A cooling spine of square crosssectional area \(A=0.25 \times 0.25 \mathrm{~m}^{2}\), length \(L=2 \mathrm{~m}\), and conductivity \(k=10 \mathrm{~W} / \mathrm{m} /{ }^{\circ} \mathrm{C}\) extends from a wall maintained at temperature \(T_{w}=200{ }^{\circ} \mathrm{C}\). The surface convection coefficient between the spine and the surrounding air is \(h=0.6\) \(\mathrm{W} / \mathrm{m}^{2} /{ }^{\circ} \mathrm{C}\), and the air temperature is \(T_{a}=20^{\circ} \mathrm{C}\). Determine the heat conducted by the spine and the temperature of the tip using five onedimensional finite elements.

Transcribed Image Text:

x Air h, Ta Tw L N