across the cone if it is constructed of pure aluminum with \(x_{1}=0.080 \mathrm{~m}\), \(T_{1}=100^{\circ} \mathrm{C}, x_{2}=0.240 \mathrm{~m}\), and \(T_{2}=20^{\circ} \mathrm{C}\) ?

Transcribed Image Text:

T T -0 x2