Solve the following problem:
Q: A rod of 10-mm diameter and 250-mm length has one end maintained at 100°C. The surface of the rod experiences free convection with the ambient air at 25°C and a convection coefficient that depends on the difference between the temperature of the surface and the ambient air. Specifically, the coefficient is prescribed by a correlation of the form, hfc = 2.89[0.6 + 0.624(T - T8)1/6]2, where the units are hfc (W/m2 · K) and T (K). The surface of the rod has an emissivity E = 0.2 and experiences radiation exchange with the surroundings at Tsur = 25°C. The fin tip also experiences free convection and radiation exchange.
Assuming one-dimensional conduction and using a finite-difference method representing the fin by five nodes, estimate the temperature distribution for the fin. Determine also the fin heat rate and the relative contributions of free convection and radiation exchange.
